Question

The relation Between Celsius and Fahrenheit temperature scales is:
A) $\dfrac{{C - 100}}{{212}} = \dfrac{{F - 18}}{{32}}$
B) $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$
C) $\dfrac{C}{9} = \dfrac{{F - 32}}{5}$
D) $\text{None of these}$

Answer 1

Hint: Temperature is the degree of hotness or coldness of the body. It is measured using a device called a thermometer and has the dimensions of the Kelvin, Celsius, Fahrenheit etc. Out of which the Kelvin is the base unit of the temperature and the Celsius is the base unit of temperature.

Formula used:
The relation between the Celsius and the Fahrenheit is
$F = \dfrac{9}{5}C + 32$
Where $F$ is the temperature in Fahrenheit and $C$ is the temperature in the scale of Celsius.

Complete step by step solution:
In the scale of the Celsius, the zero degree represents the freezing point of the water and the $100$ degree represents the boiling point of the water. Let us consider the basic formula between the Celsius and the Fahrenheit which is given above.
$F = \dfrac{9}{5}C + 32$
Rearranging the above formula based on the given options,
$\left( {F - 32} \right)5 = 9C$
Forming the denominators from the above equation,
$\Rightarrow$ $\dfrac{{F - 32}}{9} = \dfrac{C}{5}$
By interchanging the left and right hand side of the equation.
$\Rightarrow$ $\dfrac{C}{5} = \dfrac{{F - 32}}{9}$
By dividing both the sides by $20$ ,
$\Rightarrow$ $\dfrac{C}{{5 \times 20}} = \dfrac{{F - 32}}{{9 \times 20}}$
By performing the basic arithmetic operation,
$\Rightarrow$ $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$
Hence among the given option for the relation between the Celsius and the Fahrenheit scales, $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$ is the correct answer.

Thus the option (B) is correct.

Note: The Fahrenheit scale is used for the measurement of the body temperature, and it is used in the weather forecasting in the United states and other countries. Even though there emerged many temperature naming units, the Americans still use Fahrenheit for their easy dimensioning.