Solved Problem on Temperature
Português
English
advertisement
Determine:
a) The temperature with the same numerical value on the Celsius and Fahrenheit scales;
b) The temperature with the same magnitude but with opposite signs on the Celsius and Fahrenheit scales.
Solution
a) The relationship for conversion of temperatures into the Celsius and Fahrenheit scales is given by
\[
\begin{gather}
\bbox[#99CCFF,10px]
{\frac{t_{C}}{5}=\frac{t_{F}-32}{9}} \tag{I}
\end{gather}
\]
with the condition that temperatures should be equal on both scales, we have
\[
\begin{gather}
t_{C}=t_{F} \tag{II}
\end{gather}
\]
substituting the condition (II) into the expression (I), we obtain
\[
\begin{gather}
\frac{t_{F}}{5}=\frac{t_{F}-32}{9}\\
9t_{F}=5\times (t_{F}-32)\\
9t_{F}=5t_{F}-160\\
9t_{F}-5t_{F}=-160\\
4t_{F}=-160\\
t_{F}=-{\frac{160}{4}}
\end{gather}
\]
\[ \bbox[#FFCCCC,10px]
{t_{F}=-40 °\text{F}}
\]
and the condition (II) we also have
e da condição (II) também temos
\[ \bbox[#FFCCCC,10px]
{t_{C}=-40 °\text{C}}
\]
b) With the condition that temperatures must have the same numerical values and opposite signs on the two scales, we have
\[
\begin{gather}
t_{C}=-t_{F} \tag{III}
\end{gather}
\]
substituting the condition (III) in the expression (I), we obtain
\[
\begin{gather}
\frac{-t_{F}}{5}=\frac{t_{F}-32}{9}\\
-9t_{F}=5\times (t_{F}-32)\\
-9t_{F}=5t_{F}-160\\
-9t_{F}-5t_{F}=-160\\
-14t_{F}=-160\\
t_{F}=\frac{160}{14}
\end{gather}
\]
\[ \bbox[#FFCCCC,10px]
{t_{F}=11.4 °\text{F}}
\]
and the condition (III), we also have
\[ \bbox[#FFCCCC,10px]
{t_{C}=-11.4 °\text{C}}
\]
advertisement
Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .