Question

The lengths of the mercury column of a mercury thermometer are 1.26cm and 20.86cm respectively at the standard fixed points. What is the temperature of body, which produces 9.0cm of this mercury column?

Answer 1

If this this a thermometer calibrated in Celsius degrees, the first standard fixed point (the lowest one) corresponds to 0°C and the second (the highest) to 100°C. Therefore, we can write for temperature elongation of mercury:

$$20.86-1.26=k(100-0),\\ k=0.196\text{ cm/°C}.$$

Now all we have to do is to repeat this for the readings (9 cm):

$$H-1.26=k(T-0),\\ 9-1.26=0.196(T-0),\\ T=39.49\text{°C}.$$