# Temperature and heat-thermal properties of matter

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Question

# A faulty thermometer has its fixed points marked as 5° and 95°. The temperature of a body as measured by the faulty thermometer is 59°. Find the correct temperature of the body on Celsius scale.

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Solution

## Let ${\mathrm{\theta }}_{0}$ be the lower fixed point of the faulty thermometer and n be the number of divisions between its lower and the upper fixed points. If a temperature C on Celsius scalecorresponds to temperature q on the scale of faulty thermometer, then   $\frac{\mathrm{C}-0}{100}=\frac{\mathrm{\theta }-{\mathrm{\theta }}_{0}}{\mathrm{n}}$   ……..(i)Here, Therefore, the Eq. (i) becomes$\begin{array}{c}\frac{\mathrm{C}-0}{100}=\frac{59-5}{95-5}\\ \mathrm{C}=\frac{54}{90}×100\\ \mathrm{C}={60}^{\circ }\mathrm{C}\end{array}$

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