Question

Which of the following pairs may give equal numerical values of the temperature of a body?
(a) Fahrenheit and Kelvin
(b) Celsius and Kelvin
(c) Kelvin and Platinum

Answer 1

(a) Fahrenheit and Kelvin

Let θ be the temperature in Fahrenheit and Kelvin scales.

We know that the relation between the temperature in Fahrenheit and Kelvin scales is given by
$\frac{T_{\mathrm{F}}-32}{180}=\frac{T_{\mathrm{K}}-273.15}{100}$
T_F = T_K = θ

Therefore,
$$\begin{gathered} \frac{\theta -32}{180}=\frac{\theta -273.15}{100} \\ 5\theta -160=9\theta -2458.5 \\ 4\theta =2298.35 \\ \theta =574.59{}^{\mathrm{o}} \end{gathered}$$

If we consider the same for Celsius and Kelvin scales
$\frac{T_{\mathrm{C}}-0}{100}=\frac{T_{\mathrm{K}}-273.15}{100}$

Let the temperature be t
$$\begin{gathered} \frac{t-0}{100}=\frac{t-273.15}{100} \\ t=t-273.15 \end{gathered}$$
Thus, t does not exist.

The Kelvin scale uses mercury as thermometric substance, whereas the platinum scale uses platinum as thermometric substance. The scale depends on the properties of the thermometric substance used to define the scale. The platinum and Kelvin scales do not agree with each other. Therefore, there is no such temperature that has same numerical value in the platinum and Kelvin scale.