We have been asked the following: "For fixed compositions, show that T = (partial U/partial S)_V = (partial H/partial S)_P". There are 7 other equations after this one, but I think once I know how to solve the first one I will be ok with the rest. We have not been provided with any relevant equations. My knowledge of partial differential equations is a bit rusty, but I have been doing some reading today to brush up. I initially tried to differentiate H = U + PV and substitute that in, but I ended up with an extra Pdv/S, which with constant P I am not sure how to cancel out. I suspect it has something to do with C_v = T(ds/dt)_v and C_p = T(dt/ds)_p but am not sure how to apply them or how to convert from equations at constant volume to equations at constant pressure. I have ordered Classical Thermodynamics by Van Ness and Abbott at the recommendation of our professor, but it won't arrive until next week. The homework isn't due in for another 2 weeks, but if anyone could help me get started, I would really appreciate it. Maybe just some basic pointers so that I had an idea of what path to follow. Thanks in advance.