Thermodynamics

JEE Main level, single correct, medium

172 of 190

Question 172 of 190

The pressure of an ideal gas varies with volume as P=αVP=\alpha V, where α\alpha is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes ' mm ' times its initial volume. The work done by the gas in the process is

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Answer: (D) αV22(m2−1)\frac{\alpha V^2}{2}\left(m^2-1\right)

Given P=αVP=\alpha V
Work done, w=∫VmVPdVw=\int_V^{m V} P d V
=∫VmVαVdV=αV22(m2−1)=\int_V^{m V} \alpha V d V=\frac{\alpha V^2}{2}\left(m^2-1\right).

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