Question

If α is the coefficient of performance of a refrigerator and 'Q₁' is heat released to the hot reservoir, then the heat extracted from the cold reservoir 'Q₂' is ______.

Options

• `(alpha"Q"_1)/(alpha - 1)`

• `(alpha - 1)/alpha "Q"_1`

• `(alpha"Q"_1)/(1 + alpha)`

• `(1 + alpha)/alpha "Q"_1`

Answer 1

If α is the coefficient of performance of a refrigerator and 'Q₁' is heat released to the hot reservoir, then the heat extracted from the cold reservoir 'Q₂' is `underlinebb((alpha"Q"_1)/(1 + alpha))`.

Explanation:

As we know that the coefficient of performance of a refrigerator,

`alpha = "Q"_2/"W"    ...(therefore "W" = "Q"_1 - "Q"_2)`

`=> alpha = "Q"_2/("Q"_1 - "Q"_2)`    ...(i)

where, Q₂ = heat extracted from the cold reservoir,

Q₁ = heat released to the hot reservoir,

W = work done by heat pump and

α = coefficient of performance

So, `alpha("Q"_1 - "Q"_2) = "Q"_2`   (from Eq. (i))

`=> "Q"_2 = (alpha"Q"_1)/(1 + alpha)`