An ice machine is to convert 10^∘ C water to 0^∘ C ice. If the machine has a COP of 2.0 and cons

step 1 So as we know the COP of the engine, COP can be written as Q COD divided by work input. So here,

An ice machine is to convert 10^∘ C water to 0^∘ C ice. If...

An ice machine is to convert $10^{\circ} \mathrm{C}$ water to $0^{\circ} \mathrm{C}$ ice. If the machine has a COP of 2.0 and consumes electrical power at a rate of $1.0 \mathrm{~kW}$, how much ice can it make in $1.0 \mathrm{~h} ?$

Key Concepts

Coefficient of Performance (COP)

The COP of a refrigerator or heat pump is a measure of its efficiency, defined as the ratio of the useful heat transfer (in this case, the energy removed to freeze water) to the work input. A COP of 2.0 means that for every unit of electrical energy consumed, twice that amount of thermal energy is removed from the system. This concept is crucial in determining how much cooling (or ice production) can be achieved with a given power input.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy needed to change a substance from its liquid phase to its solid phase at constant temperature, without changing its temperature. In the context of freezing water to ice, it is the critical energy parameter required to overcome the phase change process, and knowing this value is essential for calculating how much energy must be extracted to produce a given mass of ice.

Sensible Heat and Specific Heat Capacity

Sensible heat refers to the energy required to change the temperature of a substance without changing its phase. For water, this involves using its specific heat capacity to cool it from an initial temperature down to its freezing point. In practical problems, both the removal of sensible heat (cooling the water) and the latent heat of fusion (freezing the water) must be taken into account to determine the total energy required for the process.

Energy Conversion and Unit Consistency

This concept involves understanding how electrical energy (measured in kilowatt-hours, for instance) is converted into thermal energy via the refrigeration process, and ensuring that all units are consistent throughout the calculation. Converting power over time to total energy and then relating that energy to the heat removal requirements (both sensible and latent) is a fundamental step in solving problems that deal with thermal systems and efficiency.

Transcript

Please give Ace some feedback