# 8th wall formula about the Van der Waals-equation for gases

Despite the rain and awful weather, the painting job has been finished within a week. The Van der Waals-state equation is the eighth Leiden wall formula.

The official opening was Saturday 31 October, the wall formula, painted by artist Jan Willem Bruins, in the presence of emeritus professor Joan van der Waals. Centenarian Van der Waals is a distant relation of Nobel Prize winner Johan Diderik van der Waals, who introduced the equation in his 1873 PhD thesis at Leiden University.

The equation is an addition to the general gas law, that describes the link between temperature  (T), pressure (p) and volume (V) of a so-called ideal gas, which you can imagine as a multitude of infinitesimally small particles that don't collide and don't feel each other. This law did a decent job of describing real gases, but there is a number of measurements and phenomena that it can't explain.

## Attraction

Van der Waals reasoned that the atoms or molecules in a gas occupy a certain volume. This is the term ‘nb’ in the equation. Also, the particles can 'feel' each other: they attract or repel each other. These forces, later coined Van der Waals-forces, are accounted or by the term ‘an2/V2’.

Not only did the new equation predict measurements more accurately, but it also explained phenomena such as liquid water condensing from gas, something that flummoxed the old equation.

The wall, opposite the Stedelijk Gymnasium, belongs to the home of Wim van Saarloos, professor of theoretical physics, and ex-president of the KNAW. Each wall formula consists of the formula itself, a short text (('de structuur der moleculen dicteert het samenspel tussen vloeistof en gas', 'the structure of the molecules dictates the interplay between liquid and gas'), and a graphical illustration.

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## Liquid Surace

In this case, the illustration depicts a spherical volume, with gas molecules (the dark blue dots) above a liquid surface (the dark blue below).

The wall formulas are an initiative of Leiden physicist  Sense Jan van der Molen (Leiden University) and Ivo van Vulpen (University of Amsterdam) and artists Ben Walenkamp en Jan Willem Bruins. Walenkamp and Bruins, operating as the TEGEN-BEELD foundation, are also responsible for more than a hundred poems, painted in many languages on Leiden city walls.

## Poëzie

Just like the poetry in many languages, physics formulas are pithy, on-point descriptions of the world around us, written in a language that not everybody can fully grasp.

All eight Leiden wall formulas are connected to a Leiden scientist. Already, other European cities have bought into the idea, with wall formulas in Utrecht, and plans for them in  Groningen, Copenhagen, Vienna, and Prague.

text: Bruno van Wayenburg