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# Calibrating liquid thermometers

The calibration of a thermometer involves marking the thermometer so that the temperature can be read accurately. The scale is based on the thermometric property used by the thermometer.

In a certain mercury thermometer, the mercury column is 3 cm long when the temperature is $0^{\circ}\text{C}$. If the thermometer was accurately calibrated, there should be a $0^{\circ}\text{C}$ marking at the 3 cm point.

To calibrate a thermometer using the Celsius scale without using another thermometer:

• Place the thermometer next to melting ice and record the length of the liquid column, $\Tblue{x_{1}}$.
• Place the thermometer in boiling water and record the length of the liquid column, $\Tred{x_{2}}$.

Only record the length of the liquid column once it has reached a steady level.

The temperature of an unknown source T (in $^{\circ}\text{C}$) can then be calculated: $$\Tgreen{\text{temperature}} = \frac{\Tgreen{x_{3}} - \Tblue{x_{1}}} {\Tred{x_{2}}-\Tblue{x_{1}} } \times 100$$

A thermometer is calibrated to the Celsius scale.