Question

What must be the temperature in Fahrenheit so that it will be twice its value in Celsius?

Answer 1

Hint: In order to solve this question we need to understand the temperature and its measurement. Temperature is defined as a parameter to measure how hot or cold a body is. And heat is defined as energy which flows only due to temperature difference. There are three basic scales to measure the temperature of a body, first is Degree Fahrenheit, second is Degree Celsius, and third is Kelvin.

Complete step by step answer:
Now temperature could be measured in all three scales but according to Standard international Units, the standard scale to measure temperature is Kelvin and $0K$ is considered as absolute zero. There are interchange formulas in all three scales. Let the Degree Fahrenheit be denoted as, $F$ and degree Celsius be denoted as, $C$.

So according to problem, let the temperature measure in degree Celsius be $C = T$.So the temperature measured in Degree Fahrenheit would be, $F = 2T$.Since we know, the conversion formula of Fahrenheit and Celsius is given by,
$F = 32 + \dfrac{9}{5}C$
Putting values we get,
$2T = 32 + \dfrac{9}{5}T$
$\Rightarrow 2T - \dfrac{9}{5}T = 32$
$\Rightarrow \dfrac{{10T - 9T}}{5} = 32$
$\Rightarrow \dfrac{T}{5} = 32$
$\Rightarrow T = 5 \times 32$
$\Rightarrow T = 160^\circ C$
So in Fahrenheit temperature would be,
$F = 2T$
Putting values we get,
$F = 2 \times 160$
$\therefore F = 320^\circ F$

Hence, the temperature in Fahrenheit is $320^\circ F$.

Note:It should be remembered that out of three scales, kelvin, Celsius and Fahrenheit, Kelvin is SI unit for temperature measure it is due to fact that Kelvin measurement is independent of working substance in thermometer, it is always positive however Celsius and Fahrenheit both could be negative and thus create error in measurement of temperature, not only at macro scales but at micro also.