Ideal Refrigeration Cycle

The refrigeration cycle is a thermodynamic cycle that is used in refrigerators and air conditioners. The ideal refrigeration cycle consists of four components: a compressor, a condenser, an expansion valve, and an evaporator.

Operating Temperatures

The ideal refrigeration cycle has a condenser and evaporator temperature of 27 C and 3C respectively. The condenser temperature is the temperature at which the refrigerant gives off heat to the surroundings, while the evaporator temperature is the temperature at which the refrigerant absorbs heat from the surroundings.

Coefficient of Performance (COP)

The coefficient of performance (COP) is a measure of the efficiency of a refrigeration cycle. It is defined as the ratio of the heat removed from the cold space to the work required to remove that heat. The higher the COP, the more efficient the refrigeration cycle.

Calculation of COP

The COP of the refrigerator with the given operating temperatures is calculated as follows:

COP = (Heat Removed from Cold Space)/(Work Required)

Heat Removed from Cold Space = (Heat Absorbed by Refrigerant in the Evaporator)/(Coefficient of Performance)

Work Required = (Heat Rejected by Refrigerant in the Condenser)/(Coefficient of Performance)

Given that the evaporator temperature is 3C, the heat absorbed by the refrigerant in the evaporator is Q1 = 1000 kJ/kg. Also, given that the condenser temperature is 27 C, the heat rejected by the refrigerant in the condenser is Q2 = 250 kJ/kg.

Therefore, the COP of the refrigerator is:

COP = Q1/(Q2 - Q1)

COP = 1000/(250 - 1000)

COP = 9

Therefore, the correct answer is option A, which is 9.