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enth,
When you say a bowl of water is at such-and-such a temperature, that effectively specifies the average kinetic energy in each molecule. At any instant, though, some will have more, some less, according to a standard probability distribution.
The more energetic ones may have enough energy to escape the bowl and become vapour.
At the same time, the water vapour molecules in the air are bouncing around, gaining and losing energy. Some lose so much that they get caught by the water.
When these two processes are in balance, no net evaporation or condensation occurs.
Make the air a bit drier and fewer are available to recondense, so net evaporation does occur. Make the water a bit warmer and more are available to evaporate.
So at a given water temperature, there's a certain density of vapour above it (the saturation vapour pressure at that temperature) at which the system is in equilibrium.
In all cases, evaporation cools the water and condensation heats it.
The fan in your model is there purely to ensure a steady supply of air at the given temperature and humidity (otherwise the air just above the water gets saturated and cold). Similarly, the surface layer of the water will cool first, inhibiting further evaporation, but as long as it's above 4C convection should kick in and redistribute the heat.
Based on the above, you can do the calculation exactly as SophieC said.
temperature drop in bowl = heat required to vaporise lost water / thermal capacity of remaining water.
Once the water starts to cool, it will be cooler than the air above. This means some heat will flow from the air to the water. As a result, the temperature drop will not be quite as great.
When you say a bowl of water is at such-and-such a temperature, that effectively specifies the average kinetic energy in each molecule. At any instant, though, some will have more, some less, according to a standard probability distribution.
The more energetic ones may have enough energy to escape the bowl and become vapour.
At the same time, the water vapour molecules in the air are bouncing around, gaining and losing energy. Some lose so much that they get caught by the water.
When these two processes are in balance, no net evaporation or condensation occurs.
Make the air a bit drier and fewer are available to recondense, so net evaporation does occur. Make the water a bit warmer and more are available to evaporate.
So at a given water temperature, there's a certain density of vapour above it (the saturation vapour pressure at that temperature) at which the system is in equilibrium.
In all cases, evaporation cools the water and condensation heats it.
The fan in your model is there purely to ensure a steady supply of air at the given temperature and humidity (otherwise the air just above the water gets saturated and cold). Similarly, the surface layer of the water will cool first, inhibiting further evaporation, but as long as it's above 4C convection should kick in and redistribute the heat.
Based on the above, you can do the calculation exactly as SophieC said.
temperature drop in bowl = heat required to vaporise lost water / thermal capacity of remaining water.
Once the water starts to cool, it will be cooler than the air above. This means some heat will flow from the air to the water. As a result, the temperature drop will not be quite as great.