Solved Problem on Temperature
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In the Sahara desert, the temperature of X °C was recorded. If the scale used had been Fahrenheit, the reading would be 72 units higher. Determine the value of these temperatures.
Problem data:
- Temperature in the Celsius scale: tC = X °C;
- Temperature on the Fahrenheit scale: tF = tC+72 °F.
The equation for converting temperatures into the Celsius and Fahrenheit scales is given by
\[
\begin{gather}
\bbox[#99CCFF,10px]
{\frac{t_{C}}{5}=\frac{t_{F}-32}{9}}
\end{gather}
\]
substituting the values given in the problem
\[
\begin{gather}
\frac{X}{5}=\frac{X+72-32}{9}\\[5pt]
9X=5(X+40)\\[5pt]
9X=5X+200\\[5pt]
9X-5X=200\\[5pt]
4X=200\\[5pt]
X=\frac{200}{4}\\[5pt]
X=50°C
\end{gather}
\]
\[
\begin{gather}
\bbox[#FFCCCC,10px]
{t_{C}=50\;\text{°C}}
\end{gather}
\]
substituting this value in the relationship between the temperatures given in the problem
\[
\begin{gather}
t_{F}=t_{C}+72\\[5pt]
t_{F}=50+72
\end{gather}
\]
\[
\begin{gather}
\bbox[#FFCCCC,10px]
{t_{F}=122\;\text{°F}}
\end{gather}
\]
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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .