Question

You work in a materials testing lab and your boss tells you to enhance the temperature of a sample by $40.0{}^\circ C$. The only thermometer you are having at your workbench will read in ${}^\circ F$. Let us assume that the initial temperature of the sample is $68.2{}^\circ F$. What will be its temperature in ${}^\circ F$, if the required temperature increase has been achieved?

Answer 1

Hint: The temperature at Fahrenheit scale will be equivalent to nine times the temperature at Celsius scale divided by five and a thirty two is added to it. Find out the temperature increment in the Fahrenheit scale using the temperature increment in the Celsius scale. This will help you in answering this question.

Complete answer:
As we all know the temperature at Fahrenheit scale will be equivalent to nine times the temperature at Celsius scale divided by five and a thirty two is added to it. This can be written as an equation like,
${{T}_{F}}=\dfrac{9}{5}{{T}_{C}}+32$
The temperature increment in the Fahrenheit scale can be written as,
$\Delta {{T}_{F}}=\dfrac{9}{5}\Delta {{T}_{C}}$
It has been already given that the temperature increment in the Celsius scale can be written as,
${{T}_{C}}=40.0{}^\circ C$
Substituting this value in the equation will give,
$\Delta {{T}_{F}}=\dfrac{9}{5}\times 40=72{}^\circ F$
The initial temperature in the Fahrenheit scale has been mentioned in the question as,
${{T}_{I}}=68.2{}^\circ F$
Therefore we can write that,
$\Delta {{T}_{F}}=T-{{T}_{I}}$
Substituting the values in the equation will give,
$\begin{align}
  & 72=T-68.2 \\
 & \Rightarrow T=72+68.2=140.2{}^\circ F \\
\end{align}$
Therefore the final temperature in the Fahrenheit scale can be written as,
$T=140.2{}^\circ F$
Therefore the temperature has been calculated.

Note:
The Fahrenheit scale is defined as a temperature scale which uses the degree Fahrenheit as the unit. The degree Celsius is the unit for measuring temperature on the Celsius scale. This scale of temperature is initially called the centigrade scale. ​