JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · Heat & Thermodynamics

In the given

P - V

diagram, a monoatomic gas

(γ = \frac{5}{3})

is first compressed adiabatically from state

A

to state

B

. Then it expands isothermally from state

B

to state

C

. [Given:

(\frac{1}{3})^{0.6} ≃ 0.5, ln 2 ≃ 0.7

].

Which of the following statement(s) is(are) correct?

(A)The magnitude of the total work done in the process $A \to B \to C$ is $144 k J$ .
(B)The magnitude of the work done in the process $B \to C$ is $84 k J$ .✓ Correct
(C)The magnitude of the work done in the process $A \to B$ is $60 k J$ .✓ Correct
(D)The magnitude of the work done in the process $C \to A$ is zero.✓ Correct

Answer: (B), (C), (D)

Solution

From the diagram:

P_{A} = 1 0^{5}

Pa,

V_{A} = 0.8

m³,

P_{B} = 3 \times 1 0^{5}

Pa,

V_{C} = 0.8

m³.

Process A→B (adiabatic):

P_{A} V_{A}^{γ} = P_{B} V_{B}^{γ}

gives

V_{B} = 0.4

m³

Work:

W_{A B} = \frac{P _{A} V _{A} - P _{B} V _{B}}{γ - 1} = \frac{1 0 ^{5} \times 0.8 - 3 \times 1 0 ^{5} \times 0.4}{2/3} = - 60

kJ

(C) Correct:

∣ W_{A B} ∣ = 60

kJ

Process B→C (isothermal):

W_{B C} = P_{B} V_{B} ln \frac{V _{C}}{V _{B}} = 3 \times 1 0^{5} \times 0.4 \times ln 2 = 84

kJ

(B) Correct

Process C→A (isochoric):

W_{C A} = 0

(constant volume)

(D) Correct

Total work:

W_{A B C} = - 60 + 84 + 0 = 24

kJ, not 144 kJ.

(A) Incorrect

JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · One or more correct options