The cyclic process form a circle on a PV diagram as shown in figure. The work done by the gas is

\frac{π}{4} (P_{2} - P_{1})^{2}

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\frac{π}{4} (V_{2} - V_{1})^{2}

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\frac{π}{2} (P_{2} - P_{1}) (V_{2} - V_{1})

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\frac{π}{4} (P_{2} - P_{1}) (V_{2} - V_{1})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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Solution

The correct options are
A $\frac{π}{4} (P_{2} - P_{1})^{2}$
B $\frac{π}{4} (V_{2} - V_{1})^{2}$
C $\frac{π}{4} (P_{2} - P_{1}) (V_{2} - V_{1})$
The work done is area enclosed in the loop.
The loop is a circle.
Hence the diameters $P_{2} - P_{1} = V_{2} - V_{1}$
Area of circle = $\frac{π D^{2}}{4}$
$D^{2} = (P_{2} - P_{1})^{2} = (V_{2} - V_{1})^{2} = (P_{2} - P_{1}) (V_{2} - V_{1})$

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