Question

The temperature of an iron piece is increased from ${30}^{\circ }\text{C}$ to ${90}^{\circ }\text{C}$. Find the change in its temperature on the Fahrenheit scale and on the Kelvin scale.

• A. ${108}^{\circ }\text{F},60\text{K}$
• B. ${132}^{\circ }\text{F},60\text{K}$
• C. ${108}^{\circ }\text{F},32\text{K}$
• D. ${132}^{\circ }\text{F},32\text{K}$

Answer 1

The correct option is A ${108}^{\circ }\text{F},60\text{K}$

By using the formula,
$\frac{C}{5}=\frac{F-32}{9}$
We find the relation between change in temperature in Celsius scale and Fahrenheit scale as $\Delta T_F=\frac{9}{5}\Delta T_C.......\left(1\right)$
From the data given in the question, change in temperature measured in Celsius scale is given by
$\Delta T_C={90}^{\circ }\text{C}-{30}^{\circ }\text{C}={60}^{\circ }\text{C}.......\left(2\right)$

Using $\left(2\right)\text{in}\left(1\right)$,
$\Delta T_F=\frac{9}{5}\Delta T_C=\frac{9}{5}\left({60}^{\circ }\text{C}\right)={108}^{\circ }\text{F}$
Relation between Celsius and Kelvin scale is given by $C=K-273$
Using this, we find the relation between the change in temperature measured in Celsius scale and Kelvin scale as
$\Delta T_K=\Delta T_C.......\left(3\right)$

From $\left(3\right)$, we can conclude that,
$\Delta T_K=60\text{K}$
Hence, option (a) is the correct answer.