Homework Statement
Show that (∂(βA)/∂β)N,V = E, where A = E - TS is the Helmholtz Free Energy and E is the Internal Energy.
Homework Equations
A = E - TS
dE = TdS - pdV + ΣUidni
β = 1 / (kBT)
The Attempt at a Solution
(∂(βA)/∂β)N,V = (∂/∂β) * (βE - βTS)
(∂(βA)/∂β)N,V = (∂/∂β) * (βE -...