An ideal gas is taken around the cycle `ABCA` shown in `P - V` diagram. The net work done by the gas during the cycle is equal to

Options

A. `12 P_(1) V_(1)`
B. `6 P_(1) V_(1)`
C. `3 P_(1) V_(1)`
D. `P_(1) V_(1)`

Answer

C

Explanation

c. Work done = area of the `Delta ABC`
`= (1)/(2) xx AC xx AB = (1)/(2) xx (3 V_(1) - V_(1)) xx (4 P_(1) - P_(1))`
`= (1)/(2) xx 2 V_(1) xx 3 P_(1) = 3 P_(1) V_(1)`