Definition
A similar law was discovered by Jacques Charles and Joseph Louis Gay-Lussac, describing the relationship between volume and temperature.
If the previous setup is modified so that the temperature of the gas can be increased by supplying heat, then a proportionality between volume and temperature can be observed, provided that the number of weights, and thus the piston pressure, is kept constant.
This corresponds to an isobaric process.
Accordingly, Gay-Lussac’s law can be written analogously to Boyle–Mariotte’s law as follows.
Law of Guy-Lussac
The temperature and the volume of a gas volume is given by the constant fraction
$$
\frac{V}{T} = \text{const}
$$
Here, the temperature must of course be expressed in Kelvin in order to obtain meaningful results.
Application
An example of the effect of Gay-Lussac’s law can be seen in gas thermometers or in rooms and containers where the pressure remains approximately constant while the temperature of the enclosed gas changes.
The change in volume with temperature is used in gas thermometers. The glass tube is filled with a gas, which can simply be air. The gas is sealed by a drop of mercury. The mercury drop exerts its weight on the enclosed gas, so that a certain constant pressure exists in the gas.
If the temperature increases, the volume of the enclosed gas increases proportionally. As a result, the mercury drop rises upward. If the temperature decreases, the volume of the enclosed gas decreases, and the mercury drop sinks downward. The height of the mercury drop is thus a measure of the respective temperature. If a scale is attached and the thermometer is calibrated, the temperature can be read directly at the height of the mercury drop.
In living spaces, the pressure is equal to atmospheric pressure. At a given temperature, there is a certain amount of air in such a room. If the temperature is increased by heating, the air expands and takes up a larger volume. Since the size of the room does not change, part of the air escapes. On the other side, if the temperature decreases, the volume of a given amount of air decreases, and outside air would flow into the room.