A heat pump, shown in Figure P 22.26 , is essentially an air conditioner installed backward. It

step 1 In this question, we are asked to find the coefficient of performance of the heat pump. Okay, so

A heat pump, shown in Figure P 22.26 , is essentially an air...

A heat pump, shown in Figure $\mathrm{P} 22.26$ , is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Sup- pose that the ratio of the actual energy entering the room to the work done by the device's motor is 10.0$\%$ of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor, given that the inside temperature is $20.0^{\circ} \mathrm{C}$ and the outside temperature is $-5.00^{\circ} \mathrm{C} .$

Key Concepts

Temperature Conversion

In thermodynamic calculations, it is essential to convert temperature values from Celsius to Kelvin because the Kelvin scale is the absolute temperature scale used in thermodynamic formulas. This conversion ensures that the proper relationships between temperature and energy are maintained in calculations involving heat engines or heat pumps.

Carnot Efficiency

Carnot efficiency represents the maximum possible efficiency for any cyclic device operating between two thermal reservoirs, as dictated by the laws of thermodynamics. For a heat pump, the theoretical maximum COP is determined by the temperatures of the hot and cold reservoirs (converted to an absolute temperature scale), indicating an ideal performance level that actual devices approach within a fraction of their theoretical limits.

Heat Pump

A heat pump is a device that transfers thermal energy from a colder area to a warmer area by doing work, acting essentially as an air conditioner in reverse. It operates based on thermodynamic cycles and can be used for space heating, making it a key technology in energy transfer applications.

Coefficient of Performance (COP)

The coefficient of performance, or 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 required to produce that heating or cooling. For heating, it is expressed as the amount of heat delivered to the heated space per unit of work input.

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