The temperature -entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `(1)/(3)`
D. `(2)/(3)`

Answer

C

Explanation

According to the figure
`Q_(1) = T_(0)S_(0) +(1)/(2)T_(0)S_(0) = (3)/(2) T_(0)S_(0)`
`Q_(2) = T_(0) (2S_(0)-S_(0)) = T_(0)S_(0)`
`Q_(3) = 0`
`eta = (W)/(Q_(1)) = (Q_(1)-Q_(2))/(Q_(1)) = 1 - (Q_(2))/(Q_(1))`
` =1 -(2)/(3) = (1)/(3)`