In the cyclic process shown on `P_V` diagram, the magnitude of the work done is

Options

A. `pi((P_(2)-P_(1))/(2))^(2)`
B. `pi((V_(2)-V_(1))/(2))^(2)`
C. `(pi)/(4) (P_(2)-P_(1)) (V_(2)-V_(1))`
D. `pi(P_(2)V_(2) - P_(1)V_(1))`

Explanation

Work done `=` Area under the curve
Area of sphere `= pir^(2) = pi = pi((V_(2)-V_(1))^(2))/(2) (r=(V_(2)-V_(1))/(2))`
`=(pi(P_(2)^(2)-P_(1))^(2))/(2) (r =(P_(2)-P_(1))/(2))`
`:. `(b) and (a)