When snow falls, temperature rises. Is this due to entropy?

Question

A friend of mine told me that temperature rises when snow falls. And this is because condensation of water in snowflakes reduces entropy and the temperature of the air rises to compensate for this.

Is this explanation correct?

Answer 1

Yes. A simpler way to look at this is that because freezing, as well as resublimation (turning a gas directly into a solid) emits heat. It may seem strange but consider this: you need to put in heat to make water turn from solid into liquid, so the inverse process should transfer the heat in the opposite direction. And that's what it does. In cold air the water droplets and the water vapor can turn into ice crystals, but doing so they need to expel some heat into the air. So cold air and cold water vapor turn into slightly warmer air and ice.

It can be also said in terms of entropy, as entropy and heat transfer are corelated. Turning water droplets and water vapor into ice decreases its entropy, and that requires an outward heat transfer into the surrounding air.

Answer 2

Weather is... complex.

Turning water vapor to solid releases heat, but this happens up in the sky. You end up with somewhat hotter and drier air somewhere at altitude and some amount of snow that falls down. (If "down" is hot enough, you get rain instead. The rain almost always starts as a snow.)

The point is, you may, or more often may not get the heat released from the water vapor crystalization, at the surface.

Then again, few different mechanisms may make the weather somewhat hotter (or, at least, feel hotter).

1. The wind stops. The usual weather pattern, at least in a temperate climate regions, is to have cold winds that bring the snow (it is called a cold front) and then snow without winds. Winds cool down both buildings and human bodies way better than the still air.

2. Clouds reflect a great deal of the infrared radiated from the surface back down (they are white not only in visible light). This helps the surface to retain some heat, in contrast with the clear sky that allows the same infrared to escape. The clouds also reflect the sunlight back to the space, but the former effect prevails, because we don't get much sunlight in winter in the first place.

3. The snow on the roofs acts as an additional thermal insulation. (And in some buildings, e.g. the one I live in currently, stops air circulation between the shingles.) This improves the heat comfort indoors. In some places, the snow can pretty much insulate not only the roof, but the walls as well.

4. People get the hint from the view in their windows and put on adequate clothes before going out.

Considering that almost everything in our lives is more or less driven by entropy, then yes, it is due to entropy. In a ways.

Answer 3

As a former meteorologist, I do not really agree here. Snow is produced in clouds from water vapour. Broadly speaking (actual cloud microphysics is more complex), you have air flowing up inside clouds. More exactly, clouds are produced when moist air particles go up: the pressure decreases which causes temperatures to decrease too. When an air particle reaches its dew point (or icing point), the temperature stops decreasing and water vapour is transformed into liquid water or ice (snow). In theory, the temperature should remain constant until all the water vapour is changed into liquid water or ice, but the temperature does not increase. On the contrary, temperature can fall when it starts snowing in plains while the air is at 2 °C to 5 °C at the ground level. Because in a strong snow fall the snow goes down quickly and is still much colder that the air when it reaches the ground, you get a significant mass of cold snow and only a little amount of warm air => the air soon gets to the temperature of snow and you get air at -2 °C which causes the snow to remain on the ground instead of changing into water. This is rather common in mid latitudes for example in France (one or two times a year).

What is true is that (still at mid latitudes) in winter the weather is more cold when there are no clouds: clouds block the infrared radiations from earth and the coldest moments are at the end of the night with no clouds above. So when a depression comes after a cold period, it often comes with both warmer air and snow. So when you look at your thermometer, you can see that the temperature is higher on the first day of snowfall. But is is because warmer air has arrived, not because of entropy conservation.

Answer 4

Warmer-than-average air rises, it cools due to the drop in pressure at higher altitude resulting in adiabatic expansion, and that causes the moisture in it to precipitate and fall as rain or snow. Because the air is rising, heat released up here has a hard time getting back to the surface. The arrival of a warm moist buoyant air mass suddenly replacing a cold dry one sometimes causes snow to start falling, rather than snow causing the warmth.

The latent heat of condensation does indeed release heat into the upper atmosphere, the consequence is that air cools with altitude less quickly than it would if it was dry. The moist adiabatic lapse rate - the rate at which moist air cools with increasing altitude - is about 6 C/km on average compared to about 10 C/km for perfectly dry air. If the air is moist enough, the heat dumped by condensing water vapour can drive further convection, sucking in even more moist air at the bottom which also dumps its heat, amplifying the effect. This self-amplifying feedback drives thunderstorms and hurricanes.

Answer 5

Let’s calculate. Suppose a cloud approaches at the height of 1 km, its water freezes and it starts snowing. Water releases 333 kJ/kg when it freezes, and a 1 m × 1 m × 1 cm layer of new snow conveniently weighs about a kilogram. Consider one square meter of area. Each centimeter of snowfall means 333 kJ of heat was released above it. How much could it have heated the 1 km high column of air? At STP, air weighs 1.2 kg/m³ and it takes 1 kJ/kg·°C to heat it. This all works out to an average temperature increase of about $\frac{\Delta t}{h_\text{snow}} = \frac{\lambda\rho_\text{snow}}{C_P\rho_\text{air} H_\text{cloud}} \approx 0.3$ °C per centimeter of snowfall. The real increase at ground level is likely lower as the warmer air will try to escape upwards, or not to descend from the cloud in the first place.

Now where did the cloud come from? The wind brought it from some humid place, a far away sea or something. Is the temperature there the same as where the snow eventually falls? Most likely not, and this temperature difference dwarfs the 0.3 °C per cm from snowfall.

Probably, your main source of snow is humidity from a warm sea and that’s the main reason your snowy days are warmer than days without snow.

Answer 6

What does your refrigerator do?

It does the same what others mentioned. It takes out some heat from the water and this causes the random intermolecular motions in water to seize down and form a crystal structure with very less thermal motion which we call ice.

If the same happens in the open atmosphere (for this you need to have very less temperature of the surrounding or lesser pressure than what you feel everyday), the energy released from water molecules need to go somewhere and thus the surrounding air becomes warm.

Answer 7

Is this due to entropy?

No. When water changes phase from liquid to solid (or vapor to liquid or solid), heat is released (termed latent heat). One could take various approaches to explaining why this is so--one way would be to focus on the inter-molecular forces, which could be done satisfactorily without mentioning entropy. That is not to say entropy is not relevant. But the claim that the effect is due to entropy is a stretch.

Here is an analogy: Yesterday there was a basketball game between the Lakers and the Nuggets. The Nuggets won. Is this due to the fact that tackling is against the rules?

Well, if it weren't for that rule, the game would have looked very different. The outcome may well have been different. But you could perfectly well discuss why things came out the way they did without ever bringing up the fact that tackling isn't allowed. To point to that rule as the sole reason for the outcome is disingenuous.

Answer 8

For one thing, the snow is a significant mass falling a considerable distance. At least some heat is released due release of simple gravitational potential energy. But mostly, the snow and its clouds present a very good thermal insulator, preventing further heat loss via radiation into clear skies.

1kg of snow falling 2km from the clouds releases 20kj, which is enough to heat that same 1kg of snow by 10C