# 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?

• No it doesn’t. A certain amount of gas (counting molecules/atoms) will always occupy a specific volume at a certain pressure. Otherwise Earth’s atmosphere would extend into infinity, too, wouldn’t it?
– Jan
Commented Oct 8, 2015 at 13:25

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.

• Yes, but what if it was in a hard container, such as a glass jar? It wouldn't be able to expand 1/273 of the volume. (What I'm meaning to say is, if a balloon is filled up with gas that matches the volume of a glass jar, and the same glass jar is filled with the same amount of gas (in mass) than when the temperature rises by 1 degree Celsius, the glass jar couldn't expand to fit the gas.) Commented Sep 7, 2015 at 14:12
• If it is a rigid container then the pressure rises by a factor of 1/273. According to my knowledge it is impossible to rise the temperature by keeping both pressure and volume constant. Commented Sep 7, 2015 at 14:21
• That makes sense. But in my textbook it speaks as if the volume must be increased Commented Sep 7, 2015 at 15:36
• The glass jar your are referring to, may blast due to the increase in volume. But I assume that is not the case. Commented Sep 7, 2015 at 15:40
• Yes, so is this a limitation to Charles's law? The pressure may increase but does the Volume HAVE to increase? It is the same case in balloons, surely the balloon limits the increase of volume at least somewhat? Commented Sep 7, 2015 at 22:55

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: $$\Delta V = \left(\frac{\Delta T}{T_1}\right)V_1$$

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