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