Please print this sheet, sign the statement at the bottom, use it as cover page when you submit your homework, and write your solutions on separate sheets of paper. Remember to always include a complete explanation in full sentences of your reasoning, and to show all calculations.

• 1: Adiabatic constant
  The pressure and volume for an ideal gas undergoing a reversible adiabatic transformation are related by \(pV^\gamma =\) constant, where the adiabatic constant \(\gamma\) depends on the type of gas. Show that \(\gamma\) is equal to the ratio between heat capacities, \(C_p/C_V^~\).

• 2: Ideal gas chemical potential
  Using the pressure and energy equations of state for an ideal gas, the definitions of the main thermodynamic potentials, and the expression for the entropy of an ideal gas derived in class (see also the lecture notes L04) show all the steps leading to an expression for the chemical potential of an ideal gas as a function of V and T.
   
• 3: Van der Waals fluid
  Consider a van der Waals gas, and assume that its energy equation of state is \(E = \frac32 NkT – a/V\). Calculate its (a) constant-volume heat capacity and (b) isothermal compressibility. Comment on whether the compressibility is higher or lower than that of an ideal gas at the same temperature and density, and justify your result in terms of the physical meaning of the parameters a and b. Your answer may be different for different values of the temperature and density.

You are allowed, in fact encouraged, to discuss these problems and how to solve them with other students in the class, but you are not allowed to copy or use in any way anyone else's written solution to any of these problems. This includes solutions that may be provided to you by a student who took the course previously, or solutions you may find online or in print. This policy will hold for all assignments in this class.

Aside from oral discussions I may have had with other students in the class, the solutions to this homework set I am submitting are entirely my own.

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