Sulfur dioxide vapor at 520 K and 100 bar fills one-half of a rigid, adiabatic cylinder. The other half is evacuated, and the two halves are separated by a metal diaphragm Assume that the vapor is well mixed and that expansion is sufficiently rapid so that negligible heat transfer occurs between the walls and the sulfur dioxide vapor. The sulfur dioxide vapor is well- described by the Peng-Robinson equation of state. For SO, T = 430.8 K, P = 78.8 bar, v, 1.22 x 10-*m/mol, w = 0.251. The ideal gas heat capacity C = 23.852 +6.699 x 10-27 -4.961 x 10-572 +1.328 10-87 with Tin K. (a) Derive an expression for the change in internal energy u(T,P) -u(T, P) where P represents low pressure at which the vapor behaves like an ideal gas. (b) If the diaphragm should rupture, what would be the final temperature and pressure?