A certain brand of freezer is advertised to use 730 kW•h of energy per year. (c) What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at 20.0°C?

Verified step by step guidance

1. Calculate the energy required to cool water from 20.0°C to 0°C using the specific heat capacity of water. Use the formula: Q = mcΔT, where m is the mass of water, c is the specific heat capacity of water (approximately 4.18 J/g°C), and ΔT is the change in temperature.
2. Calculate the energy required to freeze the water at 0°C into ice using the latent heat of fusion of water. Use the formula: Q = mL, where m is the mass of water and L is the latent heat of fusion of water (approximately 334 J/g).
3. Add the energy calculated in step 1 and step 2 to find the total energy required to turn water at 20.0°C into ice.
4. Convert the freezer's energy usage from kW•h to Joules to match the units used in the calculations above. Use the conversion factor: 1 kW•h = 3.6 × 10^6 J.
5. Divide the freezer's hourly energy usage in Joules (from step 4) by the total energy required per gram of ice (from step 3) to find the theoretical maximum mass of ice the freezer can produce in an hour.

Key Concepts

Energy Transfer

Energy transfer refers to the movement of energy from one system to another. In the context of the freezer, it involves the conversion of electrical energy into thermal energy, which is used to lower the temperature of water to freeze it. Understanding this concept is crucial for calculating how much energy is required to change the state of water from liquid to solid.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a substance from solid to liquid or vice versa without changing its temperature. For water, this value is approximately 334 kJ/kg. This concept is essential for determining how much energy is needed to freeze water into ice, as it directly influences the amount of ice that can be produced by the freezer.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is about 4.18 kJ/kg°C. In this scenario, it is important to calculate the energy needed to cool water from 20.0°C to 0°C before it can freeze, which is a necessary step in determining the total ice production capacity of the freezer.