What is the maximum possible coefficient of performance of a...

What is the maximum possible coefficient of performance of a heat pump that brings energy from outdoors at $-3.00^{\circ} \mathrm{C}$ into a $22.0^{\circ} \mathrm{C}$ house? Note that the work done to run the heat pump is also available to warm up the house.

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Key Concepts

Coefficient of Performance (COP) for Heat Pumps

The COP of a heat pump is a measure of its efficiency in transferring heat relative to the work input. It is defined as the ratio of the heat delivered to the hot reservoir to the work required to drive the heat pump. This concept is fundamental in evaluating how effectively a system can heat a space by moving thermal energy from a cold reservoir to a warm space.

Carnot Cycle and Maximum Performance

The Carnot cycle represents an idealized reversible process that sets the theoretical upper limit on the efficiency of heat engines and the coefficient of performance for heat pumps. For heat pumps, the maximum possible COP is determined by the temperatures of the hot and cold reservoirs and is given by COP_max = T_hot / (T_hot - T_cold), where the temperatures are expressed in Kelvin. This principle provides a benchmark for the performance of real-world systems.

Temperature Conversion (Celsius to Kelvin)

Temperature conversion is essential in thermodynamics because all formulas involving absolute temperatures require temperatures in Kelvin. Converting temperatures from Celsius to Kelvin by adding 273.15 ensures that calculations such as the maximum COP based on the Carnot cycle are accurate.

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