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Question

24 J of heat is added to a diatomic gas in a process in which the gas performs 8 J of work. Find the molar heat capacity of the gas during the process.

A
4R
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B
6R5
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C
3R
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D
15R4
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Solution

The correct option is D 15R4
Given,
Heat added to the gas Q=24 J
work done by the gas W=8 J
According to first law of thermodynamics
Q=ΔU+W
24=ΔU+8
ΔU=16 J
But we know that, ΔU=nCVΔT
nCVΔT=16 J ...........(1)
Also, Q=nCΔT
Thus, nCΔT=24 J .........(2)
from (1) & (2) we get,
CCV=32C=3CV2
For a diatomic gas we know that,CV=5R2
C=32×5R2
C=15R4
Thus, option (d) is the correct answer.

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