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Question

For an ideal gas, an illustration of three different paths A, (B+C) and (D+E) from an initial state P1, V1, T1 to a final state P2, V2, T1 is shown in the given figure.
Path A represents a reversible Isothermal expansion from
P1, V1toP2,V2. Path (B+C) reperesents a reversible adiabatic expansion
(B) from P1V1, T1toP3, V2, T2 followed by reversible heating the gas at constant volume (C) from P3, V2, T2toP2, V2, T1. Path ?
(D+E) represents a reversible expansion at constant pressure P1(D)
from P1, V1, T1 to P1, V2, T3 followed by a reversible cooling at constant volume V2(E)
from P1, V2, T3toP2, V2, T1
What is qrev, for path (A)?

250715.PNG

A
P(V2V1)
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B
nRT3lnV2V1
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C
nRlnV2V1
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D
nRT1lnV2V1
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Solution

The correct option is D nRT1lnV2V1
According to the first law of Thermodynamics, ΔU=qw in an isothermal process.
ΔU=0, hence
q=w or w=nRT1lnV2V1

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