[Physics] Confusion about energy taken to evaporate water with air instead of heat

energy-conservationthermal-radiationthermodynamics

So I know that water will take up 4200 J/Kg°C (specific heat capacity) if we heat it. Then when it reaches 100°C, it will take 2260kJ/Kg (latent heat of vaporisation) until all the water is gas. Then it takes the steam's specific heat capacity at its pressure as it continues to increase in temperature.

But what happens when, say, a powerful fan, evaporates water from the surface of the water? Here there is no "energy" being provided to the water, so it (the bulk of it, at least) remains at the same temperature as opposed to evaporation following boiling. But if the water at the surface manages to evaporate, that means some energy must be taken from the surroundings!

It helps to use examples. Suppose 5 kg of water evaporated by boiling and another 5 kg evaporated by a powerful fan.

Can I say that in the fan situation too, the water at the surface took 4200kJ/Kg°C until it reached 100°C; then it took in 2260Kg°C until it all became steam?

Does this mean both cases take in the same amount of energy? Thanks in advance.

Best Answer

But what happens when, say, a powerful fan, evaporates water from the surface of the water? Here there is no "energy" being provided to the water, so it (the bulk of it, at least) remains at the same temperature as opposed to evaporation following boiling. But if the water at the surface manages to evaporate, that means some energy must be taken from the surroundings!

Although the temperature of a liquid is a measure of the average kinetic energy of the molecules of the water, individual molecules can have velocities (and thus kinetic energy) above and below the average.

Evaporation only occurs at the surface of the water. It is due to the fact that that some of the water molecules at the surface have higher velocities (they are more energetic). These molecules may have sufficient energy to overcome the intermolecular attractive forces between molecules at the surface, allowing them to fly off and become gaseous H$_2$O molecules above the surface. The average kinetic energy of the molecules remaining at the surface becomes lower, cooling the water at the surface. This is called evaporative cooling.

A powerful fan blowing air across the surface removes water vapor near the surface (lowers the vapor pressure) making it easier for the more energetic water molecules at the surface to escape. In effect, the fan increases the rate of evaporation at the surface.

Hope this helps.