Answer Happy

1) Starting from the semiclassical partition function for a monatomic ideal gas (potential energy zero) of N atoms (a) find expressions for the Helmholtz and Gibbs free energies, the enthalpy, the energy, the entropy, in terms of the thermodynamic 'natural' variables for each of those functions. You may ignore electronic degrees of freedom for the purpose of this problem. Please make use of the thermal de Broglie wavelength to put your expressions in simpler forms. (b) Derive expressions for the chemical potential of this gas in terms of the choices of variables appropriate for the Helmholtz free energy, and (separately) for the Gibbs free energy. (c) For the case of a gas of argon, simply assuming one is in conditions under which it may be considered as an ideal gas, make quantitatively accurate plots of the thermal de Broglie wavelength vs. temperature, and contour plots of the Gibbs free energy vs. both temperature and pressure, using whatever software you find to be most convenient. (In a problem to be assigned after this, we will follow up on this by considering second-order in density contributions to the pressure equation of state and other thermodynamic quantities.)