Question

At what temperature will the reading on the Fahrenheit scale be double of the reading on the Celsius scale?

Answer 1

Calculation of the temperature at which the reading on the Fahrenheit scale be double the reading on the Celsius scale:

Let the temperature on the Celsius scale is represented by C and the temperature on the Fahrenheit scale is represented by F, then

According to the question;

F=2C

Now, we have, the temperature on the Fahrenheit scale is related to the temperature on the celsius scale by ;

$\frac{C}{5}=\frac{F-32}{9}$

Thus, using the above relation, we get

$\frac{C}{5}=\frac{2C-32}{9}$

$9C=10C-160$

$10C-9C=160$

$C={160}^{0}C$

Therefore the temperature on the Fahrenheit scale will be;

$F=2\times 160$

$F={320}^{0}F$

Thus,

The required temperature is ${160}^{0}C$ on the Celsius scale and ${320}^{0}F$ on the Fahrenheit scale.