An ideal gas goes through a cycle consisting of ischoric adiabatic and isothermal lines. The isothermal process is perform at minimum temperature. If the absolute temperature varies `K` times with tn the cycle then find out its effcincy.

Options

A. `1-(ln K)/(l)`
B. `1+(ln K)/(l)`
C. `(ln K)/(l)`
D. `(l)/(ln K)`

Answer

A

Explanation

Process `2rarr3` is adiabatic expansion and `3rarr1` is isothermal compression.
From process `2rarr3` , the internal energy continuosly decrease (I.e., temperature continuously decrease) Point `2` is at highest temerature
`Q_(g)=Nc_(v)(KT-T)`, `Q_(r)=nRT"In"(V_(3))/(V_(1))`
Process
`2rarr3(KT)V_(1)^(gamma-1)=TV_(3)^(gamma-1)implies(V_(3))/(V_(1))=(K)^(1//(gamma-1))`
`eta=(Q_(g)-Q_(r))/(Q_(8))=1-(Q_(r))/(Q_(g))=1-("In"K)/(l)`