`A` cycle is made of three process is iso barie, adiabatic and isothermal. Isothermal process has minimum temperature. Absolute temperature charges by `k` times withing the cycle. Find out the efficiency.

Options

A. `1-(1nK)/((K-1))`
B. `1+(1nK)/((K-1))`
C. `1+(1nK)/((K+1))`
D. none of these

Answer

A

Explanation

`Q_(g)=nC_(p)(KT-T)`
`Q_(r)=nRT"in"(V_(3))/(V_(1)) , ((V_(3))/(V_(2)))/((V_(1))/(V_(2)))=(K)^(1/(gamma-1))/(1/K)`
Process `1rarr2` is isobaric,
`(V_(1))/(T)=(V_(2))/(KT)(V_(3))/(V_(1))=K(K)^(1/(gamma-1))`
Process `2rarr3` is adiabatic, `KTV_(2)^(gamma-1)=TV_(3)^(gamma-1)`
`(V_(3))/(V_(2))=(K)^(1/gamma-1) KTV_(2)^(gamma-1)=TV_(3)^(gamma-1)`
`eta=1(R"in"V_(3)//V_(1))/((gammaR)/(gamma-1)(K-1))=1-("in"K)/((K-1))`