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 500 K until the pressure of the cylinder reaches 3 MPa. The valve is then closed. The volume of the cylinder is 50 L. For ethane, use truncated virial equation of state, in pressure:
Z = PV/RT = 1+B′P
with B′ = -2.8×10-8 m3/J.
a) What is the temperature immediately after the valve is closed.
b) If the cylinder then sits in the storage at 293 K for a long time, what is the entropy change of the universe (from the original unfilled state)?