A thermometer reads 2.0 °C in melting ice and 97.0 °C in steam at one atmosphere…

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

A thermometer reads $2.0\ ^\circ\text{C}$ in melting ice and $97.0\ ^\circ\text{C}$ in steam at one atmosphere. It reads $50.0\ ^\circ\text{C}$ in a bath. What is the bath's true temperature? At what temperature does the thermometer read correctly?

Need a reminder? The key ideaShow

Heat flows from hot to cold; temperature decides the direction. $T_F = \tfrac95 T_C + 32$ and $T = T_C + 273.15$ . A thermometer's readings between its ice point and steam point are scaled to the true $100$ degrees.

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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