We propose to heat a house in the winter with a heat pump....

We propose to heat a house in the winter with a heat pump. The house is to be maintained at $20^{\circ} \mathrm{C}$ at all times. When the ambient temperature outside drops to $-10^{\circ} \mathrm{C}$, the rate at which heat is lost from the house is estimated to be $25 \mathrm{kW}$. What is the minimum electrical power required to drive the heat pump?

Key Concepts

Heat Pump

A heat pump is a device that moves thermal energy from one location to another by using mechanical work. It transfers heat from a colder area to a warmer area, making it possible to heat a space even when the outside temperature is low.

Coefficient of Performance (COP)

The coefficient of performance (COP) measures the efficiency of a heat pump by comparing the amount of heat delivered to the work input needed to drive the pump. It is a key concept in determining how much electrical power is required to achieve the desired heating, with the ideal COP given by the Carnot efficiency.

Carnot Cycle

The Carnot cycle represents an ideal reversible process that sets an upper limit on the efficiency of heat engines and heat pumps. In the context of heating, the Carnot COP is determined by the ratio of the absolute indoor temperature to the temperature difference between the indoor and outdoor conditions.

Temperature Conversion to Kelvin

Thermodynamic calculations, including those involving the Carnot cycle and COP, require the use of the Kelvin scale. Converting temperatures from Celsius to Kelvin is essential for accurately applying these concepts, as the formulas depend on absolute temperature values.

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