Assignment:
Question 1. Consider n moles of a Van der Waals gas. Show that (dU/dV)_T = n^2a/V^2. Hence show that the internal energy is U = the integral from zero to T of C_vdT - an^2/V + U0 where U0 is a constant. {Hint: Express U = U(T,V)}.
Question 2. As in the previous question, consider n moles of Van der Waals gas. Show that
(a) S = the integral from zero to T of C_v/TdT + nRln(V - nb) + S0
where S0 is a constant. {Hint: Use dS = 1/T(dU + PdV)
(b) The equation for a reversible adiabatic process is
T(V -nb)^(nR/C_v) = a constant
if C_v is assumed to be independent of T.