Charles Law (Volume-temperature relationship)

J. A. C. Charles studied how the volume of a fixed mass of gas responds to a change in temperature at constant pressure, and found that volume is directly proportional to the Kelvin temperature (at constant P and n):

For the same system at constant pressure, comparing two states,

A simple demonstration: a balloon moved from an ice-water bath into boiling water visibly swells (Figure 6.4), because the gas molecules inside move faster at the higher temperature and the balloon must expand to keep the internal pressure matched to the (roughly constant) atmospheric pressure outside.

The V-T graph and absolute zero. Plotting the volume of a fixed mass of gas against its Celsius temperature at constant pressure gives a straight line (called an isobar, Figure 6.5): $V=mT+C$, where T is in degrees Celsius. At $T=0\,^\circ\text{C}$ the volume is some value $V_0$, so $C=V_0$, and the slope $m=\Delta V/\Delta T$, giving

Charles and Gay-Lussac found that this relative increase in volume per degree, $\alpha=\dfrac{1}{V_0}\left(\dfrac{\Delta V}{\Delta T}\right)$, is essentially the same for every gas, and numerically close to $1/273$ -- so at constant pressure, every gas expands by about $1/273$ of its 0 $^\circ$C volume for each one-degree rise in temperature:

If the straight line of Figure 6.5 is extrapolated backwards, beyond any real experimental measurement, it crosses the temperature axis (V = 0) at $-273\,^\circ\text{C}$ (more precisely $-273.15\,^\circ\text{C}$). A gas cannot physically have negative volume, so this extrapolated point marks a genuine lower limit on temperature -- absolute zero -- and it is exactly this point that Kelvin used as the zero of his own temperature scale, the Kelvin scale. The Kelvin and Celsius scales are identical in size of degree; they differ only in where zero is placed (Table, Kelvin vs Celsius). …