An ideal monoatomic gas is taken round the cycle ABCDA as shown in the P-V diagram. Compute the work done in this process.

Explanation

Let the foot of the perpendiculars drawn from points A,B,C and D on the volume axis be named as `A^(1), B^(1), C^(1) and D^(1)` respectively. AB,BC,CD and DA will be respectively, given by, the areas `(+ABB^(1)A^(1)), (+BC C^(1)B^(1)), (-C C^(1)D^(1) D) and (-D D^(1)A^(1)A)`. Here, the work corresponding to expansion is positive, and that corresponding to compression is negative.
:. Total work done=area `(+ABB^(1)A^(1))+"area" (+BC C^(1)B^(1))+ "area" (-C C^(1)D^(1) D) + "area" (-D D^(1)A^(1)A) = "area" (+ABCD)`
`=(6V_(0)-3V_(0)) (5P_(0)-3P_(0))`
`(3V_(0))(2P_(0))=6P_(0)V_(0)` units .