5. Non-harmonic gas: let us re-examine the generalized ideal gas introduced in the previoussection, using statistical mechanics rather than kinetic theory. Consider a gas of Nnon-interacting atoms in a d-dimensional box of "volume" V, with a kinetic energyH =EAPI".where i, is the momentum of the ith particle. (a) Calculate the classical partition function Z(N, T) at a temperature T. (You don'thave to keep track of numerical constants in the integration.)(b) Calculate the pressure and the internal energy of this gas. (Note how the usualequipartition theorem is modified for non-quadratic degrees of freedom.)(c) Now consider a diatomic gas of N molecules, each with energyKwhere the superscripts refer to the two particles in the molecule. (Note that thisunrealistic potential allows the two atoms to occupy the same point.) Calculate the(1)expectation value (7,(d) Calculate the heat capacity ratio y= Cp/Cy, for the above diatomic gas.at temperature T.%3D

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5. Non-harmonic gas: let us re-examine the generalized ideal gas introduced in the previous section, using statistical mechanics rather than kinetic theory. Consider a gas of N non-interacting atoms in a d-dimensional box of "volume" V, with a kinetic energy where i, is the momentum of the ith particle.

5. Non-harmonic gas: let us re-examine the generalized ideal gas introduced in the previous section, using statistical mechanics rather than kinetic theory. Consider a gas of N non-interacting atoms in a d-dimensional box of "volume" V, with a kinetic energy where i, is the momentum of the ith particle.