Question

prove that d(A/T)/dT = -E/(T^2)

Answer 1

Note that this is:
\[
\frac{d}{dT}\frac{A}{T}=\frac{dA}{dT}\cdot\frac{d}{dT}\left(\frac{1}{T}\right)
\]This becomes:
\[
\frac{dA}{dT}\cdot\frac{-1}{T^2}
\]And, I can take a guess, although I don't quite know what \(A\) is in this context, we have:
\[
\frac{dA}{dT}=E
\]So:
\[
E\cdot\frac{-1}{T^2}=-\frac{E}{T^2}
\]

Answer 2

A is the Helmholtz energy, A for Arbeit in German, E or mostly written U is the internal energy.

Answer 3

True most of the way except that:
\[A=U-TS\]
\[\left( \frac{ \partial A }{ \partial T } \right)_{V}=-S\]
S is the entropy.

Answer 4

But if you substitute the equations back and forth you come to the conclusion you did so well done by lolwolf.