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(NONE) The work done by a gas in a reversible process is equal to the area under the $P-V$ curve.For the path $ABC$,the area is a trapezoid with paral

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$48$

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(NONE) The work done by a gas in a reversible process is equal to the area under the $P-V$ curve.For the path $ABC$,the area is a trapezoid with parallel sides of length $8 \; Pa$ (from $V=2$ to $V=8$) and height $8 \; m^3$ (from $V=2$ to $V=10$ is not correct,let's re-evaluate).Looking at the graph,the area under the path $ABC$ is the area of the trapezoid formed by the points $(2, 8), (8, 8), (12, 0),$ and $(2, 0)$.Area $= \frac{1}{2} 	imes (	ext{sum of parallel sides}) 	imes 	ext{height}$.The parallel sides are the vertical line at $V=2$ (from $P=0$ to $P=8$,length $8$) and the vertical line at $V=12$ (from $P=0$ to $P=0$,length $0$). This is not a standard trapezoid.Let's calculate the area as a rectangle plus a triangle:Rectangle area (from $V=2$ to $V=8$,$P=8$): $(8-2) 	imes 8 = 6 	imes 8 = 48$.Triangle area (from $V=8$ to $V=12$,$P$ from $8$ to $0$): $\frac{1}{2} 	imes (12-8) 	imes 8 = \frac{1}{2} 	imes 4 	imes 8 = 16$.Total area $= 48 + 16 = 64 \; Joule$.

The magnitude of work done by a gas that undergoes a reversible expansion along the path $ABC$ shown in the figure is .............. $Joule$.

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