Question

The readings of a thermometer at $0^{\circ}$ C and $100^{\circ}$ C are 50 cm and 75 cm of mercury column respectively. Find the temperature at which its reading is 80 cm of mercury column?
A. $120^{\circ}$
B. $20^{\circ}$
C. $100^{\circ}$
D. $80^{\circ}$

Answer 1

Hint: As 75 cm already marks $100^{\circ}$, and we are asked to find the temperature reading for a marking of 80 cm, the answer is clearly going to be above $100^{\circ}$ as the mercury rises up in a thermometer due to a rise in temperature.

Complete step by step answer:
We can use the method of ratio and proportions to determine the correct answer.
We are given that the Difference in temperature of final and initial marks is about $100^{\circ} - 0^{\circ}$. The marking varies by a difference of (75 - 50) cm = 25 cm for this $100^{\circ}$ difference.
Therefore, for 1 cm, the change in the degrees is:
$\dfrac{100}{25} = 4^{\circ}$
So, as we are going from 75 cm to 80 cm i.e., by an amount of 5 cm, the change in the temperature will be:
$4^{\circ} \times 5 = 20^{\circ}$ .

Therefore, at a mark of 80 cm, which is 5 cm above 75 cm, mark for $100^{\circ}$, we get a reading of
$100^{\circ} + 20^{\circ} = 120^{\circ}$

Therefore, the correct answer is option (A).

Additional information:
It is quite a common experience that upon supplying heat, a solid or a liquid expands in volume. It is so because an increase in temperature implies an increase in energy of the molecules of the liquid which increases their separation. Therefore the phenomenon of rise of mercury in a thermometer is about expansion of the liquid mercury in the capillary of the thermometer.

Note:
From the given set of options it is quite clear what the correct option would be at a reading of 80 cm. We are quite familiar with the phenomenon of rise of mercury in a thermometer due to increase in temperature. Only one of the options has a temperature more than $100^{\circ}$. So, without any work one could find the right answer.