Refrigerator Heat Pump Cop Relation — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Refrigerator and Heat Pump COP Relation This relation holds for any heat pump or refrigerator operating between two thermal reservoirs, regardless of the specific working fluid or cycle type. Define the COP of the refrigerator ( ) as the heat removed from the cold source (Q C) per unit work input (W). Define the COP of the heat pump ( ) as the heat rejected to the hot sink (Q H) per unit work input (W). Apply the First Law of Thermodynamics: Q H = Q C + W. Express Q C and Q H in terms of and , and solve for the relationship between and . The system must operate in a cyclic manner. The COP values ( and ) must be positive and dimensionless. Confusing the Coefficient of Performance (COP) with the thermal efficiency ( ). Assuming the relation holds for non-cyclic processes or when considering only irreversible losses. Forgetting that the COP is a ratio of energy units (e.g., J/J) and is therefore dimensionless.