Question

A measured temperature on the Fahrenheit scale is ${200^ \circ }\,F$. What will this reading be on the Celsius scale?
A) ${40^ \circ }\,C$
B) ${94^ \circ }\,C$
C) ${93.3^ \circ }\,C$
D) ${30^ \circ }\,C$

Answer 1

Hint: Generally, the temperature has three units, they are Kelvin, Celsius and Fahrenheit. And these three units have the relation between them. One unit is changed to another unit by using that relationship. In this problem, it is given that, the temperature in Fahrenheit scale and asking the temperature in Celsius scale, so by using the relation between the Fahrenheit and Celsius the solution can be determined.

Useful formula:
The conversion of the temperature scale from Fahrenheit to the Celsius is,
$C = \dfrac{5}{9}\left( {F - 32} \right)$
Where, $C$ is the temperature in Celsius and $F$ is the temperature in Fahrenheit

Complete step by step solution:
Given that,
The temperature in Fahrenheit, $T = {200^ \circ }\,F$
The conversion of the temperature scale from Fahrenheit to the Celsius is,
$C = \dfrac{5}{9}\left( {F - 32} \right)\,.................\left( 1 \right)$
By substituting the temperature in Fahrenheit in the above equation (1), then the equation (1) is written as,
$C = \dfrac{5}{9}\left( {200 - 32} \right)$
On subtracting the terms inside the bracket, then the above equation is written as,
 $C = \dfrac{5}{9}\left( {168} \right)$
Now multiplying the terms, then the above equation is written as,
$C = \dfrac{{840}}{9}$
On dividing the above equation, then the above equation is written as,
$C = {93.3^ \circ }\,C$
Thus, the above equation shows the temperature in the Celsius scale.

Hence, the option (C) is the correct answer.

Note: The Celsius scale and the Fahrenheit scale will coincide at the temperature of $ - {40^ \circ }$, at this point both Celsius and the Fahrenheit are the same. But the conversion of Celsius to Kelvin is the simple form, zero degree Celsius is equal to the $273.15$ Kelvin.