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

An ideal monoatomic gas is taken round the cycle ABCDA as shown in the

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