Thermodynamics

JEE Main level, single correct, medium

122 of 190

Question 122 of 190

In the reported figure, there is a cyclic process ABCDAABCDA on a sample of 11 mol of a diatomic gas. The temperature of the gas during the process A→BA\rightarrow B and C→DC\rightarrow D are T1{T}_{1} and T2(T1>T2){T}_{2}\left({T}_{1}\gt {T}_{2}\right) respectively.

Choose the correct option out of the following for work done if processes
BCBC and DADA are adiabatic.

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Answer: (B) WAD=WBC{W}_{AD}={W}_{BC}

Work done in adiabatic process =−nRγ−1(Tf−Ti)=\dfrac{-nR}{\gamma -1}\left({T}_{f}-{T}_{i}\right)
∴WAD=−nRγ−1(T2−T1)∴{W}_{AD}=\dfrac{-nR}{\gamma -1}\left({T}_{2}-{T}_{1}\right)
and
WBC=−nRγ−1(T2−T1){W}_{BC}=\dfrac{-nR}{\gamma -1}\left({T}_{2}-{T}_{1}\right)
∴WAD=WBC∴{W}_{AD}={W}_{BC}

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