(Solved): [7] a) Derive the following expression starting from the differential of U in terms of its canonica ...

$$[7]$$ a) Derive the following expression starting from the differential of $$U$$ in terms of its canonical variables: $${\left(\frac{?U}{?V}\right)}_{N,T}=T{\left(\frac{?P}{?T}\right)}_{N,V}?P$$ b) Evaluate $$(?U/?V{)}_{T,N}$$ for: i) an ideal gas and ii) for a gas with the following equation of state: $$P=\frac{RT}{\underline{V}?b}$$ where $$\mathrm{b}$$ is a constant. c) Explain your $$(?U/?V{)}_{T,N}$$ result for the two equations of state.