What is the integrated form of the fundamental function Z of natural variables$($T$,$P$,\backslash$mu $),$ for a single$-$component system? Why does the integrated form have this special behavior?

Tip: Perform a Lagrange transformation of E$($S$,$V$,$N$)$ with respect to S$,$ V$,$ and N$.$

The expected answer is Z $=$ E $-$TS $+$ PV $-$ mu N $=0$

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