Charles's Law confusion

Charles's Law states that for every 1 degree Celsius increase in temperature of a gas, the volume increases by 1/273 of the original volume (at constant pressure). 


What I am wondering is, doesn't gas have an indefinite volume, therefore it is not possible for it to have volume at all? Am I missing something here?




A gas occupies the volume of whatever the container it is in. Take a balloon filled with Helium for example. Now the volume of Helium gas is the volume of the ballon. 


If you increase the temperature by 1 °C at constant pressure the volume of the balloon increase by 1/273th of the original volume of the balloon. Hope this might clear things up. 


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Charles law is for gases at constant presure which in the real world requires a vessel for containment and thus the gas would occupy the volume of its conatiner. 
$$ \text{Charles Law:}\qquad \frac{V\_1}{T\_1} = \frac{V\_2}{T\_2} \implies \frac{T\_2}{T\_1} = \frac{V\_2}{V\_1 } \qquad{P\_1 = P\_2}$$


For Example: for $T\_1 = \pu{273K}$ and $T\_2 = \pu{274K}$:
$$\frac{T\_2}{T\_1} = \frac{\pu{274K}}{\pu{273K}} = \frac{V\_2}{V\_1} = \frac{274\times V\_1}{273\times V\_1} = \left(1 + \frac1{273}\right)V\_1$$


Your statement that a 1 degree Celcius increase in temperature results in a $\frac1{273}$ increase in volume is only true at $\pu{0^\circ C}$ or rather $\pu{273K}$. A $\pu{1^\circ C}$ increase at $\pu{1^\circ C}$ or $\pu{274 K}$ results in a $\frac1{274}$ expansion of the gas. More generally:


$$\color{blue}{1 + \frac{\Delta T}{T\_1}} = \frac{T\_1 +\Delta T}{T\_1} = \frac{V\_1+\Delta V} {V\_1} = \color{blue}{1 + \frac{\Delta V}{V\_1}}\\
\\
\color{blue}{1 + \frac{\Delta T}{T\_1} = 1 + \frac{\Delta V}{V\_1}} \implies \frac{\Delta T}{T\_1} = \frac{\Delta V}{V\_1}\implies \Delta V = \left(\frac{\Delta T}{T\_1}\right)V\_1$$
Thus $\Delta V$ is dependent on $T\_1$ for a given temperature change:
$$\Delta V = \left(\frac{\Delta T}{T\_1}\right)V\_1$$


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Simply Charle's Law(change in volume is directly proportional to change in temperature) is true with the assumption of constant pressure. 


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