Question
What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, $p_{ext}$ in a single step as shown in Fig. Explain graphically.
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Answer
Let us consider a cylinder which contains one mole of an ideal gas fitted with a frictionless piston. Total volume of the gas is $V_i$ and pressure of the gas inside is $p$. If external pressure is $p_{\text {ext }}$ which is greater than $p$, piston is moved inward till the pressure inside becomes equal to $p_{\text {ext. }}$ Let this change be achieved in a single step and the final volume be $V _{ f } . w = p _{\text {ext }}(\Delta V )$. Work done is equal to the shaded area $ABV _{ i } V _{ ii }$.
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