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

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Jeroronryca · Accepted Answer

&quot;Total energy&quot; is in fact, the internal energy U (unless you give a more precise definition).We may consider also enthalpy   H  =  U  +  p  V, the Helmholtz free energy   F  =  U  −  T  S, the Gibbs free energy   G  =  U  +  p  V  −  T  SFor instance, take Helmholtz free energy, we have (assuming the chemical potentials being zero) :  d  U  =  −  p  d  V  +  T  d  S, and   d  F  =  −  p  d  V  −  S  d  TThe 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 (  Δ  F  =  0). But in this same process, you have   d  U  =  T  d  S, so unless the process is isentropic, you will have a variation in   Δ  U  ≠  0),so you have, in the general case:  Δ  F  ≠  Δ  UA analog demonstration can be done for the enthalpy and the Gibbs free energy.

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

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