JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2021
- Hard
- MCQ
\(n\) mole a perfect gas undergoes a cyclic process \(ABCA\) (see figure) consisting of the following processes. \(A \rightarrow B :\) Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V _{1}\) to \(V _{2}=2 V _{1}\) and pressure changes from \(P _{1}\) to \(P _{2}\) \(B \rightarrow C :\) Isobaric compression at pressure \(P _{2}\) to initial volume \(V _{1}\) \(C \rightarrow A\) : Isochoric change leading to change of pressure from \(P _{2}\) to \(P _{1}\) Total workdone in the complete cycle \(ABCA\) is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(nRT \left(\ln 2-\frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(W _{\text {Isothermal }}= nRT \ln \left(\frac{ v _{2}}{ v _{1}}\right)\)
\(W _{\text {Isobaric }}= P \Delta V = nR \Delta T\)
\(W _{\text {Isochoric }}=0\)
\(W _{1}= nRT \ln \left(\frac{2 V }{ V }\right)= nRT \ln 2\)
\(W _{2}= nR \left(\frac{ T }{2}- T \right)=- nR \frac{ T }{2}\)
\(W _{3}=0\)
\(\Rightarrow W _{ net }= W _{1}+ W _{2}+ W _{3}\)
\(W _{ net }= nRT \left(\ln 2-\frac{1}{2}\right)\)
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