JEE Advanced 2022 Paper 1 · Physics · Thermodynamics and Kinetic Theory of Gases · medium

One mole of a monatomic ideal gas undergoes a cyclic process A→ B→ C→ D→ A. On a P–V diagram, A=(P0,V0), B=(2P0,V0), C=(2P0,2V0) and D=(P0,2V0), each…

Numerical answer

One mole of a monatomic ideal gas undergoes a cyclic process

A\to B\to C\to D\to A

. On a

P

–

V

diagram,

A=(P_0,V_0)

B=(2P_0,V_0)

C=(2P_0,2V_0)

and

D=(P_0,2V_0)

, each leg being a straight line. The efficiency of this cycle, as a percentage, is ______ . Give the answer correct to two decimal places.

Show answer and solution

Answer: 15.38

Net work is the enclosed area,

W=P_0V_0

. Heat is absorbed in

A\to B

(isochoric, temperature rises) and

B\to C

(isobaric expansion); the other two legs reject heat.

Q_{AB}=\tfrac32\,\Delta(PV)=\tfrac32P_0V_0

Q_{BC}=\tfrac52\,\Delta(PV)=\tfrac52(4P_0V_0-2P_0V_0)=5P_0V_0

. Total input

=6.5P_0V_0

. Efficiency

=\dfrac{1}{6.5}\times100=15.38\%

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