In 1787, many years after Robert Boyle’s discovery, Jacques Charles, a French scientist, who was a balloon enthusiast, tried measuring the volumes of a balloon that was filled with a gas at various temperatures. He noticed that the volume of the balloon increases linearly with the temperature of the gas on the Celsius scale.

A modern version of Charles’ experiment uses a capillary tube immersed in a temperature controlled water bath (see diagram below). Air is trapped between the close-end of the tube and a column of mercury, with the open-end of the tube exposed to the atmosphere. The pressure exerted on the gas is therefore constant as the gas expands with increasing temperature *T*.

The linear function can be expressed as:

where *m* is the gradient of the line and *c* is the intercept the line makes with the vertical axis.

When the experiment is repeated with different gases at standard atmospheric pressure, the plots of *V* against *T* always extrapolate to -273.15 ^{o}C at zero volume (see graph below).

Since *c* is the volume of the gas at zero degrees Celsius, *V _{0}*, we can rewrite eq3 as

The gradient of the line is

Substituting eq5 in eq4,

where

In 1848, William Thompson (Lord Kelvin), a British scientist, proposed that the state at -273.15^{ o}C is the lowest temperature that could be achieved theoretically and suggested a new temperature scale called the **absolute thermometric scale** (also known as the **Kelvin scale**), which is related to the Celsius scale by:

Thomson named the temperature of -273.15^{ o}C: absolute zero (0 Kelvin). A new graph can be plotted (see diagram below) where volume is now directly proportional to temperature in Kelvin, i.e.

where *k _{2 }*is the proportionality constant.

Eq7 is eventually called ** Charles’ law**, in Jacques Charles’ honour. It states:

**The volume of a given mass of gas is directly proportional to its absolute temperature (K) at constant pressure**

Since *V _{1}* =

*k*

_{2}*T*and

_{1 }*V*=

_{2}*k*

_{2}*T*,

_{2}*Charles’ law*can also be expressed as

Note that eq6 is also known as *Charles’ law* but with *T* in Celsius. It is less often used than eq7 or eq8.

###### Question

Whether the *V*–*T* graph is plotted using the Celsius scale or the Kelvin scale, it shows that the temperature of -273.15^{ o}C or 0 K corresponds to *V* = 0, which does not seem possible as the gas would have liquefied (*V* ≠ 0) before reaching that temperature. How do we explain this?

###### Answer

The Gay-Lussac experiment is conducted at a relatively low pressure, where the gas is assumed to behave ideally (see this article for details). In reality, a gas exhibits properties that deviate from ideality and requires a different equation for description (see this intermediate level article for details).