Question

The Fahrenheit temperature $F$ decreased by $32$ is equal to nine-fifths of the centigrade temperature $C$. The correct formula framed for the above statement will be:
(A) $F + 32 = \dfrac{5}{9}C$
(B) $F - 32 = \dfrac{5}{9}C$
(C) $F + 32 = \dfrac{9}{5}C$
(D) $F - 32 = \dfrac{9}{5}C$

Answer 1

This problem is related to the conversion of the temperature between the Fahrenheit unit and the Celsius unit. And by knowing the temperature conversion from Fahrenheit unit to the Celsius unit, the correct formula can be determined.

Complete step-by-step solution :
Temperature is the physical quantity which is used to measure how hot or cold something. Generally, temperatures have three units. The same temperature has different readings on different temperature units. The three units are Fahrenheit, Celsius and Kelvin. Temperature conversion is the changing the value of temperature from one unit to another unit. For example, if we take the freezing and boiling point of water, According to the Kelvin, the freezing point of the water is $273.15\,K$ and the boiling point of the water is $373.15\,K$, where, $K$ is the unit of temperature in Kelvin. According to the Fahrenheit, the freezing point of the water is ${32^ \circ }\,F$ and the boiling point of the water is ${212^ \circ }\,F$, where $F$ is the unit of temperature in Fahrenheit. According to the Celsius, the freezing point of the water is ${0^ \circ }\,C$ and the boiling point of the water is ${100^ \circ }\,C$, where $C$ is the unit of temperature in Celsius.
In this problem, the relation between the Fahrenheit and the Celsius is given, so the conversion of temperature between Fahrenheit unit and Celsius unit is,
$C = \left( {F - 32} \right) \times \dfrac{5}{9}$
By taking the term $\dfrac{5}{9}$ from RHS to LHS, then the above equation is written as,
$\left( {F - 32} \right) = \dfrac{9}{5}C$
Thus, the above equation is the correct formula framed for the given statement.
Hence, option (D) is the correct answer.

Note:- In thermal physics, the temperature unit conversion is very important. The three temperature unit conversions are conversion of temperature between Kelvin and Celsius, conversion of temperature between Fahrenheit and Celsius and conversion of temperature between Fahrenheit and Kelvin.