The P - V diagram for a cyclic process is a triangle ABC drawn in order. The co-ordinates of A, B, C are (4,1), (2,4), and (2,1). The co-ordinates are in the order (P-V). Pressure is in Nm-2 and volume is in litre. Calculate work done during the process from A to B, B to C, and C to A. Also, calculate work done in the complete cyclic.
Asked by Topperlearning User
| 17th Apr, 2015,
04:54: PM
Expert Answer:
The P-V diagram drawn as per the question is shown in the figure.
(i) Work done during the process from A to B (expansion)
WAB = + area ABKLA
= area of triangle ABC + area of rectangle BCLK
= (1/2 BC x AC) + (KL x LC)
Now, BC = KC = 4 - 1 = 3 litres = 3 x 10-3 m3
AC = 4 - 2 = 2 Nm-2 : LC = 2 - 0 = 2 Nm-2
Therefore, WAB = 1/2 x 3 x 10-3 x 2 + 3 x 10-3 x 2 = 9 x 10-3 J
(ii) Work done during the process from B to C (compression) is
WBC = - area BCLK = -KL x LC
= -3 x 10-3 x 2 = - 6 x 10-3J.
(iii) Work done during the process from C to A. As there is no change in volume of the gas in this process, therefore, WCA = 0.
Net work done in the complete cycle
W = WAB + WBC + WCA = 9 x 10-3 + (- 6 x 10-3) + 0 = 3 x 10-3 J
Answered by
| 17th Apr, 2015,
06:54: PM
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