(II) What volume of water at 0^∘ C can a freezer make into ice cubes in 1.0 h , if the coefficie

step 1 In this problem we are asked to find the volume of water at zero degrees. So we are asked to fin

(II) What volume of water at 0^∘ C can a freezer make into...

(II) What volume of water at $0^{\circ} \mathrm{C}$ can a freezer make into
ice cubes in 1.0 $\mathrm{h}$ , if the coefficient of performance of the
cooling unit is 7.0 and the power input is 1.2 kilowatt?

Key Concepts

Mass, Volume, and Density Relationship

The relationship between mass, volume, and density is fundamental in converting between these quantities. Specifically, knowing the density of water (approximately 1 kg per liter) allows one to convert the mass of water that has been frozen into the corresponding volume. This is necessary for problems where the final result is required in terms of volume rather than mass.

Latent Heat of Fusion

Latent heat of fusion is the energy per unit mass required to change a substance from its liquid phase to its solid phase at a constant temperature, without changing its temperature. For water, this value indicates the amount of energy that must be removed to turn water at 0° C into ice, making it a crucial parameter when calculating the mass (and subsequently volume) of water that can be frozen given a specific energy extraction.

Coefficient of Performance (COP)

The coefficient of performance is a measure used in refrigeration systems to quantify how effectively the system uses work input to remove heat from a space. It is defined as the ratio of the cooling energy removed (or the energy of phase change in the case of freezing) to the work input. A higher COP indicates a more efficient system, and it allows one to calculate the amount of heat extracted from the substance being cooled given the energy supplied.

Power and Energy Calculations

Power is the rate at which energy is used or transferred, typically expressed in watts (or kilowatts). The total energy input over a time period can be calculated by multiplying the power by the time interval. This concept is essential in determining the overall energy the freezer provides, which, when combined with the COP, helps establish the amount of heat removed from the water.

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