I am stuck on a few questions in the thermodyanmics section. It is a revision sheet for the upcoming test. I have done about 2/3 of it but am stuck on a few questions. I will type up the questions in hopes of getting some help. Thank you in advance. 1. Derive a Maxwell relation by using the equality of the mixed second partial derivatives of the enthalpy H(S,p) 2. What thermodynamics state function does X represent in the following: dX = (p/nR)dV + (V/nR)dp 3. Beginning with dS = (1/T)dU + (p/T)dV and the definiton of the heat capacity at a constant volume, derive an expression for the entropy of an ideal monatomic gas as a function of the temperature T and volume V. 4. Calculate the change in entropy of an ideal gas when it undergoes an adiabatic free expansion starting from a state volume of 200cm^3, pressure 50kPa and temperature 300K to a final volume of 400cm^3. And the last one, 5. An engineer announces that he has made a new type of heat engine with a greater theoretical maximum efficiency than the Carnot cycle. The new cycle consists of: 1. Adiabatic expansion from V1 to V2 2. Isobaric compression to V3 3. Adiabatic compression to V4 4. Isobaric expansion back to V1. Derive an expression for the total work done by the engine in one cycle in terms of temperature and an expression for the heat absorbed in the isobaric expansion in terms of temperature. Thanks again for the people who attempted to help or looked at this thread.