Find relation between efficiency `(eta)` of carnot engine and coefficient of performance `(eta^(`))` of refrigerator.

Options

A. `eta=1/beta`
B. `eta=1/(beta+1)`
C. `etabeta=1/2`
D. `eta=1/(beta-1)`

Answer

B

Explanation

For a heat engine, `eta=1-T_(2)/T_(1)=(T_(1)-T_(2))/T_(1)`
and for a refrigerator, `beta=T_(2)/(T_(1)-T_(2))`
`thereforeetaxxbeta=(T_(1)-T_(2))/T_(1)xxT_(2)/(T_(1)-T_(2))=T_(2)/T_(1)`
But `T_(2)/T_(1)=1-eta" "thereforeetabeta=1-eta`
`thereforeetabeta+eta=1" "eta(beta+1)=1`
`thereforeeta=1/(beta+1)`