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Question

One mole of an ideal monoatomic gas undergoes a process described by the equation PV3=constant. The molar heat capacity of this gas during this process is

A
32R
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B
52R
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C
2R
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D
R
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Solution

The correct option is D R
We know that, for polytropic process of index x,
PVx=constant
Molar heat capacity is given as,
C=CV+R1x
C=fR2+R1x ...(1)
f=3 [monoatomic gas]
x=3 [PV3=constant,x=3]
On putting these values in Eq.(1)
C=3×R2+R13
C=3R2R2
C=R
The molar heat capacity of the gas during the given process is R

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