Three moles of an ideal gas at a pressure P_(A) and temperature T_(A)is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original , volume. Finally the gas is compressed at constant volume to its original pressure P_(A) (a) Sketch the P-V and P-T diagrams for the complete process. (b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete process.

Three moles of an ideal gas at a pressure P_(A) and temperature T_(A)i

1.	Three moles of an ideal gas at a pressure P_(A) and temperature T_(A)is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original , volume. Finally the gas is compressed at constant volume to its original pressure P_(A) (a) Sketch the P-V and P-T diagrams for the complete process. (b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete process.
Answer» Solution :The P-V and P-T diagrams are as shonw in (a) and (b) A is the initial STATE. The FIRST second and third processes are represented by AB, BC and CA respectively. (b) WORK done during the isothermal process `AB= nRT log _(e) (V_(2)//V_(1))` `= 3 xx 8.3 xx T xx 2. 303 xx log _(10) (2V//V) = 17.26 TJ` Work done during isobaric process `BC = (P//2) (V _ 2V) =- PV //2` `=- 3 xx 8.3T//2 =- 12 . 45 TJ.` Work done during the isochoric process `CA =0` because `dV =0.` Net work done `=17. 26T - 12. 45 T + 0 = 4.81 TJ` The change in internal energy `= Delta U = 0` because the final state is the same as initial state. By first LAW `Delta Q = Delta U + DeltaW=0 + 4.81 T = 4.81 TJ`