Question

On the centigrade scale, the temperature of a body increases by 30 degrees. The increase in temperature on the Fahrenheit scale is:
(A) \[50\% \]
(B) \[40\% \]
(C) \[30\% \]
(D) \[54\% \]

Answer 1

Hint:0 degrees Celsius is equal to 32 degrees Fahrenheit and the temperature T in degrees Celsius \[\left( {^\circ C} \right)\] can be converted to the temperature T in degrees Fahrenheit \[\left( {^\circ F} \right)\] by the formula
\[{T_{(^\circ F)}}\; = \;{T_{(^\circ C)}}\; \times {\text{ }}\dfrac{9}{5}{\text{ }} + {\text{ }}32\].

Complete step by step answer:
Let the temperature at first is \[{C_1}\] degree Celsius, and the it increased by 30° to \[{C_2}\] to degree Celsius, hence the difference between initial and final temperature is given by,
\[{C_1} - {C_2} = 30\]
Let the temperature is \[{F_1}\] degree Fahrenheit corresponding to \[{C_1}\] degree Celsius and \[{F_2}\]degree Fahrenheit when temperature in degree Celsius changed to \[{C_2}\] which can be calculated from the formula.
\[{T_{(^\circ F)}}\; = \;{T_{(^\circ C)}}\; \times {\text{ }}\dfrac{9}{5}{\text{ }} + {\text{ }}32\], where \[{T_{(^\circ F)}}\] is the temperature in degree Fahrenheit and \[{T_{(^\circ C)}}\]
is temperature in degrees Celsius.
\[\begin{gathered}
{F_1} = \dfrac{9}{5} \times {C_1} + 32 \\
{F_2} = \dfrac{9}{5} \times {C_2} + 32 \\
\end{gathered} \]
Then the difference in temperature in degree Fahrenheit is equal to
\[{F_1} - {F_2} = \dfrac{9}{5} \times ({C_1} - {C_2})\]
Where \[{C_1} - {C_2} = 30\]
\[ \Rightarrow {F_1} - {F_2} = \dfrac{9}{5} \times 30 = {54^ \circ }F\]
Hence the correct option is (D) The increase in temperature on the Fahrenheit scale is 54%.

Note:Degree Celsius unit of temperature is the most common unit of temperature used in most countries., degree Fahrenheit is also the unit of temperature used mostly in the US.One more commonly used unit of temperature is Kelvin. It can also be converted from degree Celsius and degree Fahrenheit.
\[{T_{(^\circ K)}}\; = \;{T_{(^\circ C)}}\; + 273.15\](Conversion of temperature from degree Celsius to degree Kelvin)
\[{T_{(^\circ K)}}\; = \;({T_{(^\circ F)}}\; + 459.67) \times \dfrac{5}{9}\] (Conversion of temperature from degree Fahrenheit to degree Kelvin)