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Question

In an adiabatic process, R=23Cv. The pressure of the gas will be proportional to

A
T5/3
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B
T5/2
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C
T5/4
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D
T5/6
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Solution

The correct option is B T5/2
We know that for an adiabatic process,
PVγ=constant
where γ=CpCv
Given, R=32CvCv=32R
Also for an adiabatic process, Cv=Rγ1
Equating the expressions of Cv we get,
1γ1=32γ=53
In general for an adiabatic process, PTγγ1
Subtituting the value of γ in the above equation we get, PT52

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