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In the descriptions below, I always assume external pressure to be constant at 1 atm, the condition where daily observations are made.

1) When I exhale on a mirror, liquid water forms on the mirror. That's condensation. Obviously, the temperature of mirror must be < 100 °C, so water vapor condensing on mirror makes sense. However, in that case why do we have water vapor in our breath when our body temperature is also < 100 °C in the first place?

2) One reason for (1) may be like 'water vapors in air is in equilibrium with liquid water', so some water vapors can exist although T < 100 °C. If this is correct, based on this reasoning, then why doesn't ice exist at T > 0 °C? [p = 1 atm only]

3) If liquid water can evaporate into gas at T < 100 °C, then why doesn't ice turn into liquid at T < 0 °C? (I never use the term 'melt' here, just like evaporate≠boil) (both have hydrogen bonds, intermolecular forces should be the same?)

4) When I exhale on a wall, no water droplets form. Why do water droplets form on mirror but not on wall (just an example)? The mirror must have the same temperature as that of the wall, both of them must have achieved thermal equilibrium with their surroundings a long time ago.

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    $\begingroup$ Posting as a comment because I have no references to back this up, perhaps someone else knows more. I have understood the difference in gas:liquid vs. liquid:solid balances to be caused by the molecules being more separated in the gas phase. If a molecule of water has enough kinetic energy to escape from ice crystal but remains bound as liquid, it is so close to the ice that it would settle back quickly. But if it has enough energy to go flying as gas molecule, it takes time until it settles back somewhere, and the equilibrium between escaping and settling back determines the concentrations. $\endgroup$ – jpa Mar 11 at 8:56
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    $\begingroup$ "If liquid water can evaporate into gas at T < 100 °C, then why doesn't ice turn into liquid at T < 0 °C?" is probably worthy as a question of its own (if done well). $\endgroup$ – A.K. Mar 11 at 16:01
  • $\begingroup$ If your look at the pressure melting point Ice can turn into liquid at T < 0 °C by raising the pressure. $\endgroup$ – A.K. Mar 11 at 16:09
  • $\begingroup$ @jpa your answer to part (3) makes sense to me. It would be good if someone knows more can actually confirm it. $\endgroup$ – The99sLearner Mar 13 at 13:31
  • $\begingroup$ @A.K. If I refer to the phase diagram, it shows that at 100kPa and 0°C<T< 100°C water should exist as pure liquid, yet commonly said that pure liquid has vapor pressure i.e be in equilibrium with its vapor in a closed container.Some water exists as vapor. This makes me wonder what does the word 'liquid' actually means in the phase diagram. Label it 'liquid' despite there being both 'liquid' and 'vapor'. $\endgroup$ – The99sLearner Mar 13 at 13:39
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Why do we have water vapors when our body temperature is also <100°C in the first place?

At normal pressure, water boils at 100°C, meaning that bubbles of pure steam form under water. At lower temperatures, water molecules reversibly move from the liquid to the gas phase and back. The higher the temperature, the higher the vapor pressure, and the higher the equilibrium concentration (partial pressure) of water in air. On the geological scale, there is no equilibrium, and we experience different temperatures, different humidity (related to partial pressure of water in air), and different pressures depending on location.

Why does ice not exist at T>0°C

Ice, as a pure solid, and water, as a pure liquid, have defined concentration at given pressure and temperature (the equilibrium constant expression for melting includes neither liquid nor solid water, it is simply 1). Above the melting temperature, all the ice melts, there is no equilibrium. This is different from the liquid:gas equilibrium, which exists at temperatures below the boiling point, with lower and lower concentrations of the gas as the temperature drops (here, the equilibrium constant expression included the concentration or partial pressure of water vapor).

If liquid water can evaporate into gas at T<100°C, then why not ice turns into liquid at T<0°C?

Again, this has to do with pure liquids and pure solids having a constant (or nearly constant) concentration. If you add salt to the liquid, however, ice will turn into liquid below the freezing point (effectively lowering the concentration of water in the liquid). Also, the surface of the ice melts at lower temperature than the bulk, so even for pure water, there can be liquid at temperatures below the bulk freezing point.

When I exhale on a wall, no water droplets form.

I would do an experiment and check. I think the water droplets are easier to see on a mirror. Try a grand piano (i.e a smooth surface painted with shiny black paint), you might see the water droplets there as well. Or take a long hot shower and check whether water droplets form on surfaces other than a mirror.

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    $\begingroup$ It should be noted that ice does turn into a gas at T<0°C readily enough. $\endgroup$ – Luaan Mar 11 at 8:30
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    $\begingroup$ w.r.t the last paragraph: how about a tiled wall? With normal fairly shiny tiles in a cool room the fogging should be clear, especially if you arrange a reflection of a light $\endgroup$ – Chris H Mar 11 at 16:17
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    $\begingroup$ @ChrisH I tried tiled wall before, it feels slippery after exhalation, but at first I actually tried concrete wall which I saw and felt no presence of water. $\endgroup$ – The99sLearner Mar 11 at 23:05
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    $\begingroup$ @The99sLearner I suspect concrete soaks up the water more than many other surfaces. On a porous surface, and you'll be unlikely to feel the moisture easily. $\endgroup$ – Roland Heath Mar 12 at 2:38
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    $\begingroup$ Water and vapour is not usually in equilibrium with liquid water under normal conditions. Condensation happens because the local situation is far from equilibrium: a cold mirror causes a local condensation because the temperature near the mirror is below the temperature of the surrounding air and the water vapour concentration in breath is higher than the concentration in the surrounding air. As the mirror warms or the surrounding air absorbs the local excess the condensation evaporates. $\endgroup$ – matt_black Mar 12 at 13:41
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The major difference is that in vapor phase, the water can leave the container (so you can tell it's in a different form), and which prevents it from immediately rejoining the liquid.

In both solid/liquid phases, the water remains in the rest of the bulk. A few molecules of liquid in a solid or a few molecules of a solid in a liquid won't be detectable, and any created will almost immediately return to the thermodynamically favored state.

why do we have water vapors when our body temperature is also <100°C in the first place?

Water exists in different forms in equilibrium. At body temperature, the equilibrium is for vapor until the vapor pressure exceeds about 7kPa. So it's expected for there to be a certain quantity of vapor present.

why not ice exists at T>0°C? [p=1atm only]

Let's imagine that there is an equilibrium between liquid-vapor and between liquid-solid.

When a bit of vapor forms, the vapor can move away from the bulk liquid. There it can be detected on its own (or mixed with other atmospheric components).

If a few molecules were to form bonds similar to that of ice within the water, the same doesn't happen. They remain within the bulk and wouldn't be detectable. Ice is a bulk phenomenon and doesn't really behave like familiar ice until you've got a lot of molecules bonded together in one place, and that's not favored at room temperature.

If liquid water can evaporate into gas at T<100°C, then why not ice turns into liquid at T<0°C

It does. There is an equilibrium between the liquid and the solid forms. Especially near the freezing point, there will be some molecules that leave the bonding and are not part of the ice crystal. But because the equilibrium points to the solid form, they will be only a tiny part of the mass and will not be seen.

In fact, there will still be some vapor as well. Even below 0°C, the vapor pressure is still positive.

Why water droplets form on mirror but not on wall(just an example)?

The finish of the glass makes a collection of even tiny drops visible. The appearance of the mirror/glass normally is dominated by light from specular reflection. Condensation droplets scatter the light, creating more diffuse reflections. A normal wall will already show diffuse reflection, so adding a little bit of condensation doesn't change that. You have to actually see the drops to notice them, and that only happens when the drops get a bit bigger.

If I look at phase diagram of water, under that conditions we actually have 'liquid', while I understand there should be vapor pressure in equilibrium, details from phase diagram contradicts with the fact. What is the meaning of 'liquid' in the phase diagram then?

In that region of the diagram, it is thermodynamically favorable for the liquid phase to exist in bulk. Outside of that region, even with sufficient amounts of water, any bulk liquid will tend to transition to vapor or solid.

can my ice actually disappear completely at T<0°C, just like liquid water evaporates completely leaving empty bucket?

Absolutely. Leave an ice cube in your freezer alone and it will sublimate away. The vapor pressure is still positive, so some amount of it turns to vapor. That vapor is replaced by dry air from the condenser coils and the ice cube shrinks over time.

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  • $\begingroup$ *Numbers refer to parts of question in this post. My further questions are based on your answer. 1) 'At body temperature, the equilibrium is for vapor until the vapor pressure exceeds about 7kPa.' If I look at phase diagram of water, under that conditions we actually have 'liquid', while I understand there should be vapor pressure in equilibrium, details from phase diagram contradicts with the fact. What is the meaning of 'liquid' in the phase diagram then? 2) Answer by BowlOfRed $\endgroup$ – The99sLearner Mar 13 at 14:11
  • $\begingroup$ 3) 'Especially near the freezing point, there will be some molecules that leave the bonding and are not part of the ice crystal.' Assuming this is true, if I somehow manage to remove that part of water which is 'not part of the ice crystal',can my ice actually disappear completely at T<0°C, just like liquid water evaporates completely leaving empty bucket? 4) Answer by Geoffrey Brent and jeffB $\endgroup$ – The99sLearner Mar 13 at 14:14
  • $\begingroup$ @The99sLearner You're missing one important thing - phase diagrams show what happens to a material in an ideal closed container. That is, if you have a full can of water at 32 °C at standard pressure, it will be liquid, and if it's at 110 °C, it will be a vapor. But the same is not true if you have an open can - water at 32 °C will then tend towards an equilibrium given roughly by the vapor pressure of the liquid and the partial pressure of the gas. The same is true of ice, but there the equilibrium tends to be skewed towards liquid/gas - it's hard for the solid phase to form spontaneously. $\endgroup$ – Luaan Mar 14 at 7:23
  • $\begingroup$ @The99sLearner All liquids always evaporate (or solidify) - even liquids like mercury at standard conditions (though that takes thousands of hours per gram!). Strictly speaking this is true even in the closed container, however, you need to account for the fact that the inside is not going to stay "standard" - any liquid that evaporates greatly increases the pressure (1L of water produces about 1700L of steam at the same pressure!), which makes it liquify again almost instantly. So there's still an equilibrium between the liquid and gas, but I doubt the gas is even measurable. $\endgroup$ – Luaan Mar 14 at 7:27
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When I exhale on a wall, no water droplets form. Why do water droplets form on mirror but not on wall (just an example)? The mirror must have the same temperature as that of the wall, both of them must have achieved thermal equilibrium with their surroundings a long time ago.

Yes, the mirror and the wall will be at the same temperature, but that's only part of the story.

Put one hand on a mirror, and the other on the wall next to that mirror. Which feels colder?

Or, leave a wooden block and a glass cup in water at about 70C/160F, long enough for them to reach equilibrium. Then pick them out quickly with tongs and hold one in each hand. Which feels hotter?

The hot glass is at the same temperature as the wooden block. But the glass is a much better conductor of heat, which means that when you pick it up, it's much better at transmitting that heat into your fingers - so hot glass feels hotter than hot wood at the same temperature, and cold glass feels colder than cold plasterboard at the same temperature.

The same thing is going on here: although the mirror is at the same temperature as the wall, the mirror is much better at cooling the air that passes over it, so you'll see far more condensation.

(Heat capacity is also a consideration here, but the difference in heat capacity between wood/plasterboard and glass is much less than the difference in conductivity.)

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Liquid water has a vapor pressure that increases with temperature. 100°C is special only because that's the temperature where water's vapor pressure equals atmospheric pressure. When that happens, water can boil.

Even while water isn't boiling, though, it can evaporate, because its vapor pressure is still non-zero. In fact, this is true for ice as well.

Meteorologists use the concept of dewpoint. It's a characteristic of an air mass containing water vapor, and it represents the temperature at which that air mass becomes saturated with water vapor. (Technically, at that point, the partial pressure of water vapor in the air equals the vapor pressure of water at the same temperature.)

If you expose a surface to air, and the surface temperature is below the air's dewpoint, condensation will form on the surface.

As it turns out, air that you exhale is quite moist; its dewpoint is high. Breathe onto a surface below that dewpoint temperature, and you'll see condensation.

So why don't you see condensation on a wall? As another answer already stated, wall material doesn't conduct heat as well as glass, and it has lower heat capacity. As a result, your breath quickly warms the surface until it's above the dewpoint, and condensation stops.

Edit to add: The point @Luaan makes below is probably even more important for many wall materials! A surface that absorbs water won't show condensation as quickly as one that is impermeable.

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    $\begingroup$ It should also be noted that when you spray water on a wall, it gets wet - while on a mirror, it gives you droplets. If you breathe on a surface that doesn't wet (laquered wood, some plastics, metal...), you'll get condensation, though not always very visible. A surface that does get wet will absorb the water instead (by the time it's wet enough to show actual droplets, you're probably deep in moldy trouble :)). $\endgroup$ – Luaan Mar 14 at 7:31

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