Work is path function, work done by a gas or done on a gas can be found from pressure-volume (P-V) graph. Area enclosed by P-V graph (also known as P-V indicator) is equal to work done. In the following figure, work done can be calculated as follows.
DIFFERENT CASES TO FIND WORK DONE
Suppose P as a function of V is known, P = f(V)
Then work done can be found by,
Case (i): When P-V graph is given in which volume is constant
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When volume is fixed then work done is zero in isochoric process
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V = constant
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WAB = 0
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Case (ii):When volume is increasing
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V is increasing
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WAB> 0 , WAB = Area enclosed by PV diagram (gas is expanding)
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Case (iii)When volume is decreasing
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V is decreasing
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WAB< 0 , WAB = - area enclosed by PV diagram (gas is bring compressed)
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Case (iv):When process is cyclic
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WCB = WDA = 0
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As WCD > 0 and WBD < 0
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Also |WCD| > |WAB|
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+ve work done = (WCD) + (WAB)
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Case (VI):When process is incomplete cyclic.
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WBC = 0, WAD < 0, WCD > 0
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But |WAB| > |WCD|
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Total work done = (WAB) + (WCD) (<0)
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