\[COP_{HP}=\frac{Q_H}{W}\]
Variables
COPhp[COP_HP]heat pump coefficient of performance (dimensionless)
Qh[Q_H]heat delivered to the hot reservoir (J)
Wwork input (J)
Description
What is this formula?
The coefficient of performance (COP) of a heat pump measures how effectively a heat pump delivers thermal energy to a heated space for a given amount of input work. Unlike thermal efficiency, the COP of a heat pump can be greater than one because it transfers existing heat in addition to the supplied work.
When to use it
Use this formula when evaluating heat pumps, heating systems, reversible refrigeration cycles, and HVAC equipment where the heating output and required work are known.
Example
Given:
QH = 6000 J
W = 1500 J
Formula:
COPHP = QH/W
Substitution:
COPHP = 6000/1500
Result:
COPHP = 4.0
Applications
Residential heat pumps, commercial heating systems, HVAC design, geothermal heat pumps, building energy analysis, and thermal management systems.