Libby Owens

Answered

2022-07-17

What are the state functions telling me or how are they related to total energy?

Answer & Explanation

Jeroronryca

Expert

2022-07-18Added 13 answers

"Total energy" is in fact, the internal energy U (unless you give a more precise definition).
We may consider also enthalpy $H=U+pV$, the Helmholtz free energy $F=U-TS$, the Gibbs free energy $G=U+pV-TS$
For instance, take Helmholtz free energy, we have (assuming the chemical potentials being zero) :
$dU=-pdV+TdS$, and $dF=-pdV-SdT$
The natural variables associated to F are V and T, so if they are unchanged in some process, that means that F is constant in this process ($\mathrm{\Delta }F=0$). But in this same process, you have $dU=TdS$, so unless the process is isentropic, you will have a variation in $\mathrm{\Delta }U\ne 0$),so you have, in the general case:
$\mathrm{\Delta }F\ne \mathrm{\Delta }U$
A analog demonstration can be done for the enthalpy and the Gibbs free energy.

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