An ideal gas of volume 005 ft3 and pressure 120 ibin2

Question

(a) Show that the heat transferred during an infinitesimal quasi-static process of an ideal gas can be written

dQ = (C_V/nR)V dP + (C_P/nR)P dV.
Applying this equation to an adiabatic process, show that PP = const.

(b) An ideal gas of volume 0.05 ft³ and pressure 120 Ib/in² undergoes a quasi-static adiabatic expansion until the pressure drops to 15Ib/in². Assuming, to remain constant at the value 1.4, calculate the final volume. Calculate the work.