Question

The length of mercury thread in a mercury thermometer is 2 mm at the ice point and 26 mm at the boiling point of water. What will be the length of the mercury thread in this thermometer if it is used to measure a temperature of 75 ℃?

Answer 1

At standard atmospheric pressure, the ice and boiling points of water are 0 °C and 100 °C, respectively.

For a temperature difference of 100 °C (100 °C - 0 °C = 0 °C), the difference in the length of the mercury column is 24 mm (26 mm - 2 mm = 24 mm).
Therefore, for a temperature difference of 1 °C, the difference in the length of the mercury column will be $\frac{24}{100}$ mm/°C.

So, for 75 °C - 0 °C = 75 °C temperature difference, the difference in mercury length will be:
$\frac{24}{100}$$\times$ 75 mm = 18 mm

This is the difference in mercury length between 75 °C and 0 °C. At 0 °C, the length of the mercury column is 2 mm.
Therefore the total length of the mercury column or thread for a reading of 75 °C is 18 mm + 2 mm = 20 mm.