Question

The temperature rises by $18{}^\circ F$. What is the rise on the Celsius scale?

Answer 1

As a first step, one could read the question and hence note down the values from it. Then recall the conversion formula between Fahrenheit and Celsius and then find how the rise in temperature can be expressed. Thus find the corresponding rise in temperature in Celsius scale.

Formula used:
Conversion formula for Fahrenheit to Celsius,
${}^\circ F=32+\dfrac{9}{5}\left( {}^\circ C \right)$

Complete step-by-step solution:
In the question, we are given the rise of temperature in Fahrenheit scale to be $18{}^\circ F$ and we are supposed to find the corresponding rise in temperature in Celsius scale.
As a very first step, one could recall the conversion formula for temperature in Fahrenheit scale to that of Celsius scale. The expression given by,
${}^\circ F=32+\dfrac{9}{5}\left( {}^\circ C \right)$
Now the initial temperature of the substance be given by,
${}^\circ {{F}_{1}}=32+\dfrac{9}{5}\left( {}^\circ {{C}_{1}} \right)$……………………………………… (1)
The final temperature after the rise in temperature be,
${}^\circ {{F}_{2}}=32+\dfrac{9}{5}\left( {}^\circ {{C}_{2}} \right)$……………………………………… (2)
On subtracting equation (1) from equation (2) will give us the rise in temperature, that is,
${{F}_{2}}-{{F}_{1}}=1.8\left( {{C}_{2}}-{{C}_{1}} \right)$
From the given values,
${{C}_{2}}-{{C}_{1}}=\dfrac{{{F}_{2}}-{{F}_{1}}}{1.8}=\dfrac{18}{1.8}$
$\therefore \Delta T=10{}^\circ C$
Therefore, we found the given rise in temperature in Celsius scale to be $10{}^\circ C$.

Note: One could actually think of an alternate method that would save some steps and thereby some time in competitive exams. One could recall the number of divisions in both temperature scales. Thereby, you may find that 100 divisions in Celsius scale is equivalent to 180 divisions in Fahrenheit scale. Therefore, $18{}^\circ F$would be equivalent to,
$18{}^\circ F\Rightarrow \dfrac{100}{180}\times 18=10{}^\circ C$.