Heat and Thermodynamics

Step 1: Understand the COP formulaThe coefficient of performance (COP) for a refrigerator shows how well it works. The formula is:$COP = \frac{Q_H}{Q_H - Q_C}$Step 2: Identify what the symbols mean$Q_H$ stands for the heat given to the room (hot side). This is the heat released.$Q_C$ 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 numbersWe are told the COP is 5 and $Q_C$ is 250 J . So, we use:$5 = \frac{Q_H}{Q_H - 250}$Step 4: Solve for $Q_H$Multiply both sides by $(Q_H - 250)$ :$5 (Q_H - 250) = Q_H$Expand:$5 Q_H - 1250 = Q_H$Bring $Q_H$ to one side:$5 Q_H - Q_H = 1250$$4 Q_H = 1250$Divide both sides by 4 :$Q_H = \frac{1250}{4}$$Q_H = 312.5 \, \text{J}$