Question

Write down the expression for thermal efficiency of heat engine and coefficient of performance (COP) of the heat pump and refrigerator.

Answer 1

Performance of HP: is measured by coefficient of performance (COP). Which is the ratio of amount of heat rejected by the system to the mechanical work received by the system.

(COP)HP = Q₁/W = Q₁/(Q₁ – Q₂) = T₁/ (T₁ – T₂)

Refrigerator 

The primary function of a heat pump is to transfer heat from a low temperature system to a high temperature system, this transfer of heat can be utilized for two different purpose, either heating a high temperature system or cooling a low temperature system. Depending upon the nature of use. The heat pump is said to be acting either as a heat pump or as a refrigerator. If its purpose is to cause heating effect it is called operating as a H.P. And if it is used to create cold effect, the HP is known to be operating as a refrigerator. 

(COP)_ref = Heat received/ Work Input

= Q₂/W = Q₂/(Q₁ – Q₂)

(COP)_ref = Q₂/(Q₁ – Q₂) = T₂/(T₁ – T₂)

(COP)_HP = (COP)_ref + 1

COP is greater when heating a room than when cooling it