2.25 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 = 310.K. and P = 1.00 bar. Calculate q, w, ΔU, ΔH, and ΔS for each process.

a. The gas is heated to 675 K at a constant external pressure of 1.00 bar.

b. The gas is heated to 675 K at a constant volume corresponding to the initial volume.

c. The gas undergoes a reversible isothermal expansion at 310.K until the pressure is one third of its initial value.