Consider the reversible processes for 1.0 mol of an ideal gas as shown in the figure. [figure] w1, w2, w3 and w4 represent work done (in calories) in the processes 1, 2, 3 and 4, respectively; U2 and U4 are changes in the internal energy for the processes 2 and 4, respectively. [use R = 2 cal K-1 mol-1] The correct option is
- w1 + w2 + w3 + w4 = 0
- w1 + w3 = -2T1 V2V1 - 2T2 V4V3
- w2 + w4 = U2 - U4
- w1 + w2 = 2T1 V2V1
Answer
(2) w1 + w3 = -2T1 V2V1 - 2T2 V4V3
Solution
For n = 1.0 mol of an ideal gas:
Process 1 is isothermal reversible expansion at temperature T1 from V1 to V2:
w1 = -n R T1 V2V1 = -2T1 V2V1
Process 3 is isothermal reversible compression at temperature T2 from V3 to V4:
w3 = -n R T2 V4V3 = -2T2 V4V3
Summing the work done in processes 1 and 3:
w1 + w3 = -2T1 V2V1 - 2T2 V4V3
Answer: (2)