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Question

An ideal gas of one mole is at temperature T and expands slowly according to the law PV=constant, such that its final temperature is 15T. If the work done by the gas is xRT, the value of x is
[Answer upto two decimal points]

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Solution

We know workdone by the gas is given by,
W=PdV
It is given, PV=k (constant).
So, W=V2V1kV dV =k2[V22V21]....(i)
As, PV=knRTV2=kT2T1=(V2V1)2(V2V1)2=15.....(ii)
From (i) and (ii),
W=k2[15V21V21] =142kV21=7kV21....(iii)
We know, PV=nRTkV21=1×RTkV21=RT....(iv)
From (iii) and (iv),
W=7RT, Hence x=7.

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