Question

Find the change in temperature on a Fahrenheit scale and on a Kelvin scale if an iron piece is heated from $30^\circ {\text{C}}$ to $90^\circ {\text{C}}$ .
A) $108^\circ {\text{F, }}60{\text{K}}$
B) $100^\circ {\text{F, 55K}}$
C) $100^\circ {\text{F, }}65{\text{K}}$
D) $60^\circ {\text{F, 108K}}$
E) $140^\circ {\text{F, }}60{\text{K}}$

Answer 1

Hint:The change in temperature corresponds to the difference between the initial temperature and final temperature. To express the temperature in Fahrenheit scale we multiply the temperature in degree Celsius by a factor of $\dfrac{9}{5}$ and then add $32 \cdot 0$ to it. The temperature difference on the Kelvin scale will be the same as that on the Celsius scale.

Formulas used:
-The change in temperature of an object is given by, $\Delta T = {T_f} - {T_i}$ where ${T_f}$ is the final temperature of the object and ${T_i}$ is the initial temperature of the object.
-The temperature on the Fahrenheit scale is given by, $F = \left( {C \times \dfrac{9}{5}} \right) + 32$ where $C$ is the temperature on the Celsius scale.

Complete step by step answer.
Step 1: List the parameters given in the question and obtain the change in temperature of the iron piece.
The initial temperature of the iron piece is given to be ${T_i} = 30^\circ {\text{C}}$ .
The final temperature of the iron piece is given to be ${T_f} = 90^\circ {\text{C}}$ .
Then the change in temperature is expressed as $\Delta T = {T_f} - {T_i}$ -------- (1)
Substituting for ${T_i} = 30^\circ {\text{C}}$ and ${T_f} = 90^\circ {\text{C}}$ in equation (1) we get, $\Delta T = 90 - 30 = 60^\circ {\text{C}}$
Thus the temperature change on the Celsius scale is $\Delta T = 60^\circ {\text{C}}$ .
Step 2: Express the relation for the conversion of temperature from Fahrenheit to degree Celsius to obtain the temperature change of the iron piece on the Fahrenheit scale.
The relation for the conversion of temperature from Fahrenheit to degree Celsius is given by, $F = \left( {C \times \dfrac{9}{5}} \right) + 32$ where $C$ is the temperature on the Celsius scale.
The change in the temperature on the Fahrenheit scale can be expressed as
$\Delta {T_F} = \left( {\Delta {T_C} \times \dfrac{9}{5}} \right) + 32$ ------- (2)
Substituting for $\Delta {T_C} = 60^\circ {\text{C}}$ in equation (2) we get, $\Delta {T_F} = \left( {60 \times \dfrac{9}{5}} \right) + 32 = 140^\circ {\text{F}}$
Thus the change in the temperature of the iron piece on the Fahrenheit scale is obtained as $\Delta {T_F} = 140^\circ {\text{F}}$ .
The change in temperature on the Celsius scale and the Kelvin scale will be the same. So the temperature change of the iron piece on the Kelvin scale is $\Delta {T_K} = 60{\text{K}}$ .

So the correct option is E.

Note:In the Kelvin scale, a temperature difference of one Kelvin corresponds to a temperature difference of one degree Celsius in the Celsius scale. We can check if the temperature change on the Kelvin scale and the Celsius scale is the same.
The initial temperature of the iron piece in the Kelvin scale will be ${T_i}\left( {\text{K}} \right) = 30 + 273 = 303{\text{K}}$ and the final temperature of the piece in the Kelvin scale will be ${T_f}\left( {\text{K}} \right) = 90 + 273 = 363{\text{K}}$ .
Then the change in temperature on the Kelvin scale will be $\Delta {T_K} = 363 - 303 = 60{\text{K}}$ .