Virial Equation of State
The y axis shows the pressure P in pascal, and the x-axis shows the volume V_m of one mole of a substance in cubic metres. Two curves are shown:

• The blue curve shows the ideal gas equation: P=RT/V_m
• The red curve shows the virial equation of state incorporating terms up the the second virial coefficient. P=RT/V_m+B(T)RT/V_m²

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The curves shown correspond argon at a temperature of around 570 K. Notice that:

• Both curves are qualitatively similar.
• The pressures are modestly high: around 200 atmospheres at the top of the graph.
• At this temperature (570 K) the pressure according to the virial equation is slightly higher than one would expect from the ideal gas equation. This is not always the case. At lower temperattures, the pressure predicted by the virial equation falls below that predicted by the ideal gas equation. This effect is illustrated in the movie below.
• The animation below shows the effect of heating argon gas from 270 K up to 570 K. In this range, the virial equation predictions deviate from experiment by only a few parts per million. Notice that at high temperatures, the pressure is slighly greater than would be expected from ideal gas theory. However, at low temperatures, the pressure is slighly less than would be expected from ideal gas theory.

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The equations below show how the graphs were produced in Graphing Calculator