Why does liquid water form when we exhale on a mirror?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 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.

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.)

Answer 5

It has been almost two years, yet reading this question again will still confuse me. The answers and comments given by the users are really helpful and excellent, but different answers/comments explain different parts of the questions to different extents. I decided to write a compilation based on the answers/comments which gave the most convincing explanation, IMO.

1. jeffB's answer

Dewpoint is the temperature characteristic of an air sample, such that, when the air is at this temperature, it is saturated with water vapour, and if cooled further, condensation of water will happen, and liquid water formed. The air sample from our body has higher water content than air sample from surrounding and so higher dewpoint. When this air sample is exposed to mirror which is at slightly lower temperature, that lower temperature is already below the dewpoint of the air sample, co condensation happens.

Actually this question is nothing special; the answer by Karsten Theis explained this well too. Our body temperature higher, so vapour pressure higher; mirror lower the temperature, so vapour pressure will decrease, so water vapour condenses, that's all.

$\space$$\space$$\space$2 and 3. Karsten Theis's answer

The theoretical view is that, for liquid-vapour case, you are on the line (means that liquid and vapour at equilibrium) in phase diagram of water, and when the vapour pressure changed due to temperature changed, you will still be on the line (equilibrium preserved). For the solid-liquid case, your pressure is fixed (the pressure is just pressure experienced by the condensed phases), when you change T from 0 $^\mathrm{o}$C the equilibrium between solid and liquid will just be broken, and you are no longer on the line, you are on the solid region with 2 degree of freedom. The discrepancy in behaviour is because the pressure of vapour can change when temperature change and so preserving equilibrium, and there is no similar analogous behaviour for solid-liquid case.

The physical reason by BowlOfRed and the comment by jpa (on the main question) do make sense. 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.

4. Geoffrey Brent's answer

Argument based on heat conductance and heat capacity: in essence, mirror can 'spread' heat well. Exhaling on a wall, the local temperature at the point of contact will increase fast, reducing the efficiency of condensing water vapour further.

PS: IMHO all four answers help at different parts of the question, so I am not sure which to accept. But I do consider this question solved. I will accept the most upvoted answer.