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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:

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.

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.

## 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.

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.

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

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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