In an air conditioner, 12.65 MJ of heat transfer occurs from...

In an air conditioner, 12.65 MJ of heat transfer occurs from a cold environment in 1.00 h. (a) What mass of ice melting would involve the same heat transfer? (b) How many hours of operation would be equivalent to melting $900 \mathrm{kg}$ of ice? (c) If ice costs 20 cents per $\mathrm{kg}$, do you think the air conditioner could be operated more cheaply than by simply using ice? Describe in detail how you evaluate the relative costs.

Key Concepts

Latent Heat of Fusion

This is the amount of energy required to change a unit mass of a substance from a solid to a liquid without a change in temperature. It is essential when calculating how much ice will melt given a certain amount of heat transfer, as it relates directly to phase change energy requirements.

Heat Transfer

Heat transfer involves the movement of thermal energy from one body or substance to another. In problems like this, understanding how much energy is transferred over a period (for example, in an hour) is critical in quantifying and comparing energy usage in different processes, such as melting ice versus operating an air conditioner.

Energy Cost Analysis

Energy cost analysis compares the operational cost based on energy consumption against alternate methods, such as using an equivalent amount of another energy resource like ice. It involves quantifying the energy needed for a process, converting that energy requirement into physical quantities, and then comparing the economic costs, taking into account various factors such as energy prices and operational efficiency.

Unit Conversions

Unit conversions are necessary to ensure that all measurements are in compatible units before performing calculations. This could include converting time units, energy units, or mass units to match the parameters required by physical formulas, ensuring consistent and accurate outcomes in evaluating energy transfer and cost.

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