Question

A temperature difference of${25^o}C$ is equivalent to a temperature difference of
(A) ${13^o}F$
(B) ${45^o}F$
(C) ${67^o}F$
(D) ${77^o}F$

Answer 1

Hint We are given here with a temperature difference and are asked to find its equivalent temperature in a different unit. The options are given in degrees Fahrenheit and thus we have to convert the given temperature into a Fahrenheit unit.
Formulae Used
$\dfrac{{{T_{new}} - {L_{new}}}}{{{U_{new}} - {L_{new}}}} = \dfrac{{{T_{old}} - {L_{old}}}}{{{U_{old}} - {L_{old}}}}$
Where,${T_{new}}$ is the temperature in the new scale,${L_{new}}$ is the lower limit of the new temperature scale,${U_{new}}$ is the upper limit of the new temperature scale,${T_{old}}$ is the temperature in the old scale,${L_{old}}$ is the lower limit of the old temperature scale and ${U_{old}}$ is the upper limit of the old temperature scale.

Complete Step By Step Answer
Here,
Given,
The temperature difference,${T_{old}} = {25^o}C$
Now,
The old temperature scale is the Celsius scale.
Thus,
${L_{old}} = {0^o}C$
${U_{old}} = {100^o}C$
Also,
The new temperature scale is the Fahrenheit scale.
Thus,
${L_{new}} = {32^o}F$
${U_{new}} = {212^o}F$
Now,
Applying the formula
$\dfrac{{{T_{new}} - {L_{new}}}}{{{U_{new}} - {L_{new}}}} = \frac{{{T_{old}} - {L_{old}}}}{{{U_{old}} - {L_{old}}}}$
Now,
Substituting the values, we get
$\dfrac{{{T_{new}} - 32}}{{212 - 32}} = \dfrac{{25 - 0}}{{100 - 0}}$
Now,
Calculating the values, we get
$\dfrac{{{T_{new}} - 32}}{{180}} = \dfrac{{25}}{{100}}$
Then, we try to cancel out the most probable terms and the terms which will be beneficial for us to cancel out.
$\dfrac{{{T_{new}} - 32}}{{180}} = \dfrac{1}{4}$
Again, we look for cancellation pairs and we cancel them we get
$\dfrac{{{T_{new}} - 32}}{{45}} = \dfrac{1}{1}$
Then, we get
${T_{new}} - 32 = 45$
Finally, we get
${T_{new}} = {77^o}F$

Hence, the correct option is (d).

Additional Information
The formula we have used is a generic formula for any sort of conversion of temperature into different physical units. But this formula does not apply for conversion into Kelvin scale as the Kelvin scale is a theoretical scale and the formula only applies for a physical scale.

Note
We have found the value as ${77^o}F$ which is equivalent to a temperature difference of ${25^o}C$ in the Celsius scale. This sort of conversion physically signifies that if the temperature of a body is measured in two different scales at the same time, then the temperature which the two scales shows is what this conversion signifies.