A heat pump removes 2090 J of heat from the outdoors and delivers 3140 J of heat to the inside

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A heat pump removes 2090 J of heat from the outdoors and...

A heat pump removes $2090 \mathrm{~J}$ of heat from the outdoors and delivers $3140 \mathrm{~J}$ of heat to the inside of a house. (a) How much work does the heat pump need? (b) What is the coefficient of performance of the heat pump?

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics, also known as the principle of energy conservation, states that the total energy change in a system is equal to the energy added to the system minus the energy removed. In the context of a heat pump, it implies that the energy delivered to the interior (the sum of the heat extracted from the cold reservoir and the work input) must equal the total energy output as heat to the interior, establishing a relationship between the work done and heat transfers.

Work in Thermodynamic Systems

In thermodynamic processes, work represents the energy transfer that occurs when a force is applied over a distance or when energy is converted from one form to another. For a heat pump, work is the energy input required to transfer heat from a low-temperature reservoir to a high-temperature reservoir. It is calculated by finding the difference between the heat delivered and the heat extracted, emphasizing that energy must be supplied to move heat against its natural direction of flow.

Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure of the efficiency of a heat pump. It is defined as the ratio of the useful heating or cooling provided to the work input required to achieve that transfer. In essence, a higher COP indicates a more efficient heat pump, as it delivers more heat per unit of work. This concept is crucial in evaluating the energy efficiency of heating and cooling systems in practical applications.

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