Question

A Kelvin thermometer and a Fahrenheit thermometer used to record the temperature of melting metal, read the same. What will a Celsius thermometer read at that temperature?
A) ${301.25}^{\circ }C$
B) ${273}^{\circ }C$
C) ${457}^{\circ }C$
D) ${760}^{\circ }C$

Answer 1

Hint: A thermometer is a device used for measuring the temperature. It indicates the degree of hotness or coldness of a body. Sir Thoams Allbut in 1867 invented the first real medical thermometer. The Zeroth law of thermodynamics principle is used in thermometers.

Complete solution:
Let t be the temperature which is reading the same on the Kelvin and Fahrenheit thermometer.
We know that, ${\displaystyle \frac{K-273}{100}}={\displaystyle \frac{F-32}{180}}$
Substituting K and F values as t, we get
$\Rightarrow$ ${\displaystyle \frac{t-273}{100}}={\displaystyle \frac{t-32}{180}}$
$\Rightarrow$ $9t-2457$ = $5t-160$
$\Rightarrow$ $4t=2297$
$\Rightarrow$ $t=574.25$
Thus, the Temperature on the Celsius thermometer = $574.25-273=301.25$
$\therefore$ The Temperature on the Celsius thermometer = ${301.25}^{\circ }C$.

Hence the correct option is A.

Note: 1) The Celsius thermometer and the Fahrenheit thermometer use degrees to measure the temperature whereas the Kelvin thermometer does not use degrees. It uses the kelvin and is represented by K as a unit of measurement.
2) Mercury is used in thermometers because it has a high coefficient of expansion which enables easy movement in the thermometers as per the temperatures.
3) There is no point at which the Kelvin scale and Celsius scale are equal, even though the size of the degree is the same between them. Celsius temperature can be negative and is always higher than the Kelvin scale. Kelvin cannot be negative but can go down to absolute zero.
4) In the Celsius thermometer, the boiling point of water is 100${}^{\circ }$C and the freezing point is at 0${}^{\circ }$C. In the Fahrenheit thermometer, the boiling point of water at 212${}^{\circ }$F, and the freezing point is at 32${}^{\circ }$F.