Consider filling a gas cylinder with ethane from a high-pressure supply line. Before filling, the cylinder is empty (vacuum). The valve is then opened, exposing the tank to a 3-MPa line at 500K until the pressure of the cylinder reaches 3MPa. The valve is then closed. The volume of the cylinder is 50L. For ethane, use the truncated virial equation of state, in pressure: Z=PVm/(RT)=1+B’P with B’=-2.8 x 10^-8 m^3 /J

a. What is the temperature immediately after the valve is closed?
b. If the cylinder then sits in storage at 293K for a long time, what is the entropy change of the universe (from the original unfilled, state)?