How long would a 3.00-kW space heater have to run to put...

How long would a $3.00-\mathrm{kW}$ space heater have to run to put into a kitchen the same amount of heat as a refrigerator ( (coefficient of performance $=3.00$ ) ) does when it freezes $1.50 \mathrm{~kg}$ of water at $20.0{ }^{\circ} \mathrm{C}$ into ice at $0.0^{\circ} \mathrm{C}$ ?

Key Concepts

Specific Heat Capacity and Latent Heat

This concept involves the calculation of energy required to change the temperature of a substance and to change its phase. In this problem, one has to compute the energy required to cool water from an initial temperature to its freezing point using the specific heat capacity, and then the additional energy needed to freeze the water by using the latent heat of fusion. These calculations form the basis for determining the total amount of heat extracted during the process.

Coefficient of Performance (COP) in Refrigeration

The coefficient of performance is a measure of a refrigerator's efficiency and is defined as the ratio of the cooling effect (heat removed from the refrigerated space) to the work input required to remove that heat. Understanding COP is crucial in problems that involve comparing different methods of heat transfer, as it allows one to determine the actual work or energy cost associated with a given cooling effect, and subsequently, the total heat expelled into the surrounding space.

Energy, Power, and Time Relationship

This key concept relates to the fundamental relationship between energy, power, and time where power is defined as the rate of energy transfer (energy per unit time). In practical applications, once the total energy associated with a process is known, the time required to deliver or remove that energy can be calculated by dividing the energy by the power of the heating or cooling device. This plays an essential role in converting the computed energy quantities into time durations needed for the process to occur.

Transcript

Please give Ace some feedback