Question

There is a hypothetic system of N particles, there internal energy is given by U(S,L,n) = θ(S^2)V/(N^2)

where θ is a constant and V is the volume of the system and S is the entropy of the system. Assume the system is under the equilibrium.  

i) Show U(S,L,n) is a first order Euler function.

ii) Calculate the chemical potential µ(S,L,N)

iii) Calculate the chemical potential µ(L/N)

iv) Show the equation of state satisfies the Gibbs-Duhem relation below SdT + VdP + ndµ = 0

Answer 1