Hello omoplata,
Thank you very much for your reply and help with TeX. I'll re-write it out to make everything clear:
1. Homework Statement
For an elastic rod, show that
\left( \frac{\partial C_{L}}{\partial L}\right)_{T} = -T \left( \frac{\partial^2 f}{\partial T^2}\right)_{L}...
Homework Statement
For an elastic rod, show that
\[ \frac{\partial C_{L}}{\partial L}_{T} = -T*\frac{\partial^2 f}{\partial T^2}
where C_{L} is the heat capacity at constant length L.
Homework Equations
dU = Tds + fdL
F = U - TSThe Attempt at a Solution
I've used
dF = dU - Tds - SdT = fdL -...