Education
We derive the shape of the phase boundary for solid to gas transitions (sublimation), examples being dry ice (CO2) or ice at low pressure. We derive the van der Waals equation of state, which is an improvement on the ideal gas equation pV=nRT. The ideal gas equation is based on two assumptions: 1. Particles occupy zero volume, and 2. Particles do not interact. Allowing for particles to have a finite size, and also allowing for the fact that at close range, gas particles feel van der Waals attractions, we get the new improved van der Waals equation of state for a gas made of sticky but hard molecules. Van der Waals attractions work because at close range, atoms and molecules notice each other's dipole moments. The dipole moments are due to the fact that at any given instant, the electron cloud is not quite centered on the nucleus of the atom (although it will be centered on average). This instantaneous dipole moment causes atoms in the vicinity to arrange their instantaneous dipoles so as to lower their energy, which causes attraction. It turns out that geckos can cling to walls and ceilings because of van der Waals attractions. Gecko feet have tiny hairs that split many times to make many very fine tips, giving the hairs a very large total surface area. The fine hairs are able to form many contacts with any surface, and the surface-to-hair contact is adhesive due to van der Waals forces. One gecko foot can support the weight of an entire human.Video: Sticky gecko feet, and their van der Waals adhesive properties. Lecture Audio