Problem
A cup of boiling coffee left on the table cools down within a few minutes. Describe the molecular mechanisms of energy transfer to the surroundings (collisions, evaporation, conduction, convection).
Solution
Hot coffee has molecules with a higher mean kinetic energy than those of the air and the table, which are colder. Energy always flows from the hot body towards the surroundings until thermal equilibrium is reached. Four mechanisms act in parallel.
Collisions with the air (conduction/convection at the interface). The fast molecules at the surface of the liquid collide with the slower molecules of the air above and hand over kinetic energy to them: the air in contact heats up and the liquid cools down.
Evaporation. The more energetic water molecules manage to escape from the surface and pass into the vapour phase. They carry away the latent heat of vaporisation: each molecule that leaves removes from the liquid far more energy than its own average share, so the mean kinetic energy of what remains drops. This is the most effective cooling mechanism.
Conduction to the tabletop. The bottom of the cup is in contact with the table: the hot atoms of the glass/ceramic transmit vibration (energy) to the atoms of the table through direct contact, without any transfer of matter.
Convection in the air. The air heated above the cup expands, becomes less dense and rises; cold air takes its place and the cycle repeats, continually carrying away heat.
The dominant contribution in the first few minutes is typically evaporation (high latent heat), aided by convection. The cooling continues until the coffee’s temperature matches that of the surroundings.
Links
Topics: Kinetic theory of gases Concepts: Heat transmission · Latent heat and changes of state Skills: Micro-macro interpretation