# Coefficient of Performance for a Refrigeration Cycle

First Law :
For refrigeration cycles:
Food
Kitchen

## Coefficient of Performance

: COPR
a measure of the performance of a

#### refrigeration cycle

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### Ch 4, Lesson F, Page 9 - Coefficient of Performance for a Refrigeration Cycle

• The coefficient of performance is used to quantify the performance of refrigeration cycles.
• The symbol used for coefficient of performance is “COP” with a subscript “R,” for refrigeration.
• Just like the efficiency of power cycles, the COP is defined as the ratio of the desired output to the required input.
• We do not call this an efficiency because it is generally GREATER than 1.  It would seem very odd to discuss efficiencies greater than 1.  So, instead, we call it the coefficient of performance.
• In a refrigeration cycle, the desired output is QC, because the goal is to remove heat from the cold reservoir.
• The required input is the work input, Wref.
• So, COPR = QC over Wref.
• Next we use the 1st Law to eliminate Wref from the equation.
• The result is a useful equation for calculating the COPR.
• If we divide the numerator and denominator by QC, we get the most common expression for the COPR.
• COPR = 1 over the quantity QH over QC minus 1.
• Now do you see why the COPR is generally greater than 1 ?
• If you rearrange the 1st Law, you will see that QH = QC + Wref.  Therefore, QH is >QC.
• So, QH/QCis > 1.
• So, COPR is always a positive number.
• But, as long as QH/QC is < 2, beta, the COPR is > 1 !.  This is almost always the case.
• This is good news because it means that when you PAY for kJ of energy for your refrigerator it REMOVES more than 1 kJ of energy from the food in your frig !  What a deal !
• Now let’s take a look at another system that is surprisingly similar to a refrigerator…the heat pump cycle.