Question

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

Answer 1

To solve this question we need to know the formula to convert the unit of temperature from degree centigrade to degree Fahrenheit or Kelvin. After the conversion of the units of the temperature, we need to find the difference between the two given temperatures.

Formula used:
$^\circ F = \dfrac{9}{5}(^\circ C) + 32$
$K{ = ^\circ }C + 273$
where, $^ \circ C$ is the temperature given in degree centigrade,
$^ \circ F$ is the temperature given in degree Fahrenheit, and
$K$ is the temperature given in Kelvin.

Complete step by step answer:
Let us first convert the two temperature given in degree centigrade into degree Fahrenheit using the formula,
$^\circ F = \dfrac{9}{5}(^\circ C) + 32$ ……………. $(1)$
where, $^ \circ C$ is the temperature given in degree centigrade,
$^ \circ F$ is the temperature given in degree Fahrenheit.
Let the initial temperature be ${C_i} = {30^ \circ }C$ . Putting this value in the above equation $(1)$ we get,
$^ \circ {F_i} = \dfrac{9}{5}\left( {30} \right) + 32$
${ \Rightarrow ^ \circ }{F_i} = (9 \times 6) + 32$
Upon further solving the equation we get,
$^ \circ {F_i} = 54 + 32$
${ \Rightarrow ^ \circ }{F_i} = {86^ \circ }F$
Let the final temperature be ${C_f} = {90^ \circ }C$ . Putting this value in the above equation $(1)$ we get,
$^ \circ {F_f} = \dfrac{9}{5}\left( {90} \right) + 32$
${ \Rightarrow ^ \circ }{F_f} = (9 \times 18) + 32$
Upon further solving the equation we get,
$^ \circ {F_f} = 162 + 32$
${ \Rightarrow ^ \circ }{F_f} = {194^ \circ }F$
Therefore the change in temperature in degree Fahrenheit,
$^ \circ F{ = ^ \circ }{F_f}{ - ^ \circ }{F_i}$
$^ \circ F = 194 - 86$
${ \Rightarrow ^ \circ }F = {108^ \circ }F$
Now, let us convert the two temperature given in degree centigrade into Kelvin using the formula,
$K{ = ^ \circ }C + 273$
where, $K$ is the temperature given in Kelvin.
Using the value ${C_i} = {30^ \circ }C$ , we get the initial temperature in Kelvin as,
${K_i} = 30 + 273$
$\Rightarrow {K_i} = 303K$
Now, using the value ${C_f} = {90^ \circ }C$ , we get the final temperature in Kelvin as,
${K_f} = 90 + 273$
$\Rightarrow {K_f} = 363K$
Therefore the change in temperature in Kelvin is given as,
$K = {K_f} - {K_i}$
$\Rightarrow K = 363 - 303$
$\therefore K = 60K$
Hence the correct option is option (A) ${108^ \circ }F,60K$ .

Note:
As we can see from the above solution that the difference in temperature in degree centigrade and Kelvin is equal. Hence while solving questions where a temperature change is involved, conversion of the unit from degree centigrade to Kelvin, or vice versa is not required. But this is not the case for degrees Fahrenheit.