Question

The p-V diagram for a cyclic process is a triangle ABC drawn in order (see fig.) alongside. The co-ordinates 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 the work done during the process from A to B; B to C and C to A. Also calculate the work done in the complete cycle.

Answer 1

The cyclic process is a triangle ABC represented by A(4,1); B(2,4) C(2,1) on the p-V diagram.

Work done during the process from A to B:

Now, W_AB is positive, as the system expands along AB.

W_AB = + area of trapezium ABDEA

Work done during the process from B to C:

Now, W_BC is negative, as the system is compressed along BC.

W_BC = + area of rectangle BCED

= - DE X CE

Now, DE = 3 x 10^-3 m³

and  CE = 2 x 10^-3 x 2

= 6 x 10^-3 J

Work done during the process from C to A :

Since in going from C to A, there is no change in volume; 

W_CA = 0

Work done in the complete cycle,

= 9 x 10^-3 + (-6 x 10^-3)+ 0

= 3 x 10^-3 J.