taken in recognizing which natural variables correspond to which potential. For the recommended nomenclature of these potentials, see (Alberty, 2001). Equation () is useful for processes where system volume, entropy, and the number of moles of various components change because internal energy is also a function of these variables and no others. An alternative definition of internal energy does not separate available chemical potential from U. This expression is useful (when substituted into equation ()) for processes where system volume and entropy change, but no chemical reaction occurs: In this case, a given set of chemicals at a given entropy and volume will have a single numerical value for this thermodynamic potential. A multi-state system may complicate or simplify the problem because the Gibbs phase rule predicts that intensive quantities will no longer be completely independent from each other. A historical and cultural tangent In 1848, William Thomson, 1st Baron Kelvin, asked (and immediately answered) the question Is there any principle on which an absolute thermometric scale can be founded? It appears to me that Carnot’s theory of the motive power of heat enables us to give an affirmative answer. With the benefit of the hindsight contained in equation (), we are able to understand the historical impact of Kelvin's idea on physics. Kelvin suggested that the best temperature scale would describe a constant ability for a unit of temperature in the surroundings to alter the available work from Carnot's engine. From equation (): Rudolf Clausius recognized the presence of a proportionality constant in Kelvin's analysis and gave it the name entropy in 1865 from the Greek for "transformation" because it describes the quantity of energy lost during the transformation from heat to work. The available work from a Carnot engine is at its maximum when the surroundings are at a temperature of absolute zero. Physicists then, as now, often look at a property with the word "available" or "utilizable" in its name with a certain unease. The idea of what is available raises the question of "available to what?" and raises a concern about whether such a property is anthropocentric. Laws derived using such a property may not describe the universe but instead, describe what people wish to see. The field of statistical mechanics (beginning with the work of Ludwig Boltzmann in developing the Boltzmann equation) relieved many physicists of this concern. From this discipline, we now know that