Physics Asked by Aren Kakoly on June 21, 2021
I tried to find the whole connections between the thermodynamics potentials without any success,
the main potentials $U,F,G,H$ and the relations between them (derivatives), for an example what is the derivative of $dU/dT$ while $G$ and $N$ are constants.
if someone can send me to a place where i can find all of these connections it will be great.
Thanks and have a nice day!
Prof. Rebecca Brannon's scheme is an excellent resource for looking up or evaluating complex thermostatic derivatives such as $(partial U/partial T)_{G,N}$, which turns out to be $alpha_P T(VB_S-S)-P(VB_V-S)/K_T$, where $alpha_P$ is the thermal expansion coefficient at constant pressure, $B_X$ is the change in pressure with respect to temperature at constant $X$ (here, entropy or volume), and $K_T$ is the isothermal bulk modulus. (All parameters are taken at constant $N$.)
Table 5-1 here gives the equivalent $(partial U/partial T)_G=mc_P-alpha TS-Palpha V-PS/K_T$ and is easier to use but gives less explanation and insight.
Answered by Chemomechanics on June 21, 2021
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