JEE Advanced2022PhysicsThermodynamicsActual
In the given P - V diagram, a monoatomic gas γ = 5 3 is first compressed adiabatically from state A state B . Then it expands isothermally from state B to state C . [Given : 1 3 0 . 6 = 0 . 5 , ln 2 ≈ 0 . 7 ]. Which of the following statement(s) is(are) correct?
Options
- AThe magnitude of the total work done in the process A → B → C is 144   kJ
- BThe magnitude of the work done in the process B → C is 84 kJ .
- CThe magnitude of the work done in the process A → B is 60 kJ .
- DThe magnitude of the work done in the process C → A is zero.
Correct answer
B. The magnitude of the work done in the process B → C is 84 kJ .
Step-by-step solution
For adiabatic process P V γ = C ⇒ 100 0 . 8 5 3 = 300 V B 5 3 ⇒ V B = 0 . 8 3 3 / 5 = 0 . 4   m 3 Work done in an adiabatic process is given by, W = P 1 V 1 - P 2 V 2 γ - 1 ⇒ W A B = P A V A - P B V B 5 3 - 1 = 80 - 300 × 0 . 4 2 / 3   kJ ⇒ W A B = - 60 kJ Therefore, option C is correct. C → A is isochoric ⇒ D is correct. For process B C W B C = n R T ln V 2 V 1 = P V ln V 2 V 1 ⇒ W B C = 300 × 0 . 4 ln 0 . 8 0 . 4 ⇒ W B C = 120 × ln