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Graphs of Gay-Lussac's Law

20th Dec 2019 @ 2 min read

Physical Chemistry

The graph of the Gay-Lussac's law is a plot of pressure versus temperature. The pressure-temperature graph is as follows:

Gay-Lussac law graph
The graph is a straight line passing through the origin.

From the above graph, pressure increases with an increase in temperature, and vice versa. Thus, pressure is directly proportional to temperature. The graph is plotted at constant volume and a constant amount of gas, and temperature is expressed in the kelvin i.e. absolute temperature.

Mathematical explanation

Pressure is on the y-axis, and temperature is on the x-axis. The graph is a straight line with a positive slope passing the origin. The equation of the line is P = kT, which is the equation of Gay-Lussac's law, and the slope of the line is k. As temperature approaches zero kelvin, pressure also approaches zero.

Pressure is zero when temperature is zero.

Thus, pressure is zero when temperature is zero as per Gay-Lussac's law.

Note: The above graph is applicable for ideal gases. Real gases do not obey Gay-Lussac's law at higher pressures and/or lower temperatures.

In the celsius scale

When temperature is expressed in the degree celsius, the graph is a straight with the x-intercept at −273.15 °C.

Gay-Lussac's law Graph in the celsius scale
Gay-Lussac's law Graph in the celsius scale

Graphs at different volumes

The above graphs can be plotted at different volumes. When a line is plotted at constant volume, it is called an isochore. Therefore, each of the lines below is an isochore.

The graph of Gay-Lussac's law at different volumes
The plots are straight lines passing through the origin.

In the above graph, all the lines converge at the origin. As said earlier, each line is an isochore. When volume increases, the lines shift downwards. This is because the slope of lines decreases with volume.

Gay-Lussac's law graph in °C at different volumes
The plots are straight lines with the x-intercept at −273.15 °C.

In the above figure, temperature is in the degree celsius scale. All the lines converge at −273.15 °C when pressure tends zero.

The graph of Pressure by temperature versus temperature
The plots are straight lines parallel to x-axis.

From the above graph, the lines are parallel to the x-axis. The ratio of pressure to temperature is constant. It is independent of volume to temperature.

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