Question

A heat pump is an electrical device that heats a building by extracting heat in from the outside. It is similar to a refrigerator but its purpose is to war the hot reservoir rather than cool the cold reservoir, We define symbols:

Th = temperature inside
Tc = temperature outside
Qh = heat pumped into building in 1 day
Qc = heat taken from outdoors in 1 day
W = electrical energy used by heat pump in 1 day
a) Define the coefficient of performance

Answer 1

The coefficient of performance (COP) for a heat pump is a ratio of heat energy transferred to the building (Qh) to the work input (W), while for a refrigerator, COP is the ratio of heat extracted from the cold space (Qc) to the work input (W).

Step-by-step explanation:

The coefficient of performance (COP) for a heat pump is a measure of its efficiency. In the context of a heat pump, the COP is defined as the ratio of the heat energy transferred into the building (Qh) to the work input (W). Mathematically, it is expressed as COPhp = Qh/W. This value indicates how much heat energy is transferred into the building for every unit of electrical energy consumed by the heat pump.

For a refrigerator, which is a type of heat pump, the coefficient of performance (COPref) focuses on the heat extracted from the cold space (Qc) rather than the heat released into the warm space (Qh). The COP for a refrigerator is therefore given by COPref = Qc/W, reflecting the unit's efficiency in cooling.

The second law of thermodynamics informs us that a heat pump must perform work to transfer heat from a colder area to a warmer one. This working principle is the same for heat pumps used for heating buildings and for refrigerators used to cool spaces. For instance, even a household refrigerator can be considered a heat pump as it operates on the same fundamental principles.