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A refrigerator keeps its inside at 4 °C in a kitchen at 32 °C.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A refrigerator keeps its inside at $4\ ^\circ\text{C}$ in a kitchen at $32\ ^\circ\text{C}$ . (a) What is the best possible COP? (b) A real one has a COP of $3.4\ \text{J}$ and takes $1.53 \times 10^{6}\ \text{J}$ of heat out of the food in $1.5$ hours. Find the electrical work, the heat it gives to the kitchen and its average electrical power.

Need a reminder? The key ideaShow

A heat engine takes $Q_h$ from a hot reservoir, does work $W = Q_h - Q_c$ and gives $Q_c$ to a cold one: $\eta = \dfrac{W}{Q_h}$ . A refrigerator uses work $W$ to take $Q_c$ from the cold side: $\text{COP} = \dfrac{Q_c}{W}$ , and it gives $Q_h = Q_c + W$ to the warm side.

A Carnot engine is the best possible between two temperatures: $\eta = 1 - \dfrac{T_c}{T_h}$ and $\dfrac{Q_c}{Q_h} = \dfrac{T_c}{T_h}$ . The best refrigerator has $\text{COP} = \dfrac{T_c}{T_h - T_c}$ . Temperatures in kelvin.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← A Carnot engine works between 450 K and 306 K.A Carnot engine works between 880 K and 286 K and gives out 12 kW of mechanical power. →

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