1. The problem statement, all variables and given/known data Show that (du/dv)T = T(dp/dt)v - p 2. Relevant equations Using Tds = du + pdv and a Maxwell relation 3. The attempt at a solution I've solved the problem, but I'm not entirely sure my method is correct. Tds = du + pdv ---> du = Tds - Pdv - Using dF=(dF/dx)ydx +(dF/dy)xdy du=(du/dT)v+(du/dv)Tdv - Therefore Tds - Pdv = (du/dT)v+(du/dv)Tdv - Divide by dv: (du/dT)vdT/dv + (du/dv)T = T(ds/dv)T - p Now, to get the right answer, this term: (du/dT)vdT/dv must equal zero, but I'm not sure why - please can somebody explain? Then you simply insert Maxwell relation -(ds/dv)T = -(dp/dT)v and rearrange to get the correct answer. Many thanks for any help!