Given:
Power required by Carnot refrigerator = 1.5 kW/ton
Temperature maintained by Carnot refrigerator = 30°C

To find:
COP of Carnot refrigerator

Formula used:
COP = (Refrigeration effect)/Work input
Refrigeration effect = Qh - Ql
Qh = Heat absorbed by the refrigerator from the high-temperature reservoir
Ql = Heat rejected by the refrigerator to the low-temperature reservoir

Solution:
1 ton of refrigeration = 3.5 kW
Power required by Carnot refrigerator = 1.5 kW/ton
Therefore, power required by Carnot refrigerator = 5.25 kW

Refrigeration effect:
Qh = Heat absorbed by the refrigerator from the high-temperature reservoir
Qh = mCpΔT
m = Mass of refrigerant
Cp = Specific heat of refrigerant
ΔT = Temperature difference between high-temperature and low-temperature reservoirs

Given that the temperature maintained by Carnot refrigerator = 30°C
Temperature of high-temperature reservoir = 30+273 = 303 K
Temperature of low-temperature reservoir = 0+273 = 273 K
ΔT = 303 - 273 = 30 K

Let us assume that 1 kg of refrigerant is used in the Carnot refrigerator
Specific heat of refrigerant (Cp) is not given. Let us assume it to be 2.5 kJ/kg.K (for R-134a refrigerant)
Qh = mCpΔT = 1 x 2.5 x 30 = 75 kJ

Ql = Heat rejected by the refrigerator to the low-temperature reservoir
Ql = Qh - Work input
Work input = Power input x Time
Assuming that the Carnot refrigerator operates for 1 hour, Work input = Power input x Time
Work input = 5.25 kW x 1 hour = 5.25 kWh = 5.25 x 3600 = 18900 kJ

Ql = Qh - Work input = 75 - 18900 = -18825 kJ
(Note: Heat rejected cannot be negative. The negative sign indicates that the assumption made for Work input is incorrect. We need to use the actual value of Work input to calculate Ql.)

Actual Work input:
COP = (Refrigeration effect)/Work input
COP = Qh/(Qh - Ql)
COP = 75/(75 + 18825)
COP = 0.004

Power input = Work input/Time
Power input = 18900/3600 = 5.25 kW
(Note: The given power input and the calculated power input are the same.)

Refrigeration effect:
Qh = mCpΔT = 1 x 2.5 x 30 = 75 kJ

Ql = Qh - Work input
Work input = Power input x Time
Work input = 5.25 kW x 1 hour = 5.25 kWh = 5.25 x 3600 = 18900 kJ

Ql = Qh - Work input = 75 - 18900 = -18825 kJ

Actual COP:
COP = Qh/(

1ton of refrigeration = 3.51 kw.... so the COP will be (desired effect/work input) =(3.51/1.5)=2.34 (option B)