In a cyclic process shown on the `P -V` diargam 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))`

Answer

C

Explanation

`W.D = pi xx` Pressure Radius `xx` volume Radius (area of ellipse)
`W = pi ((P_(2)-P_(1))/(2))((V_(2)-V_(1))/(2))`
`= (pi)/(4) (P_(2) -P_(1)) (V_(2)-V_(1))`