A spring has a temperature dependent k of aT(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}(L-L_{0}) and a heat capacity at constant length of C_{L}=bT, a, L_{0}, 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.

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# Entropy of a spring

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