Why does bath water get cold?

Bath water cools off because it starts off warmer than its environment. Nature tends to have forces in play that even extremes out and this is no exception. The heat leaves the tub by several routes:

• Conduction: The heat in the tub water raises the temperature in the tub walls, the floor it sits on and the pipes it is attached to.
• Convection: The hated air over the tub rises to be replaced by cooler air which inn turn is heated and rises. The rising warm air carried heat away from the tub water.
• Radiation: Like the warmth you feel near a fire the heat from the tub radiates away from the tub heating the nearby objects
• Evaporation: The principle means of heat loss is evaporation. Hot water molecules leave the tub carrying away heat. They are responding to the dryness of the air in the bathroom. Eventually th bath water temperature will cool to the wet bulb temperature of the room. This is measure of the humidity in the room, but it is usually cooler than the air temperature you sense.