and the zeroth law says that systems that are in thermodynamic equilibrium with each other have the same temperature. The law was actually the last of the laws to be formulated. First law of thermodynamics where is the infinitesimal increase in internal energy of the system, is the infinitesimal heat flow into the system, and is the infinitesimal work done by the system. The first law is the law of conservation of energy. The symbol instead of the plain d, originated in the work of German mathematician Carl Gottfried Neumann and is used to denote an inexact differential and to indicate that Q and W are path-dependent (i.e., they are not state functions). In some fields such as physical chemistry, positive work is conventionally considered work done on the system rather than by the system, and the law is expressed as . Second law of thermodynamics The entropy of an isolated system never decreases: for an isolated system. A concept related to the second law which is important in thermodynamics is that of reversibility. A process within a given isolated system is said to be reversible if throughout the process the entropy never increases (i.e. the entropy remains unchanged). Third law of thermodynamics when The third law of thermodynamics states that at the absolute zero of temperature, the entropy is zero for a perfect crystalline structure. Onsager reciprocal relations – sometimes called the Fourth law of thermodynamics The fourth law of thermodynamics is not yet an agreed upon law (many supposed variations exist); historically, however, the Onsager reciprocal relations have been frequently referred to as the fourth law. The fundamental equation The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as: Some important aspects of this equation should be noted: , , The thermodynamic space has k+2 dimensions The differential quantities (U, S, V, Ni) are all extensive quantities. The coefficients of the differential quantities are intensive quantities (temperature, pressure, chemical potential). Each pair in