MediumPhysicsHigh School (11–12)Heat & Thermodynamics › Heat Engines, the Second Law and EntropyNumericalBoard Exam IB

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

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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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