Question

At what temperature, does the temperature in Celsius and Fahrenheit scales equalize
A. \[-40\]
B. \[40\]
C. \[36.6\]
D. \[38\]

Answer 1

Hint: We have learned two equations which show the relation between two variables degree Celsius and degree Fahrenheit. Use the equations to solve the above question by assuming that the variables are equal. Then substitute it in the equations to find the values of variables.
Formula used:
\[{}^\circ F=\left( {}^\circ C\times \dfrac{9}{5} \right)+32\]
\[{}^\circ C=\left( {}^\circ F-32 \right)\times \dfrac{5}{9}\]

Complete answer:
We have equation to convert between degree Celsius and degree Fahrenheit,
\[{}^\circ F=\left( {}^\circ C\times \dfrac{9}{5} \right)+32\] -------- 1
\[{}^\circ C=\left( {}^\circ F-32 \right)\times \dfrac{5}{9}\]---------- 2
Let’s consider \[{}^\circ F={}^\circ C\]------ 3
Apply equation 3 in equation 1
\[{}^\circ F=\dfrac{9}{5}\times {}^\circ F+32\]
\[{}^\circ F-\dfrac{9}{5}\times {}^\circ F=32\]
\[-\dfrac{4}{5}\times {}^\circ F=32\]
\[{}^\circ F=32\times \left( -\dfrac{5}{4} \right)\]
\[{}^\circ F=-40\]
Or, apply equation 3 in equation 2
Then, \[{}^\circ C=\left( {}^\circ C\times \dfrac{9}{5} \right)+32\]
\[{}^\circ C-{}^\circ C\times \dfrac{9}{5}=32\]
\[\dfrac{-4}{5}\times {}^\circ C=32\]
\[{}^\circ C=32\times \left( -\dfrac{5}{4} \right)\]
\[{}^\circ C=-40\]
Hence, Celsius and Fahrenheit scales will read the same at \[-40\].

So, the correct answer is “Option A”.

Additional Information:
Thermometers are used to determine how cold or hot a substance is. We use different scales to measure temperature. Celsius scale, Fahrenheit scale, Kelvin scales are some of them. To define a temperature scale in a thermometer, we need to choose two reference points, which are known as fixed points.
In Celsius scale and Fahrenheit scale these fixed points are defined using properties of pure water. Those properties are the temperature of pure melting ice at normal atmospheric pressure and the temperature of pure boiling water at normal atmospheric pressure. The lower fixed point is determined by the temperature of pure melting ice and the upper fixed point is determined by temperature of pure boiling water. Once the Upper and lower points are fixed, we can now define a temperature scale.
 In Celsius scale upper and lower fixed points are separated by 100 divisions. Each division is a degree Celsius. The lower fixed point (LFP) is \[0{}^\circ C\] and the upper fixed point (UFP) is \[100{}^\circ C\].
In Fahrenheit scale LFP is \[32{}^\circ F\] and UFP is \[212{}^\circ F\]. This makes the boiling and freezing points of water 180 degrees apart.

Note:
Celsius scales are useful to measure water temperature, and Fahrenheit scales are useful to measure air temperature. The latter measures temperature more precisely. \[0{}^\circ C\] in the Celsius scale is not \[0{}^\circ F\] in the Fahrenheit scale. \[100{}^\circ C\] in the Celsius scale is not \[100{}^\circ F\] in the Fahrenheit scale.