The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes in which two principle forms of energy transfer, heat and thermodynamic work, are distinguished that modify a thermodynamic system of a constant amount of matter. The law also defines the internal energy of a system, an extensive property for taking account of the balance of these energies in the system. Energy cannot be created or destroyed, but it can be transformed from one form to another. In an isolated system the sum of all forms of energy is constant.

An equivalent statement is that perpetual motion machines of the first kind are impossible; work done by a system on its surroundings requires that the system's internal energy be consumed, so that the amount of internal energy lost by that work must be resupplied as heat by an external energy source or as work by an external machine acting on the system to sustain the work of system continuously.

The ideal isolated system, of which the entire universe is an example, is often only used as a model. Many systems in practical applications require the consideration of internal chemical or nuclear reactions, as well as transfers of matter into or out of the system. For such considerations, thermodynamics also defines the concept of open systems, closed systems, and other types.

Definition
The first law of thermodynamics is often formulated as the sum of contributions to the internal energy () from all work (), done on or by the system, and the amount of heat () supplied or withdrawn from the system in a thermodynamic process. The historical sign convention for the terms has been that heat supplied to the system is positive, but work done by the system is subtracted. This was the convention of Rudolf Clausius, so that a change in the internal energy () takes the form

.

Modern definitions by Max Planck, and IUPAC,  often replace the subtraction with addition, and consider all net energy transfers to the system as positive and all net energy transfers from the system as negative, irrespective of the use of the system, for example as an engine.

When a system expands in a quasistatic process, the thermodynamic work done by the system on the surroundings is the product, , of pressure, , and volume change, , whereas the thermodynamic work done on the system by the surroundings is .  The change in internal energy of the system is:

where  denotes the inexact differential of an infinitesimal amount of heat supplied to the system from its surroundings.

Work and heat are expressions of physical processes of supply or removal of energy, while the internal energy  is a mathematical abstraction that keeps account of the exchanges of energy that befall the system. Thus the term heat for  is the amount of energy added or removed as heat in the thermodynamic sense, rather than referring to a form of energy within the system. Likewise, the term work energy for  is the amount of energy gained or lost through thermodynamic work. Internal energy is a property of the system whereas work done and heat supplied are not. A significant result of this distinction is that a given internal energy change  can be achieved by different combinations of heat and work. (This may be signaled by saying that heat and work are path dependent, while change in internal energy depends only on the initial and final states of the process. It is necessary to bear in mind that thermodynamic work is measured by change in the system, not necessarily the same as work measured by forces and distances in the surroundings; this distinction is noted in the term 'isochoric work' (at constant volume).)

History
In the first half of the eighteenth century, French philosopher and mathematician Émilie du Châtelet made notable contributions to the emerging theoretical framework of energy, for example by emphasising Leibniz's concept of ' vis viva ', mv2, as distinct from Newton's momentum, mv.

Empirical developments of the early ideas, in the century following, wrestled with contravening concepts such as the caloric theory of heat.

In the few years of his life (1796–1832) after the 1824 publication of his book Reflections on the Motive Power of Fire, Carnot came to understand that the caloric theory of heat was restricted to mere calorimetry, and that heat and "motive power" are interconvertible. This is known only from his posthumously published notes. He wrote:

At that time, the concept of mechanical work had not been formulated. Carnot was aware that heat could be produced by friction and by percussion, as forms of dissipation of "motive power." As late as 1847, Lord Kelvin believed in the caloric theory of heat, being unaware of Carnot's notes.

In 1840, Germain Hess stated a conservation law (Hess's Law) for the heat of reaction during chemical transformations. This law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work.

In 1842, Julius Robert von Mayer made a statement that was rendered by Clifford Truesdell (1980) as "in a process at constant pressure, the heat used to produce expansion is universally interconvertible with work", but this is not a general statement of the first law, for it does not express the concept of the thermodynamic state variable, the internal energy. Also in 1842, Mayer measured a temperature rise caused by friction in a body of paper pulp. This was near the time of the 1842–1845 work of James Prescott Joule, measuring the mechanical equivalent of heat. In 1845, Joule published a paper entitled The Mechanical Equivalent of Heat, in which he specified a numerical value for the amount of mechanical work required to "produce a unit of heat", based on heat production by friction in the passage of electricity through a resistor and in the rotation of a paddle in a vat of water.

The first full statements of the law came in 1850 from Rudolf Clausius, and from William Rankine. Some scholars consider Rankine's statement less distinct than that of Clausius.

Original statements: the "thermodynamic approach"
The original 19th-century statements of the first law of thermodynamics appeared in a conceptual framework in which transfer of energy as heat was taken as a primitive notion, not defined or constructed by the theoretical development of the framework, but rather presupposed as prior to it and already accepted. The primitive notion of heat was taken as empirically established, especially through calorimetry regarded as a subject in its own right, prior to thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach.

The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850, referred to cyclic thermodynamic processes, and to the existence of a function of state of the system, the internal energy. He expressed it in terms of a differential equation for the increments of a thermodynamic process. This equation may be described as follows:

Reflecting the experimental work of Mayer and of Joule, Clausius also wrote:

Because of its definition in terms of increments, the value of the internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.

The concept of internal energy is considered by Bailyn to be of "enormous interest". Its quantity cannot be immediately measured, but can only be inferred, by differencing actual immediate measurements. Bailyn likens it to the energy states of an atom, that were revealed by Bohr's energy relation . In each case, an unmeasurable quantity (the internal energy, the atomic energy level) is revealed by considering the difference of measured quantities (increments of internal energy, quantities of emitted or absorbed radiative energy).

Conceptual revision: the "mechanical approach"
In 1907, George H. Bryan wrote about systems between which there is no transfer of matter (closed systems): "Definition. When energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called heat." This definition may be regarded as expressing a conceptual revision, as follows. This was systematically expounded in 1909 by Constantin Carathéodory, whose attention had been drawn to it by Max Born. Largely through Born's influence, this revised conceptual approach to the definition of heat came to be preferred by many twentieth-century writers. It might be called the "mechanical approach".

Energy can also be transferred from one thermodynamic system to another in association with transfer of matter. Born points out that in general such energy transfer is not resolvable uniquely into work and heat moieties. In general, when there is transfer of energy associated with matter transfer, work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer.

The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another adiabatically as work, and that energy can be held as the internal energy of a thermodynamic system. It also postulates that energy can be transferred from one thermodynamic system to another by a path that is non-adiabatic, and is unaccompanied by matter transfer. Initially, it "cleverly" (according to Bailyn) refrains from labelling as 'heat' such non-adiabatic, unaccompanied transfer of energy. It rests on the primitive notion of walls, especially adiabatic walls and non-adiabatic walls, defined as follows. Temporarily, only for purpose of this definition, one can prohibit transfer of energy as work across a wall of interest. Then walls of interest fall into two classes, (a) those such that arbitrary systems separated by them remain independently in their own previously established respective states of internal thermodynamic equilibrium; they are defined as adiabatic; and (b) those without such independence; they are defined as non-adiabatic.

This approach derives the notions of transfer of energy as heat, and of temperature, as theoretical developments, not taking them as primitives. It regards calorimetry as a derived theory. It has an early origin in the nineteenth century, for example in the work of Helmholtz, but also in the work of many others.

Conceptually revised statement, according to the mechanical approach
The revised statement of the first law postulates that a change in the internal energy of a system due to any arbitrary process, that takes the system from a given initial thermodynamic state to a given final equilibrium thermodynamic state, can be determined through the physical existence, for those given states, of a reference process that occurs purely through stages of adiabatic work.

The revised statement is then

For a closed system, in any arbitrary process of interest that takes it from an initial to a final state of internal thermodynamic equilibrium, the change of internal energy is the same as that for a reference adiabatic work process that links those two states. This is so regardless of the path of the process of interest, and regardless of whether it is an adiabatic or a non-adiabatic process. The reference adiabatic work process may be chosen arbitrarily from amongst the class of all such processes.

This statement is much less close to the empirical basis than are the original statements, but is often regarded as conceptually parsimonious in that it rests only on the concepts of adiabatic work and of non-adiabatic processes, not on the concepts of transfer of energy as heat and of empirical temperature that are presupposed by the original statements. Largely through the influence of Max Born, it is often regarded as theoretically preferable because of this conceptual parsimony. Born particularly observes that the revised approach avoids thinking in terms of what he calls the "imported engineering" concept of heat engines.

Basing his thinking on the mechanical approach, Born in 1921, and again in 1949, proposed to revise the definition of heat. In particular, he referred to the work of Constantin Carathéodory, who had in 1909 stated the first law without defining quantity of heat. Born's definition was specifically for transfers of energy without transfer of matter, and it has been widely followed in textbooks (examples:). Born observes that a transfer of matter between two systems is accompanied by a transfer of internal energy that cannot be resolved into heat and work components. There can be pathways to other systems, spatially separate from that of the matter transfer, that allow heat and work transfer independent of and simultaneous with the matter transfer. Energy is conserved in such transfers.

Description

Cyclic processes
The first law of thermodynamics for a closed system was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. The other way referred to an incremental change in the internal state of the system, and did not expect the process to be cyclic.

A cyclic process is one that can be repeated indefinitely often, returning the system to its initial state. Of particular interest for single cycle of a cyclic process are the net work done, and the net heat taken in (or 'consumed', in Clausius' statement), by the system.

In a cyclic process in which the system does net work on its surroundings, it is observed to be physically necessary not only that heat be taken into the system, but also, importantly, that some heat leave the system. The difference is the heat converted by the cycle into work. In each repetition of a cyclic process, the net work done by the system, measured in mechanical units, is proportional to the heat consumed, measured in calorimetric units.

The constant of proportionality is universal and independent of the system and in 1845 and 1847 was measured by James Joule, who described it as the mechanical equivalent of heat.

Various statements of the law for closed systems
The law is of great importance and generality and is consequently thought of from several points of view. Most careful textbook statements of the law express it for closed systems. It is stated in several ways, sometimes even by the same author.

For the thermodynamics of closed systems, the distinction between transfers of energy as work and as heat is central and is within the scope of the present article. For the thermodynamics of open systems, such a distinction is beyond the scope of the present article, but some limited comments are made on it in the section below headed 'First law of thermodynamics for open systems'.

There are two main ways of stating a law of thermodynamics, physically or mathematically. They should be logically coherent and consistent with one another.

An example of a physical statement is that of Planck (1897/1903):

It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.

This physical statement is restricted neither to closed systems nor to systems with states that are strictly defined only for thermodynamic equilibrium; it has meaning also for open systems and for systems with states that are not in thermodynamic equilibrium.

An example of a mathematical statement is that of Crawford (1963):

For a given system we let  large-scale mechanical energy,  large-scale potential energy, and  total energy. The first two quantities are specifiable in terms of appropriate mechanical variables, and by definition

For any finite process, whether reversible or irreversible,

The first law in a form that involves the principle of conservation of energy more generally is

Here  and  are heat and work added, with no restrictions as to whether the process is reversible, quasistatic, or irreversible.[Warner, Am. J. Phys., 29, 124 (1961)]

This statement by Crawford, for , uses the sign convention of IUPAC, not that of Clausius. Though it does not explicitly say so, this statement refers to closed systems. Usually, internal energy  is evaluated for bodies in states of thermodynamic equilibrium, which possess well-defined temperatures, but in principle, it is more generally the sum of the kinetic and potential energies of all particles in the system, usually relative to a reference state.

The history of statements of the law for closed systems has two main periods, before and after the work of Bryan (1907), of Carathéodory (1909), and the approval of Carathéodory's work given by Born (1921). The earlier traditional versions of the law for closed systems are nowadays often considered to be out of date.

Carathéodory's celebrated presentation of equilibrium thermodynamics refers to closed systems, which are allowed to contain several phases connected by internal walls of various kinds of impermeability and permeability (explicitly including walls that are permeable only to heat). Carathéodory's 1909 version of the first law of thermodynamics was stated in an axiom which refrained from defining or mentioning temperature or quantity of heat transferred. That axiom stated that the internal energy of a phase in equilibrium is a function of state, that the sum of the internal energies of the phases is the total internal energy of the system, and that the value of the total internal energy of the system is changed by the amount of work done adiabatically on it, considering work as a form of energy. That article considered this statement to be an expression of the law of conservation of energy for such systems. This version is nowadays widely accepted as authoritative, but is stated in slightly varied ways by different authors.

Such statements of the first law for closed systems assert the existence of internal energy as a function of state defined in terms of adiabatic work. Thus heat is not defined calorimetrically or as due to temperature difference. It is defined as a residual difference between change of internal energy and work done on the system, when that work does not account for the whole of the change of internal energy and the system is not adiabatically isolated.

The 1909 Carathéodory statement of the law in axiomatic form does not mention heat or temperature, but the equilibrium states to which it refers are explicitly defined by variable sets that necessarily include "non-deformation variables", such as pressures, which, within reasonable restrictions, can be rightly interpreted as empirical temperatures, and the walls connecting the phases of the system are explicitly defined as possibly impermeable to heat or permeable only to heat.

According to Münster (1970), "A somewhat unsatisfactory aspect of Carathéodory's theory is that a consequence of the Second Law must be considered at this point [in the statement of the first law], i.e. that it is not always possible to reach any state 2 from any other state 1 by means of an adiabatic process." Münster instances that no adiabatic process can reduce the internal energy of a system at constant volume. Carathéodory's paper asserts that its statement of the first law corresponds exactly to Joule's experimental arrangement, regarded as an instance of adiabatic work. It does not point out that Joule's experimental arrangement performed essentially irreversible work, through friction of paddles in a liquid, or passage of electric current through a resistance inside the system, driven by motion of a coil and inductive heating, or by an external current source, which can access the system only by the passage of electrons, and so is not strictly adiabatic, because electrons are a form of matter, which cannot penetrate adiabatic walls. The paper goes on to base its main argument on the possibility of quasi-static adiabatic work, which is essentially reversible. The paper asserts that it will avoid reference to Carnot cycles, and then proceeds to base its argument on cycles of forward and backward quasi-static adiabatic stages, with isothermal stages of zero magnitude.

Sometimes the concept of internal energy is not made explicit in the statement.

Sometimes the existence of the internal energy is made explicit but work is not explicitly mentioned in the statement of the first postulate of thermodynamics. Heat supplied is then defined as the residual change in internal energy after work has been taken into account, in a non-adiabatic process.

A respected modern author states the first law of thermodynamics as "Heat is a form of energy", which explicitly mentions neither internal energy nor adiabatic work. Heat is defined as energy transferred by thermal contact with a reservoir, which has a temperature, and is generally so large that addition and removal of heat do not alter its temperature. A current student text on chemistry defines heat thus: "heat is the exchange of thermal energy between a system and its surroundings caused by a temperature difference." The author then explains how heat is defined or measured by calorimetry, in terms of heat capacity, specific heat capacity, molar heat capacity, and temperature.

A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined along with work and internal energy. Another respected text defines heat exchange as determined by temperature difference, but also mentions that the Born (1921) version is "completely rigorous". These versions follow the traditional approach that is now considered out of date, exemplified by that of Planck (1897/1903).

Evidence for the first law of thermodynamics for closed systems
The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system. The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes.

The following is an account in terms of changes of state of a closed system through compound processes that are not necessarily cyclic. This account first considers processes for which the first law is easily verified because of their simplicity, namely adiabatic processes (in which there is no transfer as heat) and adynamic processes (in which there is no transfer as work).

Adiabatic processes

In an adiabatic process, there is transfer of energy as work but not as heat. For all adiabatic process that takes a system from a given initial state to a given final state, irrespective of how the work is done, the respective eventual total quantities of energy transferred as work are one and the same, determined just by the given initial and final states. The work done on the system is defined and measured by changes in mechanical or quasi-mechanical variables external to the system. Physically, adiabatic transfer of energy as work requires the existence of adiabatic enclosures.

For instance, in Joule's experiment, the initial system is a tank of water with a paddle wheel inside. If we isolate the tank thermally, and move the paddle wheel with a pulley and a weight, we can relate the increase in temperature with the distance descended by the mass. Next, the system is returned to its initial state, isolated again, and the same amount of work is done on the tank using different devices (an electric motor, a chemical battery, a spring,...). In every case, the amount of work can be measured independently. The return to the initial state is not conducted by doing adiabatic work on the system. The evidence shows that the final state of the water (in particular, its temperature and volume) is the same in every case. It is irrelevant if the work is electrical, mechanical, chemical,... or if done suddenly or slowly, as long as it is performed in an adiabatic way, that is to say, without heat transfer into or out of the system.

Evidence of this kind shows that to increase the temperature of the water in the tank, the qualitative kind of adiabatically performed work does not matter. No qualitative kind of adiabatic work has ever been observed to decrease the temperature of the water in the tank.

A change from one state to another, for example an increase of both temperature and volume, may be conducted in several stages, for example by externally supplied electrical work on a resistor in the body, and adiabatic expansion allowing the body to do work on the surroundings. It needs to be shown that the time order of the stages, and their relative magnitudes, does not affect the amount of adiabatic work that needs to be done for the change of state. According to one respected scholar: "Unfortunately, it does not seem that experiments of this kind have ever been carried out carefully. ... We must therefore admit that the statement which we have enunciated here, and which is equivalent to the first law of thermodynamics, is not well founded on direct experimental evidence." Another expression of this view is "... no systematic precise experiments to verify this generalization directly have ever been attempted."

This kind of evidence, of independence of sequence of stages, combined with the above-mentioned evidence, of independence of qualitative kind of work, would show the existence of an important state variable that corresponds with adiabatic work, but not that such a state variable represented a conserved quantity. For the latter, another step of evidence is needed, which may be related to the concept of reversibility, as mentioned below.

That important state variable was first recognized and denoted  by Clausius in 1850, but he did not then name it, and he defined it in terms not only of work but also of heat transfer in the same process. It was also independently recognized in 1850 by Rankine, who also denoted it  ; and in 1851 by Kelvin who then called it "mechanical energy", and later "intrinsic energy". In 1865, after some hesitation, Clausius began calling his state function  "energy". In 1882 it was named as the internal energy by Helmholtz. If only adiabatic processes were of interest, and heat could be ignored, the concept of internal energy would hardly arise or be needed. The relevant physics would be largely covered by the concept of potential energy, as was intended in the 1847 paper of Helmholtz on the principle of conservation of energy, though that did not deal with forces that cannot be described by a potential, and thus did not fully justify the principle. Moreover, that paper was critical of the early work of Joule that had by then been performed. A great merit of the internal energy concept is that it frees thermodynamics from a restriction to cyclic processes, and allows a treatment in terms of thermodynamic states.

In an adiabatic process, adiabatic work takes the system either from a reference state  with internal energy  to an arbitrary one  with internal energy , or from the state  to the state :

Except under the special, and strictly speaking, fictional, condition of reversibility, only one of the processes     or    is empirically feasible by a simple application of externally supplied work. The reason for this is given as the second law of thermodynamics and is not considered in the present article.

The fact of such irreversibility may be dealt with in two main ways, according to different points of view:

Since the work of Bryan (1907), the most accepted way to deal with it nowadays, followed by Carathéodory, is to rely on the previously established concept of quasi-static processes,Planck, M. (1897/1903), Section 71, p. 52. as follows. Actual physical processes of transfer of energy as work are always at least to some degree irreversible. The irreversibility is often due to mechanisms known as dissipative, that transform bulk kinetic energy into internal energy. Examples are friction and viscosity. If the process is performed more slowly, the frictional or viscous dissipation is less. In the limit of infinitely slow performance, the dissipation tends to zero and then the limiting process, though fictional rather than actual, is notionally reversible, and is called quasi-static. Throughout the course of the fictional limiting quasi-static process, the internal intensive variables of the system are equal to the external intensive variables, those that describe the reactive forces exerted by the surroundings. This can be taken to justify the formula
Another way to deal with it is to allow that experiments with processes of heat transfer to or from the system may be used to justify the formula () above. Moreover, it deals to some extent with the problem of lack of direct experimental evidence that the time order of stages of a process does not matter in the determination of internal energy. This way does not provide theoretical purity in terms of adiabatic work processes, but is empirically feasible, and is in accord with experiments actually done, such as the Joule experiments mentioned just above, and with older traditions.

The formula () above allows that to go by processes of quasi-static adiabatic work from the state  to the state  we can take a path that goes through the reference state , since the quasi-static adiabatic work is independent of the path

This kind of empirical evidence, coupled with theory of this kind, largely justifies the following statement:

For all adiabatic processes between two specified states of a closed system of any nature, the net work done is the same regardless the details of the process, and determines a state function called internal energy, .

Adynamic processes

A complementary observable aspect of the first law is about heat transfer. Adynamic transfer of energy as heat can be measured empirically by changes in the surroundings of the system of interest by calorimetry. This again requires the existence of adiabatic enclosure of the entire process, system and surroundings, though the separating wall between the surroundings and the system is thermally conductive or radiatively permeable, not adiabatic. A calorimeter can rely on measurement of sensible heat, which requires the existence of thermometers and measurement of temperature change in bodies of known sensible heat capacity under specified conditions; or it can rely on the measurement of latent heat, through measurement of masses of material that change phase, at temperatures fixed by the occurrence of phase changes under specified conditions in bodies of known latent heat of phase change. The calorimeter can be calibrated by transferring an externally determined amount of heat into it, for instance from a resistive electrical heater inside the calorimeter through which a precisely known electric current is passed at a precisely known voltage for a precisely measured period of time. The calibration allows comparison of calorimetric measurement of quantity of heat transferred with quantity of energy transferred as (surroundings-based) work. According to one textbook, "The most common device for measuring  is an adiabatic bomb calorimeter." According to another textbook, "Calorimetry is widely used in present day laboratories." According to one opinion, "Most thermodynamic data come from calorimetry...".

When the system evolves with transfer of energy as heat, without energy being transferred as work, in an adynamic process, the heat transferred to the system is equal to the increase in its internal energy:

General case for reversible processes
Heat transfer is practically reversible when it is driven by practically negligibly small temperature gradients. Work transfer is practically reversible when it occurs so slowly that there are no frictional effects within the system; frictional effects outside the system should also be zero if the process is to be reversible in the strict thermodynamic sense. For a particular reversible process in general, the work done reversibly on the system, , and the heat transferred reversibly to the system,  are not required to occur respectively adiabatically or adynamically, but they must belong to the same particular process defined by its particular reversible path, , through the space of thermodynamic states. Then the work and heat transfers can occur and be calculated simultaneously.

Putting the two complementary aspects together, the first law for a particular reversible process can be written

This combined statement is the expression the first law of thermodynamics for reversible processes for closed systems.

In particular, if no work is done on a thermally isolated closed system we have

.

This is one aspect of the law of conservation of energy and can be stated:

The internal energy of an isolated system remains constant.

General case for irreversible processes
If, in a process of change of state of a closed system, the energy transfer is not under a practically zero temperature gradient, practically frictionless, and with nearly balanced forces, then the process is irreversible. Then the heat and work transfers may be difficult to calculate with high accuracy, although the simple equations for reversible processes still hold to a good approximation in the absence of composition changes. Importantly, the first law still holds and provides a check on the measurements and calculations of the work done irreversibly on the system, , and the heat transferred irreversibly to the system, , which belong to the same particular process defined by its particular irreversible path, , through the space of thermodynamic states.

This means that the internal energy  is a function of state and that the internal energy change  between two states is a function only of the two states.

Overview of the weight of evidence for the law
The first law of thermodynamics is so general that its predictions cannot all be directly tested. In many properly conducted experiments it has been precisely supported, and never violated. Indeed, within its scope of applicability, the law is so reliably established, that, nowadays, rather than experiment being considered as testing the accuracy of the law, it is more practical and realistic to think of the law as testing the accuracy of experiment. An experimental result that seems to violate the law may be assumed to be inaccurate or wrongly conceived, for example due to failure to account for an important physical factor. Thus, some may regard it as a principle more abstract than a law.

State functional formulation for infinitesimal processes
When the heat and work transfers in the equations above are infinitesimal in magnitude, they are often denoted by , rather than exact differentials denoted by , as a reminder that heat and work do not describe the state of any system. The integral of an inexact differential depends upon the particular path taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the integral of an exact differential is always zero. The path taken by a thermodynamic system through a chemical or physical change is known as a thermodynamic process.

The first law for a closed homogeneous system may be stated in terms that include concepts that are established in the second law. The internal energy  may then be expressed as a function of the system's defining state variables , entropy, and , volume: . In these terms, , the system's temperature, and , its pressure, are partial derivatives of  with respect to  and . These variables are important throughout thermodynamics, though not necessary for the statement of the first law. Rigorously, they are defined only when the system is in its own state of internal thermodynamic equilibrium. For some purposes, the concepts provide good approximations for scenarios sufficiently near to the system's internal thermodynamic equilibrium.

The first law requires that:

Then, for the fictive case of a reversible process,  can be written in terms of exact differentials. One may imagine reversible changes, such that there is at each instant negligible departure from thermodynamic equilibrium within the system and between system and surroundings. Then, mechanical work is given by  and the quantity of heat added can be expressed as . For these conditions

While this has been shown here for reversible changes, it is valid more generally in the absence of chemical reactions or phase transitions, as  can be considered as a thermodynamic state function of the defining state variables  and :

Equation () is known as the fundamental thermodynamic relation for a closed system in the energy representation, for which the defining state variables are  and , with respect to which  and  are partial derivatives of . It is only in the reversible case or for a quasistatic process without composition change that the work done and heat transferred are given by  and .

In the case of a closed system in which the particles of the system are of different types and, because chemical reactions may occur, their respective numbers are not necessarily constant, the fundamental thermodynamic relation for dU becomes:

where dNi is the (small) increase in number of type-i particles in the reaction, and μi is known as the chemical potential of the type-i particles in the system. If dNi is expressed in mol then μi is expressed in J/mol. If the system has more external mechanical variables than just the volume that can change, the fundamental thermodynamic relation further generalizes to:

Here the Xi are the generalized forces corresponding to the external variables xi. The parameters Xi are independent of the size of the system and are called intensive parameters and the xi are proportional to the size and called extensive parameters.

For an open system, there can be transfers of particles as well as energy into or out of the system during a process. For this case, the first law of thermodynamics still holds, in the form that the internal energy is a function of state and the change of internal energy in a process is a function only of its initial and final states, as noted in the section below headed First law of thermodynamics for open systems.

A useful idea from mechanics is that the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating term: dU = −P dV. The pressure P can be viewed as a force (and in fact has units of force per unit area) while dV is the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two (work) is the amount of energy transferred out of the system as a result of the process. If one were to make this term negative then this would be the work done on the system.

It is useful to view the T dS term in the same light: here the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

Similarly, a difference in chemical potential between groups of particles in the system drives a chemical reaction that changes the numbers of particles, and the corresponding product is the amount of chemical potential energy transformed in process. For example, consider a system consisting of two phases: liquid water and water vapor. There is a generalized "force" of evaporation that drives water molecules out of the liquid. There is a generalized "force" of condensation that drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal is there equilibrium, and the net rate of transfer zero.

The two thermodynamic parameters that form a generalized force-displacement pair are called "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

Fluid dynamics

In fluid dynamics, the first law of thermodynamics reads .

Spatially inhomogeneous systems
Classical thermodynamics is initially focused on closed homogeneous systems (e.g. Planck 1897/1903), which might be regarded as 'zero-dimensional' in the sense that they have no spatial variation. But it is desired to study also systems with distinct internal motion and spatial inhomogeneity. For such systems, the principle of conservation of energy is expressed in terms not only of internal energy as defined for homogeneous systems, but also in terms of kinetic energy and potential energies of parts of the inhomogeneous system with respect to each other and with respect to long-range external forces. How the total energy of a system is allocated between these three more specific kinds of energy varies according to the purposes of different writers; this is because these components of energy are to some extent mathematical artefacts rather than actually measured physical quantities. For any closed homogeneous component of an inhomogeneous closed system, if  denotes the total energy of that component system, one may write

where  and  denote respectively the total kinetic energy and the total potential energy of the component closed homogeneous system, and  denotes its internal energy.

Potential energy can be exchanged with the surroundings of the system when the surroundings impose a force field, such as gravitational or electromagnetic, on the system.

A compound system consisting of two interacting closed homogeneous component subsystems has a potential energy of interaction  between the subsystems. Thus, in an obvious notation, one may write

The quantity  in general lacks an assignment to either subsystem in a way that is not arbitrary, and this stands in the way of a general non-arbitrary definition of transfer of energy as work. On occasions, authors make their various respective arbitrary assignments.

The distinction between internal and kinetic energy is hard to make in the presence of turbulent motion within the system, as friction gradually dissipates macroscopic kinetic energy of localised bulk flow into molecular random motion of molecules that is classified as internal energy. The rate of dissipation by friction of kinetic energy of localised bulk flow into internal energy, whether in turbulent or in streamlined flow, is an important quantity in non-equilibrium thermodynamics. This is a serious difficulty for attempts to define entropy for time-varying spatially inhomogeneous systems.

First law of thermodynamics for open systems
For the first law of thermodynamics, there is no trivial passage of physical conception from the closed system view to an open system view. For closed systems, the concepts of an adiabatic enclosure and of an adiabatic wall are fundamental. Matter and internal energy cannot permeate or penetrate such a wall. For an open system, there is a wall that allows penetration by matter. In general, matter in diffusive motion carries with it some internal energy, and some microscopic potential energy changes accompany the motion. An open system is not adiabatically enclosed.

There are some cases in which a process for an open system can, for particular purposes, be considered as if it were for a closed system. In an open system, by definition hypothetically or potentially, matter can pass between the system and its surroundings. But when, in a particular case, the process of interest involves only hypothetical or potential but no actual passage of matter, the process can be considered as if it were for a closed system.

Internal energy for an open system
Since the revised and more rigorous definition of the internal energy of a closed system rests upon the possibility of processes by which adiabatic work takes the system from one state to another, this leaves a problem for the definition of internal energy for an open system, for which adiabatic work is not in general possible. According to Max Born, the transfer of matter and energy across an open connection "cannot be reduced to mechanics". In contrast to the case of closed systems, for open systems, in the presence of diffusion, there is no unconstrained and unconditional physical distinction between convective transfer of internal energy by bulk flow of matter, the transfer of internal energy without transfer of matter (usually called heat conduction and work transfer), and change of various potential energies. The older traditional way and the conceptually revised (Carathéodory) way agree that there is no physically unique definition of heat and work transfer processes between open systems.

In particular, between two otherwise isolated open systems an adiabatic wall is by definition impossible. This problem is solved by recourse to the principle of conservation of energy. This principle allows a composite isolated system to be derived from two other component non-interacting isolated systems, in such a way that the total energy of the composite isolated system is equal to the sum of the total energies of the two component isolated systems. Two previously isolated systems can be subjected to the thermodynamic operation of placement between them of a wall permeable to matter and energy, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new single unpartitioned system. The internal energies of the initial two systems and of the final new system, considered respectively as closed systems as above, can be measured. Then the law of conservation of energy requires that

where  and  denote the changes in internal energy of the system and of its surroundings respectively. This is a statement of the first law of thermodynamics for a transfer between two otherwise isolated open systems, that fits well with the conceptually revised and rigorous statement of the law stated above.

For the thermodynamic operation of adding two systems with internal energies  and , to produce a new system with internal energy , one may write ; the reference states for ,  and  should be specified accordingly, maintaining also that the internal energy of a system be proportional to its mass, so that the internal energies are extensive variables.

There is a sense in which this kind of additivity expresses a fundamental postulate that goes beyond the simplest ideas of classical closed system thermodynamics; the extensivity of some variables is not obvious, and needs explicit expression; indeed one author goes so far as to say that it could be recognized as a fourth law of thermodynamics, though this is not repeated by other authors.

Also of course

where  and  denote the changes in mole number of a component substance of the system and of its surroundings respectively. This is a statement of the law of conservation of mass.

Process of transfer of matter between an open system and its surroundings
A system connected to its surroundings only through contact by a single permeable wall, but otherwise isolated, is an open system. If it is initially in a state of contact equilibrium with a surrounding subsystem, a thermodynamic process of transfer of matter can be made to occur between them if the surrounding subsystem is subjected to some thermodynamic operation, for example, removal of a partition between it and some further surrounding subsystem. The removal of the partition in the surroundings initiates a process of exchange between the system and its contiguous surrounding subsystem.

An example is evaporation. One may consider an open system consisting of a collection of liquid, enclosed except where it is allowed to evaporate into or to receive condensate from its vapor above it, which may be considered as its contiguous surrounding subsystem, and subject to control of its volume and temperature.

A thermodynamic process might be initiated by a thermodynamic operation in the surroundings, that mechanically increases in the controlled volume of the vapor. Some mechanical work will be done within the surroundings by the vapor, but also some of the parent liquid will evaporate and enter the vapor collection which is the contiguous surrounding subsystem. Some internal energy will accompany the vapor that leaves the system, but it will not make sense to try to uniquely identify part of that internal energy as heat and part of it as work. Consequently, the energy transfer that accompanies the transfer of matter between the system and its surrounding subsystem cannot be uniquely split into heat and work transfers to or from the open system. The component of total energy transfer that accompanies the transfer of vapor into the surrounding subsystem is customarily called 'latent heat of evaporation', but this use of the word heat is a quirk of customary historical language, not in strict compliance with the thermodynamic definition of transfer of energy as heat. In this example, kinetic energy of bulk flow and potential energy with respect to long-range external forces such as gravity are both considered to be zero. The first law of thermodynamics refers to the change of internal energy of the open system, between its initial and final states of internal equilibrium.

Open system with multiple contacts
An open system can be in contact equilibrium with several other systems at once.

This includes cases in which there is contact equilibrium between the system, and several subsystems in its surroundings, including separate connections with subsystems through walls that are permeable to the transfer of matter and internal energy as heat and allowing friction of passage of the transferred matter, but immovable, and separate connections through adiabatic walls with others, and separate connections through diathermic walls impermeable to matter with yet others. Because there are physically separate connections that are permeable to energy but impermeable to matter, between the system and its surroundings, energy transfers between them can occur with definite heat and work characters. Conceptually essential here is that the internal energy transferred with the transfer of matter is measured by a variable that is mathematically independent of the variables that measure heat and work.

With such independence of variables, the total increase of internal energy in the process is then determined as the sum of the internal energy transferred from the surroundings with the transfer of matter through the walls that are permeable to it, and of the internal energy transferred to the system as heat through the diathermic walls, and of the energy transferred to the system as work through the adiabatic walls, including the energy transferred to the system by long-range forces. These simultaneously transferred quantities of energy are defined by events in the surroundings of the system. Because the internal energy transferred with matter is not in general uniquely resolvable into heat and work components, the total energy transfer cannot in general be uniquely resolved into heat and work components. Under these conditions, the following formula can describe the process in terms of externally defined thermodynamic variables, as a statement of the first law of thermodynamics:

where ΔU0 denotes the change of internal energy of the system, and  denotes the change of internal energy of the  of the  surrounding subsystems that are in open contact with the system, due to transfer between the system and that  surrounding subsystem, and  denotes the internal energy transferred as heat from the heat reservoir of the surroundings to the system, and  denotes the energy transferred from the system to the surrounding subsystems that are in adiabatic connection with it. The case of a wall that is permeable to matter and can move so as to allow transfer of energy as work is not considered here.

Combination of first and second laws
If the system is described by the energetic fundamental equation, U0 = U0(S, V, Nj), and if the process can be described in the quasi-static formalism, in terms of the internal state variables of the system, then the process can also be described by a combination of the first and second laws of thermodynamics, by the formula

where there are n chemical constituents of the system and permeably connected surrounding subsystems, and where T, S, P, V, Nj, and μj, are defined as above.

For a general natural process, there is no immediate term-wise correspondence between equations () and (), because they describe the process in different conceptual frames.

Nevertheless, a conditional correspondence exists. There are three relevant kinds of wall here: purely diathermal, adiabatic, and permeable to matter. If two of those kinds of wall are sealed off, leaving only one that permits transfers of energy, as work, as heat, or with matter, then the remaining permitted terms correspond precisely. If two of the kinds of wall are left unsealed, then energy transfer can be shared between them, so that the two remaining permitted terms do not correspond precisely.

For the special fictive case of quasi-static transfers, there is a simple correspondence. For this, it is supposed that the system has multiple areas of contact with its surroundings. There are pistons that allow adiabatic work, purely diathermal walls, and open connections with surrounding subsystems of completely controllable chemical potential (or equivalent controls for charged species). Then, for a suitable fictive quasi-static transfer, one can write

where  is the added amount of species  and  is the corresponding molar entropy.

For fictive quasi-static transfers for which the chemical potentials in the connected surrounding subsystems are suitably controlled, these can be put into equation (4) to yield

where  is the molar enthalpy of species .

Non-equilibrium transfers
The transfer of energy between an open system and a single contiguous subsystem of its surroundings is considered also in non-equilibrium thermodynamics. The problem of definition arises also in this case. It may be allowed that the wall between the system and the subsystem is not only permeable to matter and to internal energy, but also may be movable so as to allow work to be done when the two systems have different pressures. In this case, the transfer of energy as heat is not defined.

The first law of thermodynamics for any process on the specification of equation  (3) can     be  defined  as

where ΔU denotes the change of internal energy of the system,  denotes the internal energy transferred as heat from the heat reservoir of the surroundings to the system,  denotes the work of the system and  is the molar enthalpy of species ,   coming into the system from  the surrounding that is in contact with the system.

Formula (6) is valid in general case, both for quasi-static and for irreversible processes. The situation of the quasi-static process is considered in the previous Section, which in our terms defines

To describe deviation of the thermodynamic system from equilibrium, in addition to fundamental variables that are used to fix the equilibrium state, as was described above, a set of variables  that are called internal variables have been introduced, which allows  to formulate for the general case

Methods for study of non-equilibrium processes mostly deal with spatially continuous flow systems. In this case, the open connection between system and surroundings is usually taken to fully surround the system, so that there are no separate connections impermeable to matter but permeable to heat. Except for the special case mentioned above when there is no actual transfer of matter, which can be treated as if for a closed system, in strictly defined thermodynamic terms, it follows that transfer of energy as heat is not defined. In this sense, there is no such thing as 'heat flow' for a continuous-flow open system. Properly, for closed systems, one speaks of transfer of internal energy as heat, but in general, for open systems, one can speak safely only of transfer of internal energy. A factor here is that there are often cross-effects between distinct transfers, for example that transfer of one substance may cause transfer of another even when the latter has zero chemical potential gradient.

Usually transfer between a system and its surroundings applies to transfer of a state variable, and obeys a balance law, that the amount lost by the donor system is equal to the amount gained by the receptor system. Heat is not a state variable. For his 1947 definition of "heat transfer" for discrete open systems, the author Prigogine carefully explains at some length that his definition of it does not obey a balance law. He describes this as paradoxical.

The situation is clarified by Gyarmati, who shows that his definition of "heat transfer", for continuous-flow systems, really refers not specifically to heat, but rather to transfer of internal energy, as follows. He considers a conceptual small cell in a situation of continuous-flow as a system defined in the so-called Lagrangian way, moving with the local center of mass. The flow of matter across the boundary is zero when considered as a flow of total mass. Nevertheless, if the material constitution is of several chemically distinct components that can diffuse with respect to one another, the system is considered to be open, the diffusive flows of the components being defined with respect to the center of mass of the system, and balancing one another as to mass transfer. Still there can be a distinction between bulk flow of internal energy and diffusive flow of internal energy in this case, because the internal energy density does not have to be constant per unit mass of material, and allowing for non-conservation of internal energy because of local conversion of kinetic energy of bulk flow to internal energy by viscosity.

Gyarmati shows that his definition of "the heat flow vector" is strictly speaking a definition of flow of internal energy, not specifically of heat, and so it turns out that his use here of the word heat is contrary to the strict thermodynamic definition of heat, though it is more or less compatible with historical custom, that often enough did not clearly distinguish between heat and internal energy; he writes "that this relation must be considered to be the exact definition of the concept of heat flow, fairly loosely used in experimental physics and heat technics." Apparently in a different frame of thinking from that of the above-mentioned paradoxical usage in the earlier sections of the historic 1947 work by Prigogine, about discrete systems, this usage of Gyarmati is consistent with the later sections of the same 1947 work by Prigogine, about continuous-flow systems, which use the term "heat flux" in just this way. This usage is also followed by Glansdorff and Prigogine in their 1971 text about continuous-flow systems. They write: "Again the flow of internal energy may be split into a convection flow  and a conduction flow. This conduction flow is by definition the heat flow . Therefore:  where  denotes the [internal] energy per unit mass. [These authors actually use the symbols  and  to denote internal energy but their notation has been changed here to accord with the notation of the present article. These authors actually use the symbol  to refer to total energy, including kinetic energy of bulk flow.]" This usage is followed also by other writers on non-equilibrium thermodynamics such as Lebon, Jou, and Casas-Vásquez, and de Groot and Mazur. This usage is described by Bailyn as stating the non-convective flow of internal energy, and is listed as his definition number 1, according to the first law of thermodynamics. This usage is also followed by workers in the kinetic theory of gases. This is not the ad hoc definition of "reduced heat flux" of Haase.

In the case of a flowing system of only one chemical constituent, in the Lagrangian representation, there is no distinction between bulk flow and diffusion of matter. Moreover, the flow of matter is zero into or out of the cell that moves with the local center of mass. In effect, in this description, one is dealing with a system effectively closed to the transfer of matter. But still one can validly talk of a distinction between bulk flow and diffusive flow of internal energy, the latter driven by a temperature gradient within the flowing material, and being defined with respect to the local center of mass of the bulk flow. In this case of a virtually closed system, because of the zero matter transfer, as noted above, one can safely distinguish between transfer of energy as work, and transfer of internal energy as heat.

See also
 Laws of thermodynamics
 Perpetual motion
 Microstate (statistical mechanics) – includes microscopic definitions of internal energy, heat and work
 Entropy production
 Relativistic heat conduction

References

Cited sources
Adkins, C. J. (1968/1983). Equilibrium Thermodynamics, (first edition 1968), third edition 1983, Cambridge University Press, .
Aston, J. G., Fritz, J. J. (1959). Thermodynamics and Statistical Thermodynamics, John Wiley & Sons, New York.
Balian, R. (1991/2007). From Microphysics to Macrophysics: Methods and Applications of Statistical Physics, volume 1, translated by D. ter Haar, J.F. Gregg, Springer, Berlin, .
Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, .
Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London.
Bryan, G. H. (1907). Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications, B. G. Teubner, Leipzig.
Balescu, R. (1997). Statistical Dynamics; Matter out of Equilibrium, Imperial College Press, London, .
Buchdahl, H. A. (1966), The Concepts of Classical Thermodynamics, Cambridge University Press, London.
Callen, H. B. (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, .
 A translation may be found here. Also a mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.
. See English Translation: On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom. Phil. Mag. (1851), series 4, 2, 1–21, 102–119. Also available on Google Books.
Crawford, F. H. (1963). Heat, Thermodynamics, and Statistical Physics, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.
de Groot, S. R., Mazur, P. (1962). Non-equilibrium Thermodynamics, North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, .
Denbigh, K. G. (1951). The Thermodynamics of the Steady State, Methuen, London, Wiley, New York.
Denbigh, K. (1954/1981). The Principles of Chemical Equilibrium. With Applications in Chemistry and Chemical Engineering, fourth edition, Cambridge University Press, Cambridge UK, .
Eckart, C. (1940). The thermodynamics of irreversible processes.  The simple fluid, Phys. Rev. 58: 267–269.
Fitts, D. D. (1962). Nonequilibrium Thermodynamics. Phenomenological Theory of Irreversible Processes in Fluid Systems, McGraw-Hill, New York.
Glansdorff, P., Prigogine, I., (1971). Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley, London, .
Gyarmati, I. (1967/1970). Non-equilibrium Thermodynamics. Field Theory and Variational Principles, translated from the 1967 Hungarian by E. Gyarmati and W. F. Heinz, Springer-Verlag, New York.
Haase, R. (1963/1969). Thermodynamics of Irreversible Processes, English translation, Addison-Wesley Publishing, Reading MA.
Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.
Helmholtz, H. (1847). Ueber die Erhaltung der Kraft. Eine physikalische Abhandlung, G. Reimer (publisher), Berlin, read on 23 July in a session of the Physikalischen Gesellschaft zu Berlin. Reprinted in Helmholtz, H. von (1882), Wissenschaftliche Abhandlungen, Band 1, J. A. Barth, Leipzig. Translated and edited by J. Tyndall, in Scientific Memoirs, Selected from the Transactions of Foreign Academies of Science and from Foreign Journals. Natural Philosophy (1853), volume 7, edited by J. Tyndall, W. Francis, published by Taylor and Francis, London, pp. 114–162, reprinted as volume 7 of Series 7, The Sources of Science, edited by H. Woolf, (1966), Johnson Reprint Corporation, New York, and again in Brush, S. G., The Kinetic Theory of Gases. An Anthology of Classic Papers with Historical Commentary, volume 1 of History of Modern Physical Sciences, edited by N. S. Hall, Imperial College Press, London, , pp. 89–110.

Kestin, J. (1966). A Course in Thermodynamics, Blaisdell Publishing Company, Waltham MA.
Kirkwood, J. G., Oppenheim, I. (1961). Chemical Thermodynamics, McGraw-Hill Book Company, New York.
Landsberg, P. T. (1961). Thermodynamics with Quantum Statistical Illustrations, Interscience, New York.
Landsberg, P. T. (1978). Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford UK, .
Lebon, G., Jou, D., Casas-Vázquez, J. (2008). Understanding Non-equilibrium Thermodynamics, Springer, Berlin, .

Münster, A. (1970), Classical Thermodynamics, translated by E. S. Halberstadt, Wiley–Interscience, London, .
Partington, J.R. (1949). An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green and Co., London.
Pippard, A. B. (1957/1966). Elements of Classical Thermodynamics for Advanced Students of Physics, original publication 1957, reprint 1966, Cambridge University Press, Cambridge UK.
Planck, M.(1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green & Co., London.

Prigogine, I. (1947). Étude Thermodynamique des Phénomènes irréversibles, Dunod, Paris, and Desoers, Liège.
Prigogine, I., (1955/1967). Introduction to Thermodynamics of Irreversible Processes, third edition, Interscience Publishers, New York.
Reif, F. (1965). Fundamentals of Statistical and Thermal Physics, McGraw-Hill Book Company, New York.
Tisza, L. (1966). Generalized Thermodynamics, M.I.T. Press, Cambridge MA.
Truesdell, C. A. (1980). The Tragicomical History of Thermodynamics, 1822–1854, Springer, New York, .
Truesdell, C. A., Muncaster, R. G. (1980). Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a branch of Rational Mechanics, Academic Press, New York, .
Tschoegl, N. W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, .

Further reading
  Chpts. 2 and 3 contain a nontechnical treatment of the first law.
  Chapter 2.

External links
 MISN-0-158, The First Law of Thermodynamics (PDF file) by Jerzy Borysowicz for Project PHYSNET.
 First law of thermodynamics in the MIT Course Unified Thermodynamics and Propulsion from Prof. Z. S. Spakovszky

Equations of physics
1

de:Thermodynamik#Erster Hauptsatz

First law of thermodynamics


The Rodope montane mixed forests is a terrestrial ecoregion of Europe defined by the WWF. It belongs in the temperate broadleaf and mixed forests biome and the Palearctic realm.

Geography
The Rodope montane mixed forests cover the higher parts of the Balkan Mountains, the Rhodope Mountains, Rila, Pirin, Vitosha, Sredna Gora, Ograzhden and Maleshevo, situated almost entirely in Bulgaria, as well as in some adjacent areas in Greece, North Macedonia and Serbia. They span an area of 31,600 km2 and are replaced at lower altitudes by the Balkan mixed forests.

Flora
The number of species of vascular plants in the ecoregion are estimated at 3,000. The lower areas are covered with mixed deciduous woods, most prominently with European beech, Oriental hornbeam, European hornbeam and several oak species. The higher zones are dominated by coniferous forests — Scots pine, Bosnian pine, Macedonian pine, Bulgarian fir, Silver fir, Norway spruce, etc. The highest altitudes support shrubs, heath and Alpine tundra.

Fauna
The Rodope montane mixed forests are sanctuary to a number of endangered mammal species, such as brown bears, wolves, European pine martens, European otters, wildcats and chamois. More common large mammals include roe deer, wild boars and foxes.

Most of the European birds of prey can be found in the region, including the rare Eastern imperial eagle, cinereous vulture and griffon vulture.

Protected areas
The Rodope montane mixed forests ecoregion holds a total of three national parks, all of them situated in Bulgaria, and they comprise the Central Balkan National Park, Pirin National Park, a UNESCO World Heritage Site, and Rila National Park.

See also
List of ecoregions in Bulgaria

External links

References

Rhodope Mountains
Ecoregions of Bulgaria
Ecoregions of Greece
Ecoregions of North Macedonia
Ecoregions of Serbia
Ecoregions of Europe

Environment of the Balkans
Balkan mountains
Montane forests
Pirin
Rila
Vitosha
Palearctic ecoregions
Temperate broadleaf and mixed forests
Forests of Bulgaria

Rodope montane mixed forests


The Clayoquot protests, also called the War in the Woods, were a series of blockades related to clearcutting in Clayoquot Sound, British Columbia. They culminated in mid-1993, when 856 people were arrested.  The blockades in the summer of 1993 against logging of the temperate rainforest were the largest act of civil disobedience in Canadian history until the 2021 Fairy Creek blockades.

The timber resources of Clayoquot Sound attracted growing numbers of foreigners, limiting access of indigenous peoples to land and creating increasing displeasure among the local population. In the 1980s and the 1990s, government support of private company resource extraction allowed for the growth of the industry over time and resulted in the presence of logging companies in Clayoquot Sound  The differing opinions between those groups led the First Nations to develop lobbying organizations and a series of negotiations over logging practices. In the late 1980s, the situation escalated when the Canadian forestry company MacMillan Bloedel secured a permit to log Meares Island.

From 1980 to 1994, several peaceful protests and blockades of logging roads occurred, with the largest in the mid-1993, when over 800 protesters were arrested and many put on trial.  Protesters included local residents of the Sound, the Tla-o-qui-aht First Nation and Ahousaht First Nation, and environmentalist groups such as Greenpeace and Friends of Clayoquot Sound.

The logging protests and blockades received worldwide mass media attention, creating national support for the environmental movement in British Columbia and fostering strong advocacy for anti-logging campaigns. Media focused on the mass arrests of people engaging in peaceful protests and blockades, aggression, and intimidation from law enforcement, which served to strengthen public support for nonviolent protests.

Background
The region had been populated by Indigenous communities for millennia before the arrival of colonial European explorers in the 18th century. In 1774, the first European to arrive in Tofino was Spaniard Juan José Pérez Hernández. Hernández and his crew recognized the potential wealth of the region's resources, such as fish and timber. Afterwards, several trading posts were erected and operated for a little over a century. In 1899, the first Catholic mission was built. Over time, the region's prosperity fluctuated similarly to many other frontier settlements, due to difficulty accessing the region from a lack of roads. In 1959, a logging road was built to Tofino, marking the beginning of the region's commercial exploitation of resources. This allowed the fishing industry to take off and by 1964, four hundred boats were tied up at the Tofino Harbor at once.

On May 4, 1971 an official dedication ceremony created Pacific Rim National Park in Clayoquot Sound. As a result, the originally unpaved logging road built in 1959 was paved in order to access Tofino. However this paving process started earlier on, as "Paving started in the late 1960's and was completed by 1972." Prior to this, logging companies had been investing into the region and with easier access, natural resources could now be exploited on a larger scale. As timber supply in the small operations in the Kennedy Lake and Ucluelet area began to diminish the logging companies' presence near Tofino increased. The new Pacific Rim National Park "was located within unceded Nuu-chah-nulth territory and went around reserve lands, thus denying those First Nations access to resources therein."

Beginning in the 1980s, what was considered 'unrestricted logging' provoked significant public protests. It began when MacMillan Bloedel announced to begin logging on Meares Island. Leaders of the Nuu-chah-nulth tribe rejected this proposal.

History of Indigenous Peoples in the Region
The Clayoquot Sound is believed to have been continuously populated by First Nations peoples for over 5,000 years according to carbon dating of discarded clamshells. Currently, the Clayoquot Sound is inhabited by three First Nations: the Ahousaht, Hesquiaht, and the Tla-o-qui-aht. These three tribes are part of the Central Region of the Nuu-chah-nulth Nations, and they share many common ancestral themes such as reliance on cedar, salmon, and whales. For Nuu-chah-nulth people, cedar serves as a vital source of heat and light, as well as being a key material in the production of "woven mats, clothing, utensils, longhouses, paddles and canoes." In addition, Cedar trees play a significant spiritual role in the life of the Nuu-chah-nulth.

Ecology and Wildlife of the Clayoquot Sound
The Clayoquot biosphere includes a diverse array of ecosystems such as temperate coastal rainforests, rocky coastal shores, and some of the only remaining old-growth forests remaining in British Columbia. About 85% of the land in the region is considered temperate rainforest. The Clayoquot rainforests are predominantly made up of Western Hemlock, Western Red Cedar, Amabilis Fir, Western Yellow Cedar, Sitka Spruce, Pine, Douglas Fir, Yew and Red Alder. The region is home to over 300 vertebrae species such as black bears, cougars, minks, and grey wolves. In addition, endangered and threatened species such as orcas, sea otters, and auklets call the Clayoquot Sound home. According to the Institute for Coastal and Oceans Research at the University of Victoria, British Columbia, "The diversity of the terrain and habitat means that this area can support a denser population of many of these species than would exist in a mono-culture of coniferous forest."

Blockades and protests
In 1984, the first opposition to logging companies in the Sound occurred, when members of Friends of Clayoquot Sound and First Nations groups set up blockades on the logging roads leading to Meares Island. The island was important to First Nations communities because it contained main sources of drinking water for the area. On Meares Island, "drinking water is sourced from reservoirs that receive an abundance of rain water filtered through the surrounding watershed." Then, the water is treated, stored, and delivered to the residents of businesses of Tofino.

Environmental groups like Friends of Clayoquot Sound and the First Nations communities were concerned with the logging companies' approach to resource management. The First Nations did not completely oppose all logging in the Sound; in fact, they acknowledged that their people had depended on the land's resources for centuries. Rather, they opposed the fact that the companies were pursuing short-term profits by extracting resources at maximum efficiency rates, with little interference from the British Columbia government.

When Macmillan-Bloedel workers arrived at Meares Island in 1984, they encountered a bigger blockade that included members of the Nuu-chah-nulth tribe, local environmental groups, and other supporters of their cause. To prevent logging operations from continuing, protesters declared the island a Tribal Park. Joe Martin, a Clayoquot band council member said of this protest: "It's the first time the whites and natives have gotten together on anything that's worthwhile." MacMillan Bloedel attempted to override this action with a court injunction, succeeding in their aims.  However, in 1985 the Ahousaht and Tia-o-qui-aht First Nations acquired their own injunction to halt logging on the island, at least until the Nuu-chah-nulth's concerns had been addressed in the form of a treaty. This consequential 1985 injunction was granted in a 3 to 2 decision by a British Columbia Appeals Court. In the decision, Justice Peter D. Seaton stated, "It has…been suggested that a decision favourable to the Indians will cast a huge doubt on the tenure that is the basis for the huge investment that has been made and is being made. There is a problem about tenure that has not been attended to in the past. We are being asked to ignore the problem as [the province of British Columbia has] ignored it. I am not willing to do that." Justice MacFarlane echoed this sentiment and went even further, arguing for increased treaty deliberations: "The fact that there is an issue between the Indians and the province based on Aboriginal claims should not come as a surprise to anyone. Those claims have been advanced by the Indians for many years. They were advanced in [the Calder case] and half the court thought they had some substance… I think it is fair to say that, in the end, the public anticipates that the claims will be resolved by negotiations and by settlement. This judicial proceeding is but a small part of the whole process which will ultimately find its solutions in a reasonable exchange between governments and the Indian nations."

Throughout the 1980s animosity continued between these groups due to each side's respective injunctions, which were in contradiction with one another over the use of the land.

In 1992, Friends of Clayoquot Sound set up another blockade. In mid-1993, the most significant protests occurred. Introduction of the Clayoquot Sound Land Use Plan by Mike Harcourt's New Democratic government — which had campaigned on protections for Clayoquot and BC old-growth forests — sparked outrage among environmentalists and the Nuu-chah-nulth people alike. Environmental groups debated the amount and type of land that had been divided, but the First Nations, who composed almost the entire population of the Sound, were concerned that the plan did not consider their spatial, environmental, or economic practices.

In March 1993, initially-peaceful protesters gathered on the lawn of the BC Legislature in Victoria, calling on the NDP government not to allow clearcut logging in Clayoquot Sound. When the assembled officials entered the legislature and attempted to close the doors, however, protesters forced their way in; in the process, an elderly security guard was knocked down and injured his hip. The protesters then swarmed into the foyer chanting slogans, and attempted to force open the inner doors separating the foyer from the Chamber, pounding on the doors and walls and chanting slogans, leading to the breakage of an historic stained glass window. Staff and MLAs successfully barricaded the doors. Victoria Police Department officers eventually arrived and cleared the protesters out; as the protest dispersed, organizers passed the hat to gather donations to cover repair of the broken window.

During the mid-1993, nearly 11,000 people came to Clayoquot Sound to take part in the protests. Activists eventually gained the support of major organizations such as Greenpeace and the Sierra Club. In addition, "Tofino doctors, lawyers, business owners and town councillors joined forces with Nuu-chah-nulth leaders and nature-loving drifters like a Greenpeace campaigner known as 'Seattle Steve.' Money and legal aid started flowing in. So did supporters from Haida Gwaii and California, and media from all over the country." Every day for three months, protesters would gather and blockade a remote logging road, preventing vehicles carrying workers from reaching their sites. The Royal Canadian Mounted Police would then read a court injunction and carry or drag protesters into a bus, which would transport them to the police station in Ucluelet to be charged and released. By the middle of the year, the sheer number of people that had been arrested made it one of the largest acts of civil disobedience in Canadian history.

Many residents of Tofino and Ucluelet worked in the logging industry and felt that the 1993 protests threatened their livelihood. In response, they organized a counter-protest called the "Ucluelet Rendezvous '93." More than 5,000 people came to support the workers and logging community, culminating in  of human excrement being poured near the environmentalists' information site. Loggers stated that they did not want to wipe out the forests, but that carrying on the industry was economically important for future generations.

Media and protest attention

Through local, national, and international news coverage, the demonstrations in the Clayoquot Sound became recognized by the public as having the potential to make significant changes to environmental policy. The logging protests and blockades received worldwide mass media attention, creating national support for environmental movements facing British Columbia and fostering a strong advocacy for anti-logging campaigns.

Mass media attention began by relaying highly controversial, and at times, violent coverage of the protest events, showcasing dramatic outcomes that would lead to higher viewing and readership rates. Reporters believed that this sort of coverage was necessary to bring attention to the cause (given the outcome of certain protests) and offered more appeal to a public that sought entertainment value in the media. Females were portrayed more often than men as being 'radical activists' and members of extremist groups, which encouraged the formation of social stigmas being attached to female protesters. The media's creation of stereotypes led to controversy surrounding the potential economic benefits for media outlets publishing sensational news. Accusations began to surround the mass media's use of language as being biased and one-sided when referring to relevant multi-stakeholder groups.

Over time, the media began to detract attention from 'radical activists' towards reports on individuals who were indirectly involved in the protests. The opinions of 'mild activists' were covered more frequently over time due to their moderation. Considering the ongoing nature of the protests, a shift was made in the media in hopes of resolving the underlying issues surrounding Clayoquot Sound. News articles began to steer reports away from extremists who, in the past, were the focus of dramatic and uniquely portrayed events. Reporters indicated that they chose to interview more moderate groups and 'mild activists' because they were believed to offer more credible and sensible information. The drive to produce more reliable information surpassed the media's need to provide entertainment, which encouraged the public to understand the seriousness behind the issue taking place.

Media attention began to focus on the perceived unfairness of the mass arrests after individuals joined in peaceful protests and blockades, violating a court injunction that forbid the occurrence of such events. News sources focused on activists as having encountered on-site aggression and intimidation, which eventually helped strengthen public support for non-violent actions. Eventually the media did not emphasize the significance of any few particular environmental leaders as central actors in the protection of Clayoquot Sound. Instead, protesters, environmental NGOs and local First Nations were portrayed together as being deeply committed to the effort of preserving Clayoquot Sound, becoming a symbol for international environmental efforts and awareness. These lobby groups, advocating for the boycott of large-scale logging corporations, successfully urged the public to join in and support the cause as activists themselves.

Land Use Deliberations
These protests posed difficulties for locals who worked in the lumber industry. The blockades prevented these workers from completing their jobs, which meant they would not be paid. In 1988, the Tin Wis Coalition was created allowing workers, environmentalists, and aboriginals to discuss mutually beneficial changes. In October 1990 the coalition ceased shortly after a conference.

In 1989 a new forum of eleven-members formed, which meant to produce more results and resolutions by finding compromises for land use in Clayoquot Sound to satisfy all stakeholders. It was formed by the Social Credit government in BC, but in October 1989 it disbanded similarly to the prior coalition.

In 1990, the Clayoquot Sound Development Steering Committee, with representatives from the logging industry, environmentalists, tourist operators, and First Nations groups formed and talked for over a year and a half until environmentalists and tourism representatives walked out, unimpressed that logging operations had continued while the groups met, and disbanded in May 1991.

The government and a separate panel of Ministry of Environment and Ministry of Forests representatives met to decide where logging could and could not occur, while the Steering Committee was gathering. In May 1991 environmentalists left for the second time failed to reach an agreement. In 1991, the British Columbia New Democratic Party (NDP) took up government and utilized all the information compiled from both the committee and the task force to create their Clayoquot Sound Land Use Plan, which they announced in 1993. The plan divided the forests of Clayoquot Sound into numerous regions, setting parts aside for preservation, logging, and other various activities including recreation, wildlife, and scenery. The plan permitted logging in two-thirds of the old growth forest in Clayoquot.

Trials

In August 1994, a British Columbia Provincial Court began the trials of the protestors, with B.C. Supreme Court Justice John Bouck overseeing the first round of prosecutions. Numerous people from a variety of backgrounds and ages were arrested daily for participating in the protests, and charged with criminal contempt of court for defying an injunction banning demonstrations on company work sites. The injunction was obtained by Macmillan Bloedel Ltd.'s logging operations at the Kennedy Lake Bridge, near Clayoquot Sound, stating that no public interference was to be allowed in the areas they were logging.  Of the 932 people arrested, 860 were prosecuted in eight trials. All those prosecuted for criminal intent were found guilty.

The sentences for guilty verdicts varied greatly, with punishments dependent on an individual's involvement in the protest, as well is if they had previously accumulated a criminal record. The sentenced parties faced penalties such as fines, probation and jail sentences. The range of jail terms was a suspended sentence, all the way up to six months in jail, while fines ranged from $250 to $3,000. The judges included Justice Bouck, Low, Murphy, Drake, and Oliver. The lightest sentences were given out by Justice Drake in December, where he gave those found guilty no jail time and  $250 fines. The first 44 people to be put on trial in front of John Bouck received jail time ranging from 45 to 60 days, and fines of $1,000 to $3,000. Justice Low judged the second group with penalties of 21 days in jail or home arrest with a security bracelet for electric monitoring during probation, in some cases allowing a choice between home arrest or jail. Many who had the choice decided to do their sentences in jail as an added protest to the issue.

Boycotts and Corporate Pressure
The intact forests that stand in Clayoquot Sound today represent the outcome of numerous protests that occurred at the end of the 20th Century, having established a solid protection plan for forests.
Greenpeace played a significant role in these protests, instigating a boycott of BC forest products in order to apply pressure on the industry. The boycott was called off once the scientific panel's recommendations were accepted by the government, deferring logging until an inventory of pristine areas was completed. The Annual Allowable Cut and clear-cuts in the area were reduced to a maximum of four hectares. In addition, Eco-Based Planning was to occur once biological and cultural inventories were completed.

As the protests had a negative impact on the reputation and sales of large-scale logging companies in Clayoquot Sound, they removed their operations from the area, and First Nations residents in the Sound were then able to purchase 50% of ownership in the region's logging rights. Iisaak Forest Resources Ltd. formed on behalf of the First Nations, allowing them to take charge over logging operations with their private company. In 1993 environmental lawyer Robert Kennedy Jr. had suggested that aboriginal people should be given full control of forest resources.

During the summer of 1993, more than 30 famous Canadians spoke out against clear-cutting as a result of the protests. Powerful individuals such as Tom Cruise, Barbra Streisand, Oliver Stone, and Robert Redford were part of this group. One of Canada's largest publishers, Knopf Canada,  as well as some German publishers also announced support for clear-cut-free paper. In addition, organizations in the United States sent out mass mailings to the country's largest media sources to encourage an end to business relations with MacMillan Bloedel. From 1993-1995, the logging giant lost $200 million in contracts related to the sale of timber products. The massive financial strain on one of Canada's largest natural resource providers forced both MacMillan Bloedel and the government to the bargaining table with representatives of the Nuu-chah-nulth First Nations. After these deliberations, "Macmillan-Bloedel gradually extricated itself from Clayoquot Sound and turned over control of the tree farm licence to the Nuu-chah-nulth First Nations."

Aftermath

In July 1995, the first significant change in government policies occurred, when all 127 unanimous recommendations made by the scientific panel on Clayoquot Sound were accepted by the Forests Minister of British Columbia, Andrew Petter, and the Environment Minister, Elizabeth Cull on behalf of the NDP government. In 1996, the provincial government financed the compromise, extending $9.3 million over three years to MacMillan Bloedel "to log the territory in an ecologically sound way". In 1999, Iisaak Forest Resources Ltd. signed an agreement known as a Memorandum of Understanding (MOU), ensuring that logging would not occur outside areas which had obviously been logged before and which were outside the intact ancient forests of Clayoquot Sound. The MOU set aside most of the Clayoquot on the western portion of Vancouver Island. Upon passage of the deal, MacMillan Bloedel stated that they would "not log in any of the region's unlogged valleys that are larger than 1,000 hectares."

In 2000, the entire Sound was designated as a Biosphere Reserve by UNESCO, further emphasizing its ecological importance; however, this was not legally binding in preventing companies from logging in the future. The designation created world recognition of Clayoquot Sound's biological diversity, and a $12M monetary fund to "support research, education and training in the Biosphere region". At the end of July 2006, a new set of Watershed Plans was approved in Clayoquot Sound, opening the door for logging to proceed a further 90,000 hectares in the forest, including pristine old-growth valleys As of 2007, both logging tenures within Clayoquot Sound are controlled by first nation logging companies.  Iisaak Forest Resources controls Timber Forest License (TFL) 57 in Clayoquot Sound. MaMook Natural Resources Ltd, in conjunction with Coulson Forest Products, manages TFL54 in Clayoquot Sound.

In 2013, the War in the Woods was said to have set the stage for the protests around the two big pipeline proposals in BC. On April 20, 2014 Tla-o-qui-aht First Nation commemorated 30 years since the beginning of the Clayoquot Protests in an event at Tofino Community Hall. The event saw members of the Tribal community engage in traditional song and dance while also celebrating the successful attempts at opposing logging on Meares Island Tribal Park.

Since the establishment of Meares Island Tribal Park in 2014, the use of Tribal Parks to maintain Indigenous sovereignty has increased in Canada. In advocating for the expansion of Tribal Parks on formerly-held indigenous land, Indigenous Canadians seek to return to traditional methods of conservation and resource management. At Tla-o-qui-aht Tribal Parks, "First Nations staff harvest only the bark of trees for uses including housing, firewood, and medicinal purposes and swim in the rivers to count fish, ensuring the health of the population."

References

Clayoquot Sound region
Nuu-chah-nulth
Environmentalism in Canada
Environmental protests in Canada

Clayoquot protests


The Forstbotanischer Garten in Hannoversch Münden (2.87 hectares) is a forest botanical garden and arboretum located at Mitscherlichstraße 5, Hannoversch Münden, Lower Saxony, Germany.

The garden was established in 1868 at the founding of the Royal Prussian Academy of Forestry Hann. Münden, and formally opened in 1870 on a site of 5.25 hectares. It fell into disuse during World War I, and after its destruction by air raids in World War II was used for vegetable cultivation. In 1962, the garden was reestablished on 4.3 hectares with about 1700 tree and shrub species, but after the academy moved to Göttingen in 1970, it was again abandoned. It reopened in 1988 on 2.87 hectares, and since 2005 has been maintained by the Lower Saxony Forestry Service (Niedersächsische Landesforsten) Münden. It currently contains 754 trees and shrubs under special protection.

See also
 List of botanical gardens in Germany
 Forstbotanischer Garten und Pflanzengeographisches Arboretum der Universität Göttingen

External links
 Forstbotanischer Garten in Hannoversch Münden
 Wiki Goettingen entry
 Cosmotourist entry
 Naturpark Muenden entry

Botanical gardens in Germany
Arboreta in Germany
Gardens in Lower Saxony


Stephanie Taylor (born 1971) is a United States artist based in Los Angeles.

Taylor was born in Port Jefferson, New York.  She works in sculpture, illustration, sound and performance.  All her work is based on sound, around which she builds narratives through other media.  She is interested in the relationships between words, art and sound and often makes soundtracks to accompany her exhibitions.

References

External links
Stephanie Taylor at artist homepage
Further information from the Saatchi Gallery

American artists
Living people
1971 births

Stephanie Taylor (American artist)


Capo or capos, may refer to:

Designation, akin to captain
Capo, short for Caporegime, a rank in the Mafia
Capo dei capi, or capo di tutti capi, Italian for "boss of bosses", a phrase used to indicate a powerful individual in organized crime
Capo (concentration camp), a prisoner who supervised forced labor or carried out tasks delegated by Nazi guards

People
Capo (surname)
Pedro Capó, or "Capó", singer-songwriter from Puerto Rico
Capo (rapper) (born 1991; as Cem Anhan) aka Capo Azzlack; German rapper
Jim Jones (rapper) (born 1976; as Joseph Guillermo Jones II), pseudonym "CAPO"; U.S. rapper
Los Capos, Mexican Lucha Libre pro-wrestlers

Places
Acquarica del Capo, town and commune in the Italian province of Lecce in the Apulia region of southeast Italy
Capistrano Valley High School, commonly known as Capo
Capo d'Orlando, a commune in the Italian province of Messina, in Sicily
Capo di Ponte, a commune in the Italian province of Brescia, in Lombardy
Capo Sandalo Lighthouse, a lighthouse on San Pietro Island, Sardinia, Italy
Capo Vaticano, a wide bathing place of the Municipality of Ricadi in Calabria, Italy
Rural Municipality of Elcapo No. 154, Saskatchewan, Canada

Music
Capo (musical device), a device that is attached to the frets of a string instrument to raise the pitch of each string
Capo (album), a 2011 album by American rapper Jim Jones
El Capo (album), a 2019 album by Jim Jones
"Capo", a 2018 single by American rapper NLE Choppa

Other uses
Harkonnen Capo Chair, one of H. R. Giger's furniture designs
El Capo (TV series), 2009 Colombian drama TV series about a drug lord, aka Marlon Moreno El Capo
El Capo (2016 TV series), Mexican telenovela

See also

Da capo (disambiguation)
Kapo (disambiguation)
Capo di tutti capi (mafioso title) boss of all bosses
Capodecina (mafioso title) boss of a squad in the Cosa Nostra
Capomandamento (mafioso title) boss of a clan in the Cosa Nostra
el Capo de Capos (born 1949) Mexican pro-wrestler
Il Capo dei Capi, a 2007 TV miniseries

Capo