Why does steam condense in a cold bathroom

In the previous example, we looked at the interactions induced when changing the external pressure, forcing the molecules into close proximity. We look here at the effects of changing the temperature. 

A bathroom mirror is usually colder than the temperature of the steam rising from a hot bath. Each molecule of steam (gaseous water) has an enormous energy, which comes ultimately from the boiler that heats the water. The particles of steam would remain as liquid if they had less energy. In practice, particles evaporate from the bath to form energetic molecules of steam. We see this energy as kinetic energy, so the particles move fast (see p. 30). The typical speeds at which gas particles move make it inevitable that steam molecules will collide with the mirror. 

We say such a collision is elastic if no energy transfers during the collision between the gas particle and the mirror but if energy does transfer - and it usually does - we say the collision is inelastic. 

The energy transferred during an inelastic collision passes from the hot molecule of steam to the cooler mirror. This energy flows in this direction because the steam initially possessed more energy per molecule than the mirror as a consequence of its higher temperature. It is merely a manifestation of the minus-oneth law of thermodynamics, as discussed in Chapter 1. 

But there are consequences to the collisions being inelastic the molecules of steam have less energy following the collision because some of their energy has transferred. 

---