## Saturday, September 3, 2011

### Latent Heat

In Evaporation Rate we considered the rate at which water evaporates from the sea, and in Condensation Point we considered the amount of water that will condense from humid air when it cools down. Today we consider the heat absorbed by evaporating water, and the heat liberated by condensing water vapor.

It takes 2.2 MJ of heat to evaporate one kilogram of water. This heat is called the latent heat of evaporation. Two million Joules is enough energy to raise a 100 kg load to the top of a two thousand meter mountain. It is the energy released by the explosion of a stick of dynamite, or the energy we obtain from eating two jelly donuts.

For the purpose of our simulation, let us suppose that only the top one meter of water supplies the heat of evaporation. The heat capacity of water is 4.2 kJ/kg, so our surface blocks of water will have heat capacity of 4.2 MJ/m2. In an earlier example, we found that roughly 1.8 kg of water will evaporate every hour from each square meter of a lake at 290 K (14°C). The latent heat carried away by the evaporating water will come from the heat of the water it leaves behind, so the lake surface will cool by roughly 1°C/hr.

As we saw in Back Radiation, the lake absorbs heat from the sun during the day, and always radiates heat upwards. In Surface Cooling, Part I, we showed how a water surface heats up by less than 1°C during the day. A lake does not get hot enough with respect to the air above to cause significant convection. Thus heat loss by a water surface is dominated by radiation and evaporation.

When water vapor condenses from cooling, humid air, it releases its latent heat into the air around it. The volume occupied by the water vapor decreases by a factor of a thousand then it condenses, but at the same time its latent heat warms up the air, causing the air to expand. In Condensation and Convection we found that the expansion due to warming dominates the contraction due to condensation by almost an order of magnitude. A single gram of water vapor condensing out of kilogram of air causes the air volume to increase by 1%. When air expands, it becomes buoyant, so it will have latent heat of fusion. This is the heat required to melt ice, which is liberated when the water freezes. Water's latent heat of fusion is roughly 330 kJ/kg. If we have one gram of water freezing in 1 kg of air, the air will warm by roughly 0.3°C.

We can now implement in our Circulating Cells program the evaporation of water from the planet surface, its subsequent condensation into clouds of droplets in rising gas cells, and its eventual freezing into ice crystals. These clouds will, however, have a strong effect upon the manner in which the atmosphere radiates heat into space.

In Thick Clouds we saw how low, thick clouds block the sun's light from reaching the ground, thus causing it to cool down. In High Clouds we saw how thin, high clouds allow the sun's light to pass through, but block radiation by the planet surface, thus causing the surface to warm up.

Before we can implement clouds properly in our simulation, we must consider how to model their effect upon sunlight and radiation.