Question

One day, the maximum temperature of Delhi is recorded as $ 42.4^\circ {\rm{C}} $ . Convert the temperature into Fahrenheit.
A. $ 108.23^\circ {\rm{F}} $
B. $ 108.32^\circ {\rm{F}} $
C. $ 108.43^\circ {\rm{F}} $
D. $ 108.34^\circ {\rm{F}} $

Answer 1

Hint: To convert the temperature given in Celsius into Fahrenheit, we will write an expression which consists of steam and ice point of water on both the scales. Since, in our question temperature for Celsius scale is already given we will substitute the steam and ice point of water in Fahrenheit and Celsius. Then, we will find the temperature in Fahrenheit by solving the expression.

Complete step-by-step answer:
We know that the steam point of water is $ 100^\circ {\rm{C}} $ and the ice point of water is $ 0^\circ {\rm{C}} $ on Celsius scale. Also, the steam point of water is $ 212\;^\circ {\rm{F}} $ and ice point of water is \[32\;^\circ {\rm{F}}\] on Fahrenheit scale. We will use these steam and ice points to find the temperature given in Fahrenheit.
 We can express the relation between any two scales which measures temperature as,
 $ {\left( {\dfrac{{t - {t_i}}}{{{t_s} - {t_i}}}} \right)_I} = {\left( {\dfrac{{t - {t_i}}}{{{t_s} - {t_i}}}} \right)_{II}} $
In this question we will relate Celsius and Fahrenheit scale.
 $ {\left( {\dfrac{{t - {t_i}}}{{{t_s} - {t_i}}}} \right)_C} = {\left( {\dfrac{{t - {t_i}}}{{{t_s} - {t_i}}}} \right)_F} $
We will substitute steam point and ice point of water on Fahrenheit and Celsius scale.
\[{\left( {\dfrac{{t - 32^\circ {\rm{F}}}}{{{{212}^{\rm{o}}}{\rm{F}} - {{32}^{\rm{o}}}{\rm{F}}}}} \right)_F} = {\left( {\dfrac{{{{42.4}^{\rm{o}}}{\rm{C}} - {0^{\rm{o}}}{\rm{C}}}}{{{{100}^{\rm{o}}}{\rm{C}} - {0^{\rm{o}}}{\rm{C}}}}} \right)_C}\]
We will rearrange the above expression as:
\[\begin{array}{c}
t - {32^{\rm{o}}}{\rm{F}} = \dfrac{{{{42.4}^{\rm{o}}}{\rm{C}}}}{{{{100}^{\rm{o}}}{\rm{C}}}} \times {180^{\rm{o}}}{\rm{F}}\\
t - {32^{\rm{o}}}{\rm{F}} = {76.32^{\rm{o}}}{\rm{F}}\\
t = {\left( {76.32 + 32} \right)^{\rm{o}}}{\rm{F}}\\
t = {108.32^{\rm{o}}}{\rm{F}}
\end{array}\]
Hence, $ {42.4^ \circ }{\rm{C}} $ in Fahrenheit will be \[{108.32^{\rm{o}}}{\rm{F}}\].
So, the correct answer is “Option B”.

Note: Questions related to conversion of temperature scales can be solved with the help of conversion formula. We should have prior knowledge about the steam and ice point of the water for different water for different temperature scales. Also, the common mistake can happen in the substitution of these values in the conversion formula. We can substitute the temperature given in the formula to find the other unknown temperature.