Question

A fridge has a coefficient of performance of 3. If 126 J of heat are absorbed from the inside of the fridge per cycle, what is the amount of heat per cycle in that is expelled into the room in which the fridge is located? A. 190 B. 128 C. 168 D. 158 E. A2

Answer 1

For the case of the fridge(refrigerator),

which absorbs an amount of heat from inside the fridge (low temperature reservoir) by doing a work by the compressor and expells the heat to the surrounding room(High temperature reservoir).

Here given the heat absorbed from inside the fridge(low temp.reservoir),
Q2 126J

Let the work done by the compressor fluid,

And the heat expelled to the surrounding room where it located(High temp.reservoir),$Q_2$

So,We have,
Q2 = Q1 + W
(Based on conservation of energy.)

Also the coefficcient of performance(COP) of the fridge is the ratio of the amount of heat absorbed from inside of fridge to the work done by the compressor fluid.

ie,$COP=\frac{Q_2}{W}$

We have,$W=Q_1-Q_2$

So,$COP=\frac{Q_2}{Q_1-Q_2}$

Given $COP=3$

So,$COP=\frac{126}{Q_1-126}=3$

$126=3Q_1-(3*126)=3Q_1-378$

$3Q_1=126+378=504$

$Q_1=\frac{504}{3}=168J$

So,The heat expelled by fridge to the room where it located is,$Q_1=168J$

Option C

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