Question

A faulty thermometer has an ice point at $-5^{\circ }C$ and the steam point at ${105}^{\circ }C$. What would be the temperature shown by this thermometer of the human body? (Assume correct temperature of human body is ${37}^{\circ }C$)
$a.\text{ 34}\text{.}{\text{8}}^{\circ }\text{C}$
$b.\text{ 39}\text{.}{\text{3}}^{\circ }\text{C}$
$c.\text{ 35}\text{.}{\text{7}}^{\circ }\text{C}$
$d.\text{ 41}\text{.}{\text{5}}^{\circ }\text{C}$

Answer 1

Hint: The ice point of water is $0^{\circ }C$ and boiling point of water is ${100}^{\circ }C$. But in the question we are provided with the faulty thermometer which has faulty readings. We can compare the difference of upper and lower fixed points of a normal thermometer and the faulty thermometer to find the reading of temperature of a normal human body.

Complete answer:
The temperature is measured in degrees Celsius for a normal scale of temperature. The water has an ice point at $0^{\circ }C$ while it starts boiling at ${100}^{\circ }C$. According to the question, the given thermometer shows ice point at $-5^{\circ }C$ and water starts boiling at ${105}^{\circ }C$ which is the fault in the thermometer. Therefore it will also show some fault in the normal temperature of the human body which in actuality is ${37}^{\circ }C$. Despite the faults in readings, the common factor for both faulty and normal thermometers is the difference of lower and upper fixed points. Therefore we will compare this difference of both the thermometer and thus hereby we will get the fault value of temperature for normal body temperature of humans.
Therefore for correct thermometer, we can write
$={\displaystyle \frac{Normal\text{ body temperature - lower fixed point}}{Upper\text{ fixed point - lower fixed point}}}$
$={\displaystyle \frac{\text{37 - 0}}{\text{100 - 0}}}$
$={\displaystyle \frac{\text{37 }}{\text{100 }}}$ ________________$\left(1\right)$
Similarly we can write for faulty thermometer, we can write
$={\displaystyle \frac{\text{Faulty body temperature - lower fixed point}}{Upper\text{ fixed point - lower fixed point}}}$
$={\displaystyle \frac{\text{X - }\left(-5\right)}{\text{105 - }\left(-5\right)}}$
$={\displaystyle \frac{\text{X + 5}}{\text{110}}}$ _______________$\left(2\right)$
On comparing both the equations we will get,
${\displaystyle \frac{\text{37 }}{\text{100 }}}$ $={\displaystyle \frac{\text{X + 5}}{\text{110}}}$
$\text{ X }=\text{ 35}\text{.}{\text{7}}^{\circ }C$
Thus the faulty thermometer will show normal body human temperature as ${35.7}^{\circ }C$ which is less than the actual body temperature.
And hence the correct answer is option C.

Note:
The difference between the upper fixed point and the lower fixed point is constant for all thermometers. Therefore we can compare this difference for faulty and original thermometers. All the temperatures should be in degrees celsius for comparison. This ratio is also called the principle of calorimetry.