Question

The temperature, at which centigrade and Fahrenheit scales give the same reading (in degrees), is:
A. $- 40$
B. $40$
C. $- 30$
D. $30$

Answer 1

Centigrade and Fahrenheit are two different scales to measure the temperature. In centigrade scale, water boils at $100{\,^ \circ }C$ while in Fahrenheit scale water boils at $212{\,^0}F$ . Also, water freezes at ${0^0}C$ in centigrade scale and ${32^0}$ in Fahrenheit scale. We can either use this relation, deduce the general formula to solve or simply use the temperature formula.

Complete step by step answer:
We can solve this easily by applying the temperature formula:
Using the temperature formula, we have:
$^0F = \left( {^0C \times \dfrac{9}{5}} \right) + 32$
Here, $^0F$ denotes temperature in Fahrenheit scale.
$^0C$ denotes temperature in Celsius scale.
$^0C = {(^0}F - 32) \times \dfrac{5}{9}$
We need to find the value of temperature at which both the scales give the same reading:
Let us assume that both the scales give the same reading at some temperature $T$ , now let’s put this value in the above equations. As the reading of centigrade scale and Fahrenheit scale is same for this temperature, hence we have:
$^0C{ = ^0}F = T$
$T = \left( {T \times \dfrac{9}{5}} \right) + 32$
And
$T = (T - 32) \times \dfrac{5}{9}$
Solving this equation, we get
$\Rightarrow T = - {40^0}C$
$\Rightarrow T = - {40^0}C$
Therefore, the centigrade scale and the Fahrenheit scale will have the same reading at $- {40^0}C$

So, the correct answer is “Option A”.

Additional Information:
Absolute zero is $273.5$ Kelvins. This is the lowest temperature any substance’s temperature can be. Celsius and Kelvins become equal when reading in centigrade scale is $273.5$Temperature is defined as a measure of the hotness or coldness of an object. Temperature is measured using a thermometer, we observe the effect of temperature on the substance inside it. In calculation purposes, the temperature is always taken in Kelvin.

Note:
The boiling point of water and the freezing point of water is important to note in all three scales. Kelvin scale is also known as absolute scale. It is technically not possible to achieve a temperature of $0$ Kelvin. Celsius and Kelvin scales are believed to have the same reading at very high temperatures.