Heat and Thermodynamics

Step 1: Understand the COP formula
The coefficient of performance (COP) for a refrigerator shows how well it works. The formula is:
COP=‌

QH

QH−QC

Step 2: Identify what the symbols mean
QH stands for the heat given to the room (hot side). This is the heat released.
QC is the heat taken from inside the fridge (cold side). This is the heat extracted, which is 250 J per cycle here.
Step 3: Set up the equation with the given numbers
We are told the COP is 5 and QC is 250 J . So, we use:
5=‌

QH

QH−250

Step 4: Solve for QH
Multiply both sides by (QH−250) :
5(QH−250)=QH
Expand:
5QH−1250=QH
Bring QH to one side:
‌5QH−QH=1250
‌4QH=1250
Divide both sides by 4 :
QH=‌

1250

4

QH=312.5J