In the given elliptical `P-V` diagram

Options

A. the work done is positive
B. the change in internal energy is non-zero
C. the work done ` = - (pi//4) (P_(2) - P_(1)) (V_(2) - V_(1))`
D. the work done `= pi (V_(1) - V_(2))^(2) - pi (P_(1) - P_(2))^(2)`

Answer

C

Explanation

c. The work done = area of `P - V` diagram
`a = (V_(2) - V_(1))/(2), b = (P_(2) - P_(1))/(2)`
`W = - pi ((V_(2) - V_(1))/(2)) ((P_(2) - P_(1))/(2))`
But the cyclic process is anitclockwise, Hence, the wor done is negative