Question

A Kelvin thermometer and a Fahrenheit thermometer used to record temperature of a melting metal are showing the same reading. What will a Celsius thermometer read at that temperature?

• A. ${574.25}^{\circ }\text{C}$
• B. ${273}^{\circ }\text{C}$
• C. ${301.25}^{\circ }\text{C}$
• D. ${760}^{\circ }\text{C}$

Answer 1

The correct option is C ${301.25}^{\circ }\text{C}$

Let $t$ be the temperature which is read same on Kelvin and Fahrenheit scale both.
We have, $\frac{K-273}{373-273}=\frac{F-32}{212-32}$

$\Rightarrow \frac{t-273}{100}=\frac{t-32}{180}$

$\Rightarrow \frac{t-273}{5}=\frac{t-32}{9}$

$\Rightarrow 9t-2457=5t-160$
$\Rightarrow 4t=2297$
$\Rightarrow t=2297/4=574.25\text{K}$
Therefore, temperature on Celsius scale will be $=574.25-273={301.25}^{\circ }\text{C}$