Thermal Expansion of Liquids and Gases

Thermal Expansion of Liquids and Gases

Liquids

A liquid has no fixed shape of its own -- it simply takes the shape of whatever vessel holds it -- so it

makes no sense to talk about a liquid's "length" or "area" changing with temperature. A liquid is

therefore described only by a single coefficient, its coefficient of cubical (volume) expansion,

$\gamma$, defined exactly as for a solid: $V = V_0(1 + \gamma\,\Delta T)$.

A liquid, however, is always held inside some container, and the container material itself also expands

on heating. What is actually observed when a liquid is heated in a graduated vessel -- the apparent expansion of the liquid -- is therefore always somewhat less than the liquid's true, real (or absolute) expansion, because part of the space the liquid's true expansion would otherwise have

occupied is used up simply keeping pace with the extra volume the container itself has gained. The three

quantities are related by

Liquids, in general, expand considerably more for the same temperature rise than solids do (a typical

liquid's $\gamma$ is roughly ten to a hundred times a typical solid's $\gamma$), because the

intermolecular forces holding neighbouring liquid molecules loosely together are much weaker than the

rigid lattice bonds holding a crystalline solid's atoms in place, so the same increase in the average

kinetic energy of vibration/motion produces a much larger increase in average molecular separation in a

liquid.

Gases

Gases expand still more than liquids for a given rise in temperature, and their expansion follows

directly from the ideal-gas equation of state, $PV = nRT$ (where $n$ is the number of moles of gas and

$R$ is the universal gas constant). At constant pressure, this equation shows that volume is directly

proportional to the absolute (Kelvin) temperature -- a result also known, on its own, as Charles's law:

An important and distinctive feature of gas expansion is that, unlike a solid's $\alpha$ or a liquid's

$\gamma$, an ideal gas's coefficient of volume expansion does not depend on which particular gas is …