A diatomic ideal gas is taken through the cyclic process shown in the figure in state 1 the pressure of the gas is 100 kPa and its temperature is 350 K in state 2 the pressure is 300 kPa What is the efficiency of the cycle in percent rounded to nearest integer` [Take l n 3=12//11]`

Answer

`0013`

Explanation

`1-2 rightarrow Isothermal`
`DeltaQ_(12)=-nRxx350l n(300/100)`
`2-3 rightarrow Isobaric`
`DeltaQ_(23)=nxxC_(p)xx[T_(3)-T_(2)]`
`T_(3)/300=350/100`
`T_(3)=1050`
`DeltaQ_(23)=nxx7/2R(1050-350)=nRxx7/2xx700`
`3-1 rightarrow Isochoric`
`DeltaQ_(31)=nC_(v)DeltaT=-nRxx5/2xx(1050-350)=-nRxx5/2xx700`
`eta=1-(nRxx350l n 3+(5//2)nRxx700)/(nR(7//2)xx700)=1-(5+l n3)/7`
`=(1-(5+(12//11))/7)xx100%=12.98 % approx 13%`