Question

Calculate the temperature at which both the Celsius and Fahrenheit scales show the same reading?
A. 40K
B. 100${}^\circ F$
C. -40${}^\circ C$
D. -100${}^\circ C$

Answer 1

Hint: To answer this question, we use the formula of conversion of Fahrenheit and Celsius scale. Here, we should need to find one common value from both the formula and equate to it.

Step by step answer:
To answer this question, we should first know the formula for Celsius and Fahrenheit scale.
Formula for converting Fahrenheit into Celsius is as follows:

Celsius (${}^\circ C$) = \[\left( {}^\circ F-32 \right)\times \dfrac{5}{9}\]

Fahrenheit (${}^\circ F$) =\[({}^\circ C\times \dfrac{9}{5})+32\]

So, now we know the formulas for Fahrenheit and Celsius scale. So, to find the temperature when both are equal, we use an old algebra trick and just set${}^\circ F$= ${}^\circ C$and solve one of the equations. So, at first we will put the value of ${}^\circ F$= ${}^\circ C$ in Fahrenheit formula.

Fahrenheit (${}^\circ F$) =\[({}^\circ C\times \dfrac{9}{5})+32\]
\[\begin{align}
  & {}^\circ C=({}^\circ C\times \dfrac{9}{5})+32 \\
 & {}^\circ C-({}^\circ C\times \dfrac{9}{5})=32 \\
 & -\dfrac{4}{5}\times {}^\circ C=32 \\
 & {}^\circ C=-32\times \dfrac{5}{4} \\
 & {}^\circ C=-40 \\
\end{align}\]

So, now we will find the value of Fahrenheit by using the Fahrenheit formula.
\[\begin{align}
  & {}^\circ F=({}^\circ F\times 9/5)+32 \\
 & {}^\circ F-({}^\circ F\times \dfrac{9}{5})=32 \\
 & -\dfrac{4}{5}\times {}^\circ F=32 \\
 & {}^\circ F=-32\times \dfrac{5}{4} \\
 & {}^\circ F=-40 \\
\end{align}\]
So, from the solution we can say that the value of both${}^\circ F$and ${}^\circ C$ is equal. Now, we can say that the value of both ${}^\circ F$and ${}^\circ C$ is equal to -40. From this we can say that temperature value at which both Celsius and Fahrenheit scales is equal to -40.
So, option C is correct.
Note:
We should note that the Celsius (or centigrade) temperature scale is the most widely used around the world, but the Fahrenheit scale is more popular in the United States. We should know the difference between the Fahrenheit and Celsius temperature scales. In the Fahrenheit system, 32 degrees is the freezing point of water, and 212 degrees is the boiling point. The Fahrenheit scale therefore divides the interval between the two into 180 degrees (212 minus 32 = 180). Each Celsius degree equals 1.80 Fahrenheit degrees.