A given mass of a gas expands from the state A to the state B by three paths 1, 2 and 3 as shown in the figure. If $W_{1}$ , $W_{2}$ and $W_{3}$ respectively be the work done by the gas along the three paths. Then :

W_{1} > W_{2} > W_{3}

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W_{1} < W_{2} < W_{3}

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W_{1} = W_{2} = W_{3}

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W_{1} < W_{2} > W_{3}

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Solution

The correct option is B $W_{1} < W_{2} < W_{3}$
Work done in a process is area under P-V graph (where Pressure is along y-axis and Volume is along the x-axis)

Also work done is positive in expansion and negative in compression.

In the given problem, volume is increasing in all the cases hence W is positive.
Process-3 covers largest area, then is Process-2 and then Process-1
hence
$W_{3} > W_{2} > W_{1}$

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