Question
Physics Question on Thermodynamics
A quantity of a substance in a closed system is made to undergo a reversible process from an initial volume of 3m3 and initial pressure 105N/m2 to a final volume of 5m3 . If the pressure is proportional to the square of the volume (i.e. p=AV2 ), the work done by the substance will be
A
3.6×102J
B
7.4×103J
C
2.2×104J
D
3.6×105J
Answer
3.6×105J
Explanation
Solution
Given, p=AV2
For a closed system, ΔQ=0
∴ΔW=ΔU
Also, work done by the substance
W=vi∫vtp⋅dV
=vi∫vtAV2dV
=A(3V3)vivt(∵A=Vi2pi)
where, A is constant.
=3A[Vf3−Vi3]
=3Vipi(Vf3−Vi3)
=3×9105(125−27)
=3×9105×98
=3.6×105J