# First Law for a Refrigeration Cycle

and
or:
Net Energy Transferred by
Heat for the Cycle
=
Net Energy Transferred by Work for the Cycle
Q
W
Kitchen
Food

## First Law for the Cycle

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### Ch 4, Lesson F, Page 8 - First Law for a Refrigeration Cycle

• The 1st Law for a refrigeration cycle is the same as the 1st law for any other cycle.
• Wcycle = Qcycle.
• The tricky part is in dealing with the sign convention and the tradition of using all positive numbers when dealing with tie-fighter diagrams.
• Because work is positive when it is done BY the system, Wcycle = -Wref
• Since heat transfer is positive when it flows into the system and both QH and QC are positive numbers, Qcycle = QC – QH.
• Both of these equations are the negative of the comparable equations presented for heat engines on page 5 for the heat engine !
• The cool part is that when we substitute for Wcycle and Qcycle in the 1st law equation, the two negatives cancel and we get the SAME result that we got for heat engines !
• Wref = QH – QC.
• Now, let’s see how we can use this result to compare the performance of different refrigerators.