Question

Which of the following temperatures will read the same value on Celsius and Fahrenheit scales.
A. $-{40}^0$
B. $+{40}^0$
C. $-{80}^0$
D. $-{20}^0$ $$$$

Answer 1

Hint: Celsius scale is also called the centigrade scale that is based on the freezing point of water at $0^{0}C$ and the boiling point of water at${100}^{0}C$.
Fahrenheit scale is a temperature scale that is based on the freezing point of water at ${32}^{0}F$ and the boiling point of water at ${212}^{0}F$

Complete step by step answer:
First we will discuss about the temperature or scales which is given in question,
Temperature is a physical quantity used to determine hotness or coldness of an object via thermometer. Various scales are used to measure temperature, out of which the most common are degree Celsius and degree Fahrenheit. It is not important that which scale we are using for measuring the temperature as they are inter-convertible. One unit can derive from another by using basic formulas. Generally zero degrees Celsius is considered as equal to 32 degree Fahrenheit. For example, water freezes at zero degrees Celsius, or at 32 degree Fahrenheit.
Now we will calculate the temperature is based on the Celsius scale or Fahrenheit scale,
 The basic formulas for conversion between degree Celsius and degree Fahrenheit are,
$\left({}^{0}C\times {\displaystyle \frac{9}{5}}\right)+32{=}^{0}F$ ……..(1)
$\left({}^{0}F-32\right)\times {\displaystyle \frac{5}{9}}{=}^{0}C$………..(2)
We can determine the temperature at which degree Celsius and degree Fahrenheit shows the same value, just by solving the above formulas.
We want, ${}^{0}F{=}^{0}C-equation.........(a)$
 Put the value of ${}^{0}F$ from above formula in equation 1,
$$\begin{gathered} \left({}^{0}C\times {\displaystyle \frac{9}{5}}\right)+32{=}^{0}C \\ \left({}^{0}C\times {\displaystyle \frac{9}{5}}\right){-}^{0}C=-32 \\ {\Rightarrow }^{0}C-\left({}^{0}C\times {\displaystyle \frac{9}{5}}\right)=32 \\ {\Rightarrow }^{{}^0}C-{1.8}^{0}C=32 \\ \Rightarrow -{0.8}^{0}C=32{ \\ }^{0}C={\displaystyle \frac{-32}{0.8}}=-40{ \\ }^{0}C=-40 \end{gathered}$$
Similarly, now we can put the value of ${}^{0}F$ in equation 2,
$$\begin{gathered} {}^{0}F=\left({}^{0}F-32\right)\times {\displaystyle \frac{5}{9}}{ \\ }^{0}F={\displaystyle \frac{5}{9}}-32\times {\displaystyle \frac{5}{9}}{ \\ }^{0}F-{\displaystyle \frac{5}{9}}=-32\times {\displaystyle \frac{5}{9}} \\ \Rightarrow {{\displaystyle \frac{5}{9}}}^{0}F{-}^{0}F=32\times {\displaystyle \frac{5}{9}} \\ \Rightarrow {{\displaystyle \frac{-4}{9}}}^{0}F=32\times {\displaystyle \frac{5}{9}} \\ {\Rightarrow }^{0}F=-32\times {\displaystyle \frac{5\times 9}{4\times 9}}=-40{ \\ }^{0}F=-40 \end{gathered}$$
So according to the numerical concept, the same value of temperature for degree Celsius and degree Fahrenheit is -40. This is the value at which the scale of degree Celsius and degree Fahrenheit converge.

So, the correct answer is Option A.

Note: Celsius scale is widely used because of the adoption of the metric system. Celsius or Fahrenheit scales is great for measuring the temperature of water. They are also used to note the body temperature. The food cooking or freezing temperatures are typically given in degrees Fahrenheit.