To prove that the equation U=-T((a/aT)*(F/T))V, N is valid between internal energy U= (E) and Helmholtz...

 

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To prove that the equation U=-T²((a/aT)*(F/T))V, N is valid between internal energy U= (E) and Helmholtz function F = -KBT In(Z), we can start by noting that U = (E) = a(F+TS)/aẞ, where ẞ = 1/kBT. How do we know that U (E) (F+TS)/aẞ? To prove that the equation U=-T²((a/aT)*(F/T))V, N is valid between internal energy U= (E) and Helmholtz function F = -KBT In(Z), we can start by noting that U = (E) = a(F+TS)/aẞ, where ẞ = 1/kBT. How do we know that U (E) (F+TS)/aẞ?

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To show that U E F TS we can differentiate both sides of the equation F kBT lnZ with ... View the full answer