Question

Assertion: The heat rejected to the hot sink is greater than the heat absorbed from the cold source, so the heating CoP is one greater than the cooling CoP.
Reason: CoP of a heat engine can be increased by decreasing its work input.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is correct.
D. Both Assertion and Reason are incorrect.

Answer 1

Hint: Here, we compare the CoP (Coefficient of Performance) of refrigerator and heat engine then we compare their expressions.

Complete step by step solution:
The CoP(coefficient of performance) it gives the relation between the power that is drawn out of the heat pump as the cooling or heating and that power which is compressed.
The Coefficient of Performance of a heat pump, refrigerator or air conditioning system is the ratio of useful heating or cooling that provide required work. The CoP is the dimensionless unit. It is the ratio of energy produced to the energy consumed.
The basic expression of CoP is
$\text{Coefficient of Performance}{\text{ (CoP)}}\; = \;\dfrac{{\text{Heat (Q)}}}{{\text{Work Done(W)}}}$
Here, Q is the heat supplied to or removed from the reservoir.
W is the work done by the heat pump.
The coefficient of Performance of the refrigerator is known as the heat taken from the cold reservoir or low temperature reservoir to work input for this process to take place.
The CoP is the ratio of how much heat required in a heat pump will produce if we give it certain energy input.
The expressions be
$\text{CoP of heat engine} = \dfrac{{\text{Heat rejected to the hot sink}}}{{\text{Work Input}}}$
The CoP is the heat removed from the cold reservoir to the work done to remove the heat.
The expressions be
$\text{CoP of refrigerator} =$ $\dfrac{\text{Heat removed from the cold reservoir}}{\text{Work done to remove the heat}}$
Here, the Assertion is correct.
On Comparing the CoP of heat engine and CoP of refrigerator it is equal to
 $ \left( {1 + \dfrac{{{Q_2}}}{W}} \right) $
Here, $Q_2$ is the heat absorbed by the cold sink

So, the correct answer is “Option A”.

Note: Coefficient Of Performance (COP) is the ratio of Coldness produced to the Heat or Work supplied.