Charles' Law

• Named after pioneer balloonist Jacques Charles
• The volume of a fixed mass of gas is directly proportional to its absolute temperature given that its pressure is constant:

$$ \begin{equation}\begin{aligned} V&\propto T\\ V&=kT\ OR\\ \frac{V}{T}&=k\\ \end{aligned}\end{equation} $$

Thus we can have $\frac{V_1}{T_1}=k$ and $\frac{V_2}{T_2}=k$. Combining these two we get: $$ \begin{equation}\begin{aligned} \frac{V_1}{T_1}=\frac{V_2}{T_2}\\ \end{aligned}\end{equation} $$ Where $V_1$ and $T_1$ are associated as are $V_2$ and $T_2$.

Example

A balloon of volume $0.006\ m^3$ is kept at a temperature of $0\degree C$. What would be the new volume if the temperature were to be raised to $91\degree C$?

Mission details

A piston made to be used as part of a Stirling Engine is shown to have a maximum volume of $0.028\ m^3$ when filled with air at room temperature ($20\degree C$). What temperature in $\degree C$ would the piston have to be balanced at in order to have the volume of the air stay at a value of $0.024\ m^3$?