- #1

- 55

- 12

- Homework Statement
- https://www.ioc.ee/~kalda/ipho/Thermodyn.pdf

Problem 22 (It contains a drawing so it's better to see it in a booklet than copying here)

- Relevant Equations
- pv = ps(T)

I have a problem at the very beginning. I don't know how to relate this vapour pressure to the temperature difference. I have read the hint:

Recall the idea 7: for dynamical processes, at first, a mechanical equilibrium is reached, which means the equality

of pressures; the other equilibria (e.g. thermal) will be

reached later (if ever within a reasonable time frame).

In particular, this means that if there is evaporation from

a water surface, and because of that, close to the water

surface, there is an higher concentration of water vapours,

then there must be a lower concentration of air molecules.

Indeed, while due to mechanical equilibrium, the total

pressure must remain equal to the atmospheric one, it also

equals to the sum of the vapour pressure and air pressure

13. Equivalently can be said that the air pressure equals

to the atmospheric pressure minus the vapour pressure.

If the saturation pressure ps(T) becomes larger than the

atmospheric pressure patm then mechanical equilibrium is

no longer possible: as we learned earlier, very close to

the water surface, there is thermal quasi-equilibrium and

r = 100% and hence, in that layer, the vapour pressure

pv = ps(T).

The total pressure p in that layer is sum of

the vapour pressure and air pressure, hence p ≥ pv > patm.

Therefore, the vapours at the liquid surface will have larger

pressure than the atmospheric one, and the surrounding

air will be pushed away. Furthermore, if there were a small

bubble inside the liquid, it would also have higher pressure

of vapours inside than the pressure of the surroundings,

hence the bubble would start growing.

It should be noted

that there are always either microscopic bubbles or other

impurities inside the liquid which can serve as evaporation

centres.

But I don't know what is happening the saturation pressure is about 100 times smaller than atmospheric. How could it be bigger than it? Or something else is the case? Could someone explain it to me? I would be very grateful.

Recall the idea 7: for dynamical processes, at first, a mechanical equilibrium is reached, which means the equality

of pressures; the other equilibria (e.g. thermal) will be

reached later (if ever within a reasonable time frame).

In particular, this means that if there is evaporation from

a water surface, and because of that, close to the water

surface, there is an higher concentration of water vapours,

then there must be a lower concentration of air molecules.

Indeed, while due to mechanical equilibrium, the total

pressure must remain equal to the atmospheric one, it also

equals to the sum of the vapour pressure and air pressure

13. Equivalently can be said that the air pressure equals

to the atmospheric pressure minus the vapour pressure.

If the saturation pressure ps(T) becomes larger than the

atmospheric pressure patm then mechanical equilibrium is

no longer possible: as we learned earlier, very close to

the water surface, there is thermal quasi-equilibrium and

r = 100% and hence, in that layer, the vapour pressure

pv = ps(T).

The total pressure p in that layer is sum of

the vapour pressure and air pressure, hence p ≥ pv > patm.

Therefore, the vapours at the liquid surface will have larger

pressure than the atmospheric one, and the surrounding

air will be pushed away. Furthermore, if there were a small

bubble inside the liquid, it would also have higher pressure

of vapours inside than the pressure of the surroundings,

hence the bubble would start growing.

It should be noted

that there are always either microscopic bubbles or other

impurities inside the liquid which can serve as evaporation

centres.

But I don't know what is happening the saturation pressure is about 100 times smaller than atmospheric. How could it be bigger than it? Or something else is the case? Could someone explain it to me? I would be very grateful.

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