Question

At what temperature, the Celsius and Fahrenheit scales will read the same?
A. $- 10^\circ \,{\text{C}}$
B. $10^\circ \,{\text{C}}$
C. $40^\circ \,{\text{C}}$
D. $- 40^\circ \,{\text{C}}$

Answer 1

Use the conversion formula to convert the temperature on Fahrenheit scale to Celsius scale. Substitute ${T_C}$ for ${T_F}$ in this formula to get the temperature on Celsius scale.

Formula used:
${T_F} = \dfrac{9}{5}{T_C} + 32$
Here, ${T_F}$ is the temperature on Fahrenheit scale and ${T_C}$ is the temperature on Celsius scale.

Complete step by step solution:
We know the conversion formula to convert Fahrenheit temperature to Celsius temperature,
${T_F} = \dfrac{9}{5}{T_C} + 32$
Here, ${T_F}$ is the temperature on Fahrenheit scale and ${T_C}$ is the temperature on Celsius scale.
We have given that the certain temperature on Fahrenheit scale and Celsius scale is the same. Therefore, we can substitute ${T_C}$ for ${T_F}$ in the above equation.
${T_C} = \dfrac{9}{5}{T_C} + 32$
$\Rightarrow {T_C} - \dfrac{9}{5}{T_C} = 32$
$\Rightarrow - \dfrac{4}{5}{T_C} = 32$
$\Rightarrow {T_C} = - \dfrac{{32 \times 5}}{4}$
$\Rightarrow {T_C} = - 40^\circ \,{\text{C}}$

Therefore, at $- 40^\circ \,{\text{C}}$, the Fahrenheit scale and Celsius scale will read the same temperature.

So, the correct answer is “Option D”.

Additional Information:
The lower fix point of Fahrenheit scale is $32^\circ {\text{F}}$ and the upper fix point is $212^\circ {\text{F}}$. The lower fix point of Celsius scale is $0^\circ \,{\text{C}}$ and upper fix point is $100^\circ \,{\text{C}}$. If we have given the temperature on the Fahrenheit scale and we have been asked to determine the corresponding temperature on Celsius scale, we can use the conversion formula,
$\dfrac{{{T_C} - LFP}}{{UFP - LFP}} = \dfrac{{{T_F} - LFP}}{{UFP - LFP}}$

Here, LFP is the lower fix point and UFP is the upper fix point. If we put the value of Fahrenheit temperature ${T_F}$ as $- 40^\circ \,{\text{F}}$, after substituting the corresponding LFP and UFP of Fahrenheit scale and Celsius scale, we will get the temperature on Celsius scale as $- 40^\circ \,{\text{C}}$.

Note:
We can also solve this question using the formula for converting the temperature on Celsius scale to Fahrenheit scale. The conversion formula is, ${T_C} = \dfrac{5}{9}\left( {{T_F} - 32} \right)$. If you substitute ${T_C}$ for ${T_F}$ in this equation, the result will be the same.