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Question

The molar heat capacity of 1 mole of a diatomic gas, if it does a work of Q/4 in a process when heat Q is supplied to it, is -

A
25R
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B
52R
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C
103R
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D
67R
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Solution

The correct option is C 103R
Given ,
Number of moles of diatomic gas, (n)=1
So, we can write that
ΔU=Cv ΔT=(52R)ΔT
ΔT=2(ΔU)5R ......(1)
From first law of thermodynamics, we can say that
ΔU=ΔQΔW
From the data given in the question
ΔU=QQ4=3Q4 .....(2)
Now, from the definition of molar heat capacity,
C=1nΔQΔT where n=1 here.
From (1) and (2),
C=Q2(ΔU)5R=5RQ2(3Q4)=103R
Hence, option (c) is the correct answer.

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