This problem deals with the classical the thermodynamics of an ideal (or perfect) gas. We shall see. for example, how the energy and entropy can be calculated with respect to a reference state, for which they are set equal to zero, In statistical physics, we find these quantities as absolute functions of the macroscopic parameters defining the thermodynamic state. This is a typical example of the relation between the two disciplines, thermodynamics and statistical physics they are consistent and the statistical treatment gives more detailed information on specific systems. The equation of state is The heat capacity per molecule is assumed to be constant, Cv = ok. where u is a constant and k is Boltzmann's constant. For an ideal gas. the energy depends only on the temperature and on the number of molecules. .N. We treat .N as a constant in this problem; a variation of N is discussed in problem 5. From a reference point. (To. V o). where the energy of the gas is set equal to zero, the system is transformed to an arbitrary state (T.V) by a combination of an isochor (constant volume V o) and an isotherm (constant temperature T) Sketch the process in a T diagram are in a P.V diagram. Find the function E(T.V.N) and determine for the two partial processes the work on the system and the heat transfer to the system Also the entropy is set equal to zero at (To. I'D). Show through application of the relation dS = dQ T that the function of state S(T. V, N) is given by In the note on thermodynamics, we showed that Determine the function E(S, V. N) for the perfect gas and check this relation Check also the formula for P(S. V, N). Calculate the Helmholtz free energy F( T. V. N) for the perfect gas check the relations for the derivatives of F (see Note on Thermodynamics, formula (16)).
