Is less....becz refer work only for cooling so it need to do less compressor work but in case of AC it ll cooling also but at a same time it also work to maintain humidity means it's compressor work against water also..so AC need more work as an input so it ll give proper output.and refer work at constant environment condition means if we place hot water inside refer than it's temp decrease continuously but in AC the room condition is change with surrounding once means same time cloudy same time sunny or rainy so it's need to maintain all ths criteria with in limit so it's cop is more.

Answer:

Introduction:
The coefficient of performance (COP) is a measure of the efficiency of a refrigeration or heating device. It is defined as the ratio of the desired output to the required input. In the case of a refrigerator or air conditioner, the COP indicates how much cooling or heating is achieved for a given amount of electricity consumed.

Explanation:
To understand why the coefficient of performance of a domestic refrigerator is less compared to a domestic air-conditioner, let's analyze the working principles of both devices.

Domestic Refrigerator:
A domestic refrigerator works on the principle of removing heat from the contents of the refrigerator and expelling it to the surrounding environment. It achieves this by using a refrigeration cycle that consists of a compressor, condenser, expansion valve, and evaporator. The compressor increases the pressure and temperature of the refrigerant, which then flows through the condenser where heat is released to the surroundings. The refrigerant then passes through the expansion valve, causing its pressure and temperature to drop. In the evaporator, the refrigerant absorbs heat from the contents of the refrigerator, cooling them down.

Domestic Air-Conditioner:
A domestic air-conditioner works on a similar principle as a refrigerator but with the additional capability of cooling the air in a room. It also uses a refrigeration cycle, but the cold air is circulated into the room instead of being confined to a closed compartment. The air-conditioner pulls in warm air from the room, which passes through the evaporator where it is cooled by the refrigerant. The cool air is then blown back into the room, while the heat absorbed by the refrigerant is expelled outside through the condenser.

Comparison:
The coefficient of performance of a refrigerator and an air-conditioner can be calculated using the following formulas:

COP_refrigerator = Q_cooling / W_compressor
COP_air-conditioner = Q_cooling / W_compressor + W_fan

Here, Q_cooling represents the amount of heat removed from the refrigerated space, W_compressor is the work done by the compressor, and W_fan is the work done by the fan to circulate air in the case of an air-conditioner.

The key difference between a refrigerator and an air-conditioner is the additional work done by the fan in the air-conditioner to move the cool air into the room. This additional work reduces the COP of the air-conditioner compared to the refrigerator, making the COP of the refrigerator greater.

Therefore, the coefficient of performance of a domestic refrigerator is less compared to a domestic air-conditioner.