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I wonder if there is any law for heat exchange. I have learnt that heat exchange between systems occurs when the temperature of respective systems differ. But in case of evaporation, the process creates a cooling effect even in an isothermal condition ( I mean by isothermal condition to be a isothermal situation between the evaporating liquid and the surrounding).

I would like to discuss the cooling effects produced by evaporation under isothermal condition.

If I am wrong in saying that, evaporation is possible at isothermal process, please correct me.

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Cooling effect doesn't necessarily mean fall in temperature.

For example, if I have 1 mole of water at 273 K, some 0.3 moles can spontaneously evaporate, producing water vapor at 273 K, thereby forming ice at 273 K from the rest 0.7 moles.
(NOTE: values are not actual ones, just for explaining this example).
Now you can see that this process is isothermal, but part of the water which evaporates produces a "cooling effect" on the rest, ultimately freezing it.

Also note that the process i described above might not be spontaneous practically, in terms of entropy change and change in Gibbs' free energy

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@udiboy-The case that you are using here is a situation where the liquid exists in equilibrium with its vapour phase. But take this experiment conducted by Benjamin Franklin for analysing the cooling effects of evaporation : en.wikipedia.org/wiki/Benjamin_Franklin#Concept_of_cooling Here, actual fall in temperature occur –  karthikeyan Jun 30 '13 at 6:01
    
In the experiment described by Franklin, the water is reducing the temperature of its **surrounding**(the thermometer or the body of Franklin), not of itself. I believe that the water might still be at room temperature(Even though the thermometer is at 7 F!) –  udiboy Jun 30 '13 at 18:00
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The concept is evaporative cooling. Essentially a liquid does work on the environment by expanding itself, thereby lowering its own internal energy.

This expansion is made possible by the fact the the liquid can convert itself into gas. The particles that manage to do this are on average possessing more KE than the other particles (remember that particle KE are not uniform but follow a Boltzmann distribution, and only particles with enough KE to break intermolecular bonds can become gas), in other words evaporation causes the remaining liquid to have on average, lower KE particles (a drop in temperature). Necessarily the particles that managed to escape are at the appropriate higher temperature, and as a result expand the volume they take up (do work) until back in thermal equilibrium with the liquid or environment or both. The result is both the liquid and it's vapor blanket being a lower temperature than before being exposed.

If there is zero convection of this vapor then net evaporation eventually stops (condensation of the vapor back into the gas liquid interface equals evaporation) and the cooling effect ceases. if the whole shebang is enclosed in fixed volume then temperature as well as pressure will increase (heat is from environment) until all the water and water vapor is at environment temperature. The gas pressure of this vapor is know as the vapor pressure, which is dependent on temperature.

In reality, convection is non zero. There are breezes, and warm vapor rises away on its own, creating more opportunity for the liquid to vaporize and continue losing energy by losing its fastest particles to the environment. Exposed water bodies are typically a few degrees below air temperature because of this.

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