Consider a cylinder that there is water inside it. The volume (and so the pressure) of the cylinder is adjustable by a piston. The thickness of the cylinder and piston is very negligible. The cylinder and piston are perfect thermal conductors. The temperature of the air surround the cylinder is $T_{surr}$.
If at first the temperature of the water is $T_w\gt T_{surr}$ we know that heat will transferred from water to surround air until $T_w=T_{surr}$. We know experimentally that it will take a while for changing $T_w$ to $T_{surr}$. If we decrease the inside pressure of the cylinder to under the vapor pressure of water at $T_w$ quickly before that $T_w$ reaches to $T_{surr}$, what will be happen?
Will the water evaporate before its temperature reaches to $T_{surr}$?
If the water evaporates, then required heat for it comes from where?
If the water doesn’t evaporate, then why?
Thanks in advance.
3 Answers
Some water will evaporate, and the heat required for this comes from the water itself. The water will cool down a little (latent heat of evaporation is a function of temperature, going from about 45 kJ/mol at 0 °C to 40.7 kJ/mol at 100 °C). The heat capacity of water is about 75 J/mol K. This means that evaporating one gram of water would extract enough heat from 600 gram of water to cool it down by one degree Celsius.
Evaporation is a really effective way to extract heat - it's why sweating works...
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$\begingroup$ Thank you because of your attention. I think so. I think the heat required for evaporation comes from the water itself. What I couldn’t get is “why we need to decrease the temperature of acting fluid in the vapor-compression refrigeration cycle to under the temperature of cold space (in a refrigerator) for cooling that space?” $\endgroup$– lucasCommented May 10, 2016 at 10:11
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$\begingroup$ If you want to make something (the cold space in the fridge) colder, then you need the heat to flow out of the cold space to somewhere else. And heat will only flow from hot to cold - or in this case, from cold to colder. That is why the working fluid of the refrigerator has to end up at a lower temperature than the thing you want to cool down. $\endgroup$– FlorisCommented May 10, 2016 at 10:17
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$\begingroup$ I know this. What I mean is we can make that space colder without doing additional work for decreasing the temperature of the worker fluid to under the temperature of the cold space. $\endgroup$– lucasCommented May 10, 2016 at 10:25
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$\begingroup$ If the temperature difference is very small the heat flow will be very slow. But there must always be a gradient. $\endgroup$– FlorisCommented May 11, 2016 at 0:31
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$\begingroup$ So, you say we can make cold even if the temperature of the worker fluid doesn't decrease to under the temperature of the cold space. But it takes much time. Is this your meaning? $\endgroup$– lucasCommented May 11, 2016 at 4:23
Some of the water will evaporate. Keep in mind that not all of the water molecules have the same energy, some are moving faster than others. The temperature measurement indicates the average energy of the water molecules.
When the piston is lifted, some of the faster molecules will escape the liquid to become water vapor. The remaining molecules have a lower average energy, and hence a lower temperature.
The water will continue to evaporate until the vapor pressure reaches the equilibrium point. In equilibrium, the average number of molecules escaping the liquid over time is equal to the number of molecules being captured by the liquid.
Evaporation can be assisted by adding heat, but adding heat is not required for evaporation. In the absence of an external heat source, the latent heat of evaporation is taken from the water itself, causing the water temperature to drop.
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$\begingroup$ Thank you because of your attention. We know that evaporation needs heat. Which source does provide that heat? $\endgroup$– lucasCommented May 9, 2016 at 22:21
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$\begingroup$ @lucas I've added more to the answer. Hope it helps. $\endgroup$ Commented May 9, 2016 at 22:29
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$\begingroup$ "adding heat is not required for evaporation" If it is true, then what is the latent heat? $\endgroup$– lucasCommented May 9, 2016 at 22:33
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$\begingroup$ Latent heat is "the heat required to convert [...] a liquid into a vapor without a change in temperature". Quote from the New Oxford American Dictionary, emphasis added. Note that in a closed system, the water temperature drops, as molecules escape to the vapor phase. So the temperature does change. $\endgroup$ Commented May 9, 2016 at 22:40
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1$\begingroup$ @lucas, the heat that evaporates the water comes from the water ITSELF. With this being the case, the water temperature has to drop. And if you are wondering regarding your question to user3386109, I happen to be one of those people who does know how a refrigerator works ... to the degree that I have written a program to implement 25 simultaneous equations for a dynamic simulator for this process. $\endgroup$ Commented May 10, 2016 at 0:20
When pressure is below the vapor pressure, evaporation occurs. Accompanying to phase change (evaporation), heat is required, which reduces the water's temperature and its vapor pressure needs to be even lower. So you need continue to reduce pressure in order to keep evaporation continue. Otherwise, it will stop.
When it reaches or lower (transient) than the surrounding temperature, you still need to reduce pressure. But this time, it is to overcome the pressure increase due to increase in water vapor from the evaporation. One need to continue reducing pressure in order to keep it evaporating. Otherwise it will stop evaporating.
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$\begingroup$ Thank you because of your attention. I couldn't get your answer. $\endgroup$– lucasCommented May 10, 2016 at 10:12