Statement (I): The COP of an air- conditioning plant is higher than the COP of a household refrigerator. Statement (II): For the same condenser temper

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Statement (I): The COP of an air- conditioning plant is higher than the COP of a household refrigerator.

Statement (II): For the same condenser temperature, the suction pressure of the evaporator is higher in the air conditioning plant than in the household refrigerator.
1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (1)
2. Both Statement (I) and Statement (II) are individually true and Statement (II) is NOT the correct explanation of Statement (1)
3. Statement (I) is true but Statement (II) false
4. Statement (I) is false but Statement (II) is true

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Correct Answer - Option 1 : Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (1)

Explanation:

The COP of refrigerating equipment is given by

$COP = \frac{{Desired\;Effect}}{{Work\;input}}$

• The COP is inversely proportional to the work input given to the compressing unit, for a given amount desired or refrigeration effect.
• In a domestic refrigerator, the temperature of the evaporator or refrigerated space is lower than the air conditioner. For example, let us say for refrigerator the evaporator temperature is around -5°C, and for the air-conditioner, the refrigerated space is the room where the conditioner delivers the air.
• Let us say this temperature desired is 17°C, and for both of the equipment, the condenser is the atmosphere which let us say is at 30°C.
• Since the heat exchange in the evaporator changes the phase of the refrigerant, and it is known that during the phase change the temperature and the pressure are dependent properties therefore the pressure of the evaporator in the air-conditioner will be more compared to the refrigerator for the same condenser pressure.
• The work input to the compressor will be more in case of the domestic refrigerator as more compression is required between -5°C and 30°C compared to 17°C and 30°C (for the same amount of refrigeration effect)
• Since work input in the case of the refrigerator is higher, the COP of the domestic refrigerator will be less than that of a comfort air conditioning plant.
• Therefore both the statements are individually true and the statement II) is the correct explanation of statement I) as the COP of the air conditioning plant is higher due to higher evaporator pressure of the evaporator in the air conditioning.