+1 vote
in Mathematics by kratos

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

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+4 votes
by kratos
 
Best answer

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

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