Question

The steam point and the ice point if mercury thermometer are wrongly marked \[{{92}^{0}}C\] and \[{{2}^{0}}C\] respectively. The correct temperature read by this thermometer is,
(A) \[{{2}^{0}}C\]
(B) \[{{5}^{0}}C\]
(C) \[{{10}^{0}}C\]
(D) \[{{20}^{0}}C\]

Answer 1

Hint: There are several types of thermometers used for measurement of temperature. In every thermometer and in any unit scale, the change in temperature at a time is the same even if the thermometer is faulty and readings go incorrectly then also the change in temperature is the same for that substance.
Formula used:
\[\dfrac{t-{{T}_{0}}}{{{T}_{b}}-{{T}_{0}}}=c\] or \[\dfrac{t-LFP}{HFP-LFP}=c\]
Both the equations are the same.

Complete answer:
In the mercury thermometer, the change in temperature is measured by observing the expansion of sensitive mercury metal. As the mercury is liquid, it is easy to expand. In faulty thermometers the readings are incorrect but a change in temperature can be predicted by a particular method. If the freezing point and boiling point of a substance is known then the change will be found with the incorrect reading also.
Most commonly the freezing point and boiling point of water is known which is \[{{0}^{0}}C\] and \[{{100}^{0}}C\] respectively.
So,
\[{{T}_{0}}={{0}^{0}}C\]
\[{{T}_{b}}={{100}^{0}}C\]
\[{{T}_{i}}={{2}^{0}}C\]
\[{{T}_{s}}={{92}^{0}}C\]
Using the above equation,
\[\dfrac{t-0}{100-0}=\dfrac{t-2}{92-2}\]
\[\Rightarrow 90t=100(t-2)\]
\[\Rightarrow 10t=200\]
\[\Rightarrow t=20\]
So the temperature read by a mercury thermometer is \[{{20}^{0}}C\].

So, the correct answer is “Option D”.

Additional Information:
Mercury thermometer
In everyday use or in general mercury thermometers are used. Because mercury is shiny liquid metal so the measurement can be easily read on the thermometer scale and if water and other substances are used for measurement it may not be easy to read. Also, mercury is sensitive metal and if a very small change in temperature occurs in mercury, the volume of it significantly expands and the correct measurement can be observed. So in everyday life mercury thermometers are widely used.

Note:
(1) The range of the mercury thermometer is \[-{{37}^{0}}C\] to \[{{356}^{0}}C\]. The temperature above or the below of range, they cannot be measured or lead to damage of the thermometer.
(2) The above formula also can be used for Fahrenheit measurement, also for gas thermometer.