An ideal gas exists in a state with pressure P0, volume V0. It is isothermally expanded to 4 times of its initial volume (V0), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is
- P0V0( 2 - 0.75)
- P0V0(2 2 - 0.75)
- P0V0(2 2 - 0.25)
- P0V0( 2 - 0.25)
Answer
(2) P0V0(2 2 - 0.75)
Solution
The gas returns to its initial state (cyclic process) ⇒ U = 0, so Qnet = Wnet.
Isothermal expansion V0 4V0:
W1 = P0V0 4 = 2P0V0 2
Pressure after it: P = P0V04V0 = P04
Isobaric compression 4V0 V0:
W2 = P04(V0 - 4V0) = -0.75P0V0
Isochoric heating: W3 = 0
∴ Qnet = W1 + W2 + W3 = P0V0(2 2 - 0.75)
Answer: (2)