Question: Calculate the total work done in the cyclical process ABCDA shown in Figure 15.12(b) by the following two methods to verify that work equals the

Calculate the total work done in the cyclical process ABCDA shown in Figure 15.12(b) by the following two methods to verify that work equals the area inside the closed loop on the PV diagram. (Take the data in the figure to be precise to three significant figures.)

(a) Calculate the work done along each segment of the path and add these values to get the total work.

(b) Calculate the area inside the rectangle ABCDA.

Strategy

To find the work along any path on a PV diagram, you use the fact that work is pressure times change in volume, or W = PΔV. So in part (a), this value is calculated for each leg of the path around the closed loop.

Data given in Figure 15.12

P A D Isobaric S.B WABC > WADC PAB P41.5 x 108 N/m PCD 2 x 105 N/m1 (a) Isochoric AV = 500 cm (b) PW = area inside loop (c) B Wtot = Wout + Win C V V

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Solution for a The work along path AB is Since the path BC is isochoric VBC 0 and so W BC 0 The work along path CD is negative since VCD is negative the volume decreases The work is Again since the pa... View full answer

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