An ideal refrigerator utilizes a Carnot cycle operating between 0℃ and 25℃. To turn 10 kg of liquid water at 0℃ into 10 kg of ice at 0℃, (a) how much heat is exhausted into the room and (b) how much energy must be supplied to the refrigerator?

Key Concepts

Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine or refrigerator operating between two temperature reservoirs. It consists of four reversible processes: two isothermal (constant temperature) and two adiabatic (no heat exchange). Understanding this cycle is crucial for calculating the performance of an ideal refrigerator, as it sets the upper limit on efficiency based on the temperatures of the hot and cold reservoirs.

Latent Heat of Fusion

Latent heat of fusion is the amount of heat energy required to change a substance from solid to liquid or vice versa at a constant temperature. For water, this value is approximately 334 kJ/kg. In the context of the question, this concept is essential for determining the heat that must be removed from the water to convert it into ice, as it quantifies the energy involved in the phase change without changing the temperature.

Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure of the efficiency of a refrigerator or heat pump, defined as the ratio of the heat removed from the cold reservoir to the work input required to remove that heat. For a Carnot refrigerator, the COP can be calculated using the temperatures of the hot and cold reservoirs. This concept is vital for determining how much energy must be supplied to the refrigerator to achieve the desired cooling effect.