Two moles of an ideal gas goes under the process shown in figure. AB and CD are reversible adiabatic process.

The efficiency of the cycle is

Options

A. `1//4`
B. `1//2`
C. `3//4`
D. `3//5`

Answer

C

Explanation

`Q_(DA) = nCP (T_(A) - T_(D))`
`= 2 xx Cp ((P_(0) xx V_(0))/(2R) - (P_(0)v_(0))/(2R))`
`= 2Cp ((P_(0)V_(0))/(2R))`
`Q_(BC) = 2Cp ((P_(0))/(32) xx (8V_(0))/(2R) - (P_(0))/(32) xx (16V_(0))/(2R))`
`= - 2Cp ((P_(0)V_(0))/(8R))`
(Negative sign shows loss in heat)
`eta = 1 - (Q_(BC))/(Q_(DA)) = (3)/(4)`