phase transitions are complicated. when something is a gas that rule applies because the forces between the constituent particles are neglible except for the el

phase transitions are complicated. when something is a gas that rule applies because the forces between the constituent particles are neglible except for the electromagnetic interaction causing scattering (i.e. particles bouncing off each other, or the surroundings). this is the pressure from that formula. increasing temperature increases the energy in the system, resulting in more collisions, and more pressure. decreasing it results in less as you correctly point out. in a solid the electromagnetic interaction is constantly present and locks the constiuent particles nearly in place, so that when excited they 'vibrate' around their location, rather than moving freely like in a gas. this has different consequences, so that decreasing the temperature will increase the rigidity of the material since the particles will become ever less likely to achieve the energy required to escape their electromagnetic 'traps'.