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Question

15 J of heat is added to a monoatomic ideal gas in a process in which the gas performs a work of 5 J on its surroundings . Find the molar heat capacity of the gas during the process.

A
2R
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B
43R
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C
75R
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D
94R
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Solution

The correct option is D 94R
Given,
Heat added to the gas Q=+15 J
Work done by the gas W=+5 J
According to first law of thermodynamics
Q=ΔU+W
15=ΔU+5
ΔU=+10 J
But we know that, ΔU=nCVΔT
nCVΔT=+10 J ....(1)

Also, heat absorbed in the process Q=nCΔT
where C is the molar heat capacity for the gas during the process.
Thus, nCΔT=+15 J .....(2)

From (1) & (2) we get,
CCV=32C=3CV2
For a monoatomic gas, we know that CV=3R2
C=32×3R2
C=94R
Thus, option (d) is the correct answer.

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