Question

At what temperature are Celsius and Fahrenheit equal?

Answer 1

Explanation,

1. There are two important temperature scales, Celsius and Fahrenheit used in the world.
2. There is a point on both scales where the temperatures in degrees are equal.
3. This is $-40°C$ and $-40°F$.

Celsius and Fahrenheit,

1. Celsius is directly proportional to Fahrenheit.
2. This says that with the increase in the temperature on the Celsius scale, its Fahrenheit temperature equivalent temperature will also rise.
3. When the temperature on the Celsius scale decreases, its Fahrenheit temperature equivalent temperature will also be low.
4. Multiply the $°C$ temperature by $1.8$ Add $32$ to this number. This is the answer in $°F$
5. The Celsius freezing point of water is $0°C$and its boiling point is $100°C$
6. $100°C-0°C=100°C$ between water's freezing and boiling points.
7. Conversion of Celsius to Fahrenheit is $F=\frac{9}{5}C+32$
8. Conversion from Fahrenheit to Celsius is:$C=\frac{5}{9}(F-32)$

Step 1: Given

Both celcius and fahrenheit have same temperature.

Let the temperature = $x$

Step 2: Formula used.

1. The formula as given is $\frac{C}{100}=\frac{(F-32)}{(180)}$

Step 3: Calculation

1. We want to know the point at which the temperatures are the same, so let's call that temperature $x$ :

$or,\frac{x}{100}=\frac{(x-32)}{\left(180\right)}$

$or,x=\frac{100\ast (x-32)}{180}$

$or,x=\frac{50\ast (x-32)}{90}$

$or,x=\frac{5\times (x-32)}{9}$

$or,x=\frac{5x-5\times 32}{9}$

$or,x=\frac{5x}{9}-\frac{(5\times 32)}{9}$

$or,x=\frac{5x}{9}-\frac{160}{9}$

$or,9x=5x-160$

$or,9x-5x=-160$

$$\begin{gathered} 4x=-160 \\ x=-40 \end{gathered}$$

Hence, at $-40°C$ and $-40°F$ temperature are Celsius and Fahrenheit equal.