1. Contrast a reversible and irreversible expansion process in both physical and thermodynamic terms. What would be different? Hint: It is helpful to put it in the context of the Fundamental Theorem of Thermodynamics.

2. Consider A as a function of volume and temperature. Derive an expression for dA(T,V). Relate this expression to other known thermodynamic variables/observables.

3. Consider B as a function of pressure and temperature. Derive an expression for dB(P,T). Identify the partial derivatives in terms of known/measurable quantities if possible.

4. Clearly and succinctly explain the concept of commensuratevariables in thermodynamics. How does this relate to natural variables in terms of questions 2 and 3? For example, the natural variables in the microcanonical ensemble are E(S,V,N).

5. Derive a state function most usefully associated with the thermodynamic variables T,P (at fixed composition, dN=0) via Legendre transformation of A or H. Derive the differential form of this state function. For what kind of thermodynamic processes will the change in this function be zero?

6. Show that deltaS =deltaH/T [Change in Entropy Formula] at constant pressure by invoking the second law of thermodynamics. Explain your reasoning. 7. Contrast the thermodynamic and mechanical interpretation of the energy. For example, in thermodynamics one speaks of heat and work in the first law, while any molecular system's energy can be described completely in terms of potential and kinetic contribution. What is the utility in such a distinction?

8. State the second law of thermodynamics with an explanation that demonstrates your understanding. Comment on the Carnot efficiency being the reciprocal of the efficiencyof a heat pump