Question

A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. The corresponding Celsius temperature is

• A. $-574{}^{\circ }C$
• B. $301{}^{\circ }C$
• C. $276{}^{\circ }C$
• D. $232{}^{\circ }C$

Answer 1

The correct option is B

$301{}^{\circ }C$

Step 1 Converting $574$Kelvin to Celsius

$$\begin{gathered} T_C=T_K-273 \\ {T}_C=574-273 \\ {T}_C=301{}^{\circ }C \end{gathered}$$

Step 2 Converting $574$degrees Fahrenheit to Celsius

$$\begin{gathered} T_C=\left(574-32\right)\times \left(\frac{5}{9}\right) \\ {T}_C=\left(542\right)\times \left(\frac{5}{9}\right) \\ {T}_C=301.12{}^{\circ }C \end{gathered}$$

After Rounding Off, it will be $301{}^{\circ }C$

Hence, the reading at which the Fahrenheit and Kelvin thermometers show equality is at $301{}^{\circ }C$

Hence option (b) $301{}^{\circ }C$ is correct.