A spring has a temperature dependent k of aT2(L-L0) and a heat capacity at constant length of CL=bT, a, L0, and b are constants. I need to calculate the derivative of entropy with respect to length at constant temperature. I can't figure out why the entropy should depend on the length. If dS=dQ/T, and when you stretch the spring you don't add any heat, why would the entropy rise? I'm not 100% sure I'm wrong, but based on the rest of the problem it doesn't seem likely that the answer actually is zero.