Question

n moles of a monoatomic gas are taken around in a cyclic process consisting of four processes along ABCDA as shown. All the lines on the p-V diagram have slope of magnitude `p_0//V_0`. The pressure at A and C is `p_0 and the volumes at A and C are `V_0//2` and `3V_0//2`, respectively. Calculate the percentage efficiency of the cycle.

Answer 1

Correct Answer - A
`eta=(W_(n et))/(sumQ_(+ve))xx100`
`W_(n et)`=Area under the cycle
`=(p_0V_0)/(2)`
`sumQ_(+ve)=Q_(ABC)`
`=W_(ABC)+DeltaU_(ABC)`
=(Area under ABC)+`nC_(V) DeltaT`
`=(5/4p_(0)V_(0))+n(3/2R)(T_C-T_A)`

`5/4p_(0)V_(0)+3/2(p_CV_C-p_AV_A)`
`=5/4p_0V_0+3/2((3p_0V_0)/(2)-(p_0V_0)/(2))`
`11/4p_0V_0`
`:.` `eta=((p_0V_0//2))/((11p_0V_0//4))xx100=18.18%`