If `alpha` is the coefficient of performance of a refrigerator and `'Q_(1)'` is heat released to the hot reservoir, then the heat extracted from the cold reservoir `'Q_(2)'` is

Options

A. `(alphaQ_(1))/(alpha-1)`
B. `(alpha-1)/(alpha)Q_(1)`
C. `(alphaQ_(1))/(1+alpha)`
D. `(1+alpha)/(alpha)Q_(1)`

Answer

C

Explanation

As we know that the coefficient of prformance of a refrigerator ,
`alpha = (Q_(2))/(W) " "(because W = Q_(1) -Q_(2))`
`rArr " " alpha = (Q_(2))/(Q_(1) -Q_(2))" "…….(i)`
where `Q_(2)` = heat extraced form the cold reservoir , `Q_(1)` = heat released to the hot reservoir , W = work done by heat pump and `alpha_(2)` = coefficient of performance
So , `alpha(Q_(1) - Q_(2)) +Q_(2) " "("from Eq.(i)")`
`rArr Q_(2) = (alphaQ_(1))/(1+alpha)`