Question

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

Answer 1

Temperature scales are used to measure temperature.
There are three scales for measuring temperature: Celsius, Fahrenheit, and Kelvin. Temperatures can be transferred from one scale to another scale by applying the temperature conversion equations. Also, if the temperature rise in one scale is known, temperature rise in another scale can be calculated from the conversion equation. Use the Celsius-Fahrenheit conversion to solve the given problem.

Formula used:
The conversion equation for Fahrenheit to Celsius scale is:
$\Rightarrow F = \dfrac{{9C}}{5} + 32$
$C$ is the value with the Celcius unit and $F$ is the value of temperature with the Fahrenheit scale.

Complete answer:
The temperature rise in the Fahrenheit scale is $18^\circ F$.
$\therefore$ The temperature in the Fahrenheit scale will be, $\left( {F + 18} \right)$
The conversion equation for Fahrenheit to Celcius scale is:
$\Rightarrow F = \dfrac{{9C}}{5} + 32.................(1)$
$C$ is the value with the Celcius unit and $F$ is the value of temperature with the Fahrenheit scale.
Let, the temperature rise in the Celcius scale is $x^\circ C$ .
$\therefore$ The temperature in Celcius scale will be, $\left( {C + x} \right)$
$\Rightarrow \left( {F + 18} \right) = \dfrac{{9(C + x)}}{5} + 32.................(2)$
Now, $\left( 2 \right)-\left( 1 \right) \Rightarrow$
$\Rightarrow \left( {F + 18} \right) - F = \dfrac{{9(C + x)}}{5} + 32 - \left( {\dfrac{{9C}}{5} + 32} \right)$
$\Rightarrow 18 = \dfrac{{9C + 9x - 9C}}{5}$
$\Rightarrow \dfrac{{9x}}{5} = 18$
$\therefore x = 10$
So, the temperature rise in the Celcius scale is $10^\circ C$

Note:
There are three scales for measuring temperature: Celsius, Fahrenheit, and Kelvin.
On the Celsius scale, the freezing point of water is $0$ degrees celsius and the boiling point is $100$ degrees celsius The unit of temperature on this scale is the degree Celsius.
Fahrenheit temperature scale is based on $32$ for the freezing point of water and $212$ for the boiling point of water, the gap between the two scales is divided into $180$ sections.
In the Kelvin scale, the lower standard point is $273K$ and the upper-lower standard point is $373K$.