The electric motor of a heat pump transfers energy as heat...

The electric motor of a heat pump transfers energy as heat from the outdoors, which is at $-5.0^{\circ} \mathrm{C},$ to a room that is at $17^{\circ} \mathrm{C}$. If the heat pump were a Carnot heat pump (a Carnot engine working in reverse), how much energy would be transferred as heat to the room for each joule of electric energy consumed?

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Key Concepts

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that defines the maximum efficiency any heat engine can achieve, or the maximum coefficient of performance when reversed to function as a heat pump. It establishes the theoretical limits set by the second law of thermodynamics by operating between two thermal reservoirs at different absolute temperatures, and serves as a benchmark for real-world systems.

Coefficient of Performance (COP) of a Heat Pump

The coefficient of performance (COP) for a heat pump quantifies its efficiency by comparing the useful heat output delivered to a heated space with the amount of energy input, typically in the form of work. For a reversible heat pump, the COP can be expressed using the absolute temperatures of the hot and cold reservoirs, illustrating the theoretical maximum performance under ideal conditions.

Temperature Scale Conversion

Accurate thermodynamic calculations require the use of absolute temperature scales, such as Kelvin. Converting temperatures from Celsius to Kelvin is essential because many thermodynamic formulas, including those for the Carnot cycle and COP, depend directly on these absolute temperature values to ensure meaningful and correct results.

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