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Question

A gas expands with temperature according to the relation V=kT2/3. What is the work done, when the temperature changes by 30C?

A
10R
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B
20R
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C
30R
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D
40R
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Solution

The correct option is B 20R
Given,
V=kT2/3
Change in Temperature, (ΔT)=T2T1=30C
Now, we know that
W=PdV
Using,ideal gas equation in the above formula we get,
W=RTVdV
Since, V=kT2/3dV=23kT1/3dT
Eliminating k, we find dVV=23dTT
Hence W=T2T123RTTdT=23R(T2T1)=23R(30)=20R
Thus, option (b) is the correct answer.

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