Work done determination from P-V graph Assignment Help

Assignment Help: >> Thermodynamics >> Work done determination from P-V graph

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.


980_Work done determination from P-V graph.png


Suppose P as a function of V is known, P = f(V)         

Then work done can be found by, 181_Work done determination from P-V graph1.png    


Case (i): When P-V graph is given in which volume is constant


   60_Work done determination from P-V graph2.png       

When volume is fixed then work done is zero in isochoric process

V = constant

WAB  = 0


Case (ii):When volume is increasing


         295_Work done determination from P-V graph3.png 

V is increasing

WAB> 0 , WAB  = Area enclosed by PV diagram (gas is expanding)


Case (iii)When volume is decreasing

162_Work done determination from P-V graph4.png

V is decreasing

WAB< 0 , WAB  = - area enclosed by PV diagram (gas is bring compressed)


Case (iv):When process is cyclic


665_Work done determination from P-V graph5.png


WCB = WDA = 0

As WCD > 0 and WBD < 0

Also |WCD| > |WAB|

+ve work done = (WCD) + (WAB)

Case (VI):When process is incomplete cyclic.


885_Work done determination from P-V graph6.png


WBC = 0, WAD < 0, WCD > 0

But |WAB| > |WCD|

Total work done = (WAB) + (WCD) (<0)

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