Question

The temperature of a body rose by \[40\,^\circ {\text{C}}\] . How much is the increase in the Fahrenheit scale?
A. \[8\,^\circ {\text{F}}\]
B. \[40\,^\circ {\text{F}}\]
C. \[62\,^\circ {\text{F}}\]
D. \[72\,^\circ {\text{F}}\]

Answer 1

Hint: First we will assume two different temperatures, which are at a difference of \[40\,^\circ {\text{C}}\] . After that we will use the relation between the centigrade scale and the Fahrenheit scale to convert them into degree Fahrenheit. After that we will find the difference to obtain the answer.

Formula used:
The formula which gives the relation between the centigrade scale and the Fahrenheit scale is given as follows:
\[F = \dfrac{{9C}}{5} + 32\] …… (1)
Where,
\[F\] indicates the temperature reading on the Fahrenheit scale.
\[C\] indicates the temperature reading on a centigrade scale.

Complete step by step answer:
To begin with, we will assume two different temperatures which are at a difference of \[40\,^\circ {\text{C}}\] .Let the two temperatures be \[30\,^\circ {\text{C}}\] and \[70\,^\circ {\text{C}}\] .Let us convert these two temperatures in Fahrenheit scale, by substituting the required values in the formula (1) and we get:
For \[30\,^\circ {\text{C}}\] :
$F = \dfrac{{9C}}{5} + 32 \\
\Rightarrow F = \dfrac{{9 \times 30}}{5} + 32 \\
\Rightarrow F = 54 + 32 \\
\Rightarrow F = 86\,^\circ {\text{F}} \\$
For \[70\,^\circ {\text{C}}\] :
$F = \dfrac{{9C}}{5} + 32 \\
\Rightarrow F = \dfrac{{9 \times 70}}{5} + 32 \\
\Rightarrow F = 126 + 32 \\
\Rightarrow F = 158\,^\circ {\text{F}} \\$
So, the difference of temperature in the Fahrenheit scale:
$\Delta F = 158\,^\circ {\text{F}} - 86\,^\circ {\text{F}} \\
\therefore \Delta F = 72\,^\circ {\text{F}} $

Hence, the temperature that has risen, equivalent to Fahrenheit is \[72\,^\circ {\text{F}}\] .The correct option is D.

Note:While solving this problem, we should remember that the reading in the Fahrenheit scale is higher than the centigrade scale for the same temperature. We can also solve it by an alternative method with assuming any temperatures, by using the formula \[\Delta C = \dfrac{5}{9} \times \Delta F\] . The formula features directly the difference in temperatures.