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A Carnot engine works between 450 K and 306 K.

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

A Carnot engine works between $450\ \text{K}$ and $306\ \text{K}$ . Find its efficiency. We want to raise it to $45\%$ . How much hotter must the hot reservoir be, if the cold one stays the same? How much colder must the cold one be, if the hot one stays the same?

Need a reminder? The key ideaShow

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

Have you tried it?

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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← An engine takes 4200 J of heat from its hot reservoir each cycle and gives 2940 J to the cold one.A refrigerator keeps its inside at 4 °C in a kitchen at 32 °C. →

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