3.75 moles of an ideal gas with C_{V ,m} = 3/2 R undergoes the transformations described in the following list from an initial state described by T = 298 K and P = 4.50 bar. Calculate q, w, ΔU, ΔH, and ΔS for each process.

a. The gas undergoes a reversible adiabatic expansion until the final pressure is one third its initial value.

b. The gas undergoes an adiabatic expansion against a constant external pressure of 1.50 bar until the final pressure is one third its initial value.

c. The gas undergoes an expansion against a constant external pressure of zero bar until the final pressure is equal to one third of its initial value.