The temperature of a household refrigerator is 5^∘ C and the room temperature is 30^∘ C. Nearly

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The temperature of a household refrigerator is 5^∘ C and the...

The temperature of a household refrigerator is $5^{\circ} \mathrm{C}$ and the room temperature is $30^{\circ} \mathrm{C}$. Nearly $3 \times 10^{8} \mathrm{~J}$ heat flows from the room to the refrigerator in a day and has to be pumped out of the refrigerator to maintain its temperature. If the coefficient of performance of the refrigerator is $60 \%$ of the efficiency of a Carnot engine working between the same temperature limits, calculate the power required to run the refrigerator.

Key Concepts

Carnot Cycle

The Carnot Cycle represents an idealized thermodynamic cycle that establishes the maximum possible efficiency for a heat engine operating between two thermal reservoirs. In problems such as these, the Carnot formula provides a benchmark for best-case performance, highlighting the role of temperature differences in dictating efficiency limits.

Coefficient of Performance (COP) for Refrigerators

The COP of a refrigerator measures its effectiveness in transferring heat from the cold interior to the warmer surroundings relative to the work input required. It is defined as the ratio of heat removed from the cold space to the work consumed, and is analogous to the efficiency of a heat engine operating in reverse.

Temperature Scale Conversion

In thermodynamic analyses, temperatures must be expressed in an absolute scale, such as Kelvin, to accurately account for energy flows and relative differences. Converting from Celsius to Kelvin is essential when applying formulas like those related to the Carnot cycle or COP calculations.

Energy and Power Relationships

This concept entails understanding how the total energy moved over a period translates to power, which is the rate at which energy is transferred or work is performed. Calculations comparing the energy per day with time scales are necessary to determine the continuous power requirements of systems like refrigerators.

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