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Graphs of Charles's Law

08th Nov 2019 @ 3 min read

Physical Chemistry

The graph of Charles's law is a volume-temperature graph. And it is as follows:

Charles's law graph
The plot in the volume vs temperature (in K) graph is a straight line passing through the origin.

The above graph is a volume vs temperature graph plotted as a constant pressure for a fixed amount of gas. As we can observe from the graph the volume increases with an increase in the temperature, and vice versa. Thus, volume is directly proportional to temperature at a constant pressure, which is the statement of Charles's law.

Atkins Physical Chemistry

Mathematical explanation

Volume is on the y- axis, and temperature is on x-axis. The graph is a straight line with a positive slope passing the origin. The equation of the line is V = kT, which is the equation of Charles's law. The slope of the line is k. As temperature approaches zero kelvin, volume also approaches zero.

Limit: As temperature tends to zero, volume tends to zero.

According to the graph, the volume of an ideal gas at zero kelvin is also zero.

Note: Real gases do not obey Charles's law at low temperatures. As temperature approaches absolute zero (0 K), the real gases start deviating significantly from Charles's law.

The graph of Charles's law in the celsius scale

In the above plot, the temperature axis is in the kelvin scale (absolute scale). However, we can also plot the graph of Charles's law with temperature in the celsius scale.

The graph of Charles's law
The plot is a straight line making x-intercept at −-273.15 °C

The equation of the line in the above figure is Charles's law equation. Here, V0 is the volume at the freezing point of water, t is temperature in the degree celsius, and V is volume at temperature t. This is also the equation of Charles's law when temperature is expressed in the degree celsius.

As from the above figure, when temperature approaches −273.15 °C, volume also approaches zero.

Volume tends to zero at −273.15 °C.

Graphs at different pressures

The above plots can be plotted at different pressures. The graphs below show four different lines. Each of the lines is at a constant pressure. Such lines that are drawn at a constant pressure are called isobars.

Charles's law graph at different pressures.
Volume vs temperature (in K) at different pressures

As we can see in the above figure, each of the lines converges at zero volume as temperature tends to zero. Also, if noticed, with an increase pressure, the lines shift inwards (towards x-axis). This is because of a decrease in the value of k with an increase in pressure. The same is true for the below figure except each of the lines converges at −273.15 °C.

Volume vs temperature (in °C) at different pressures
Volume vs temperature (in °C) at different pressures

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