Why does hot water thrown into the air at −30°C turn into a white cloud in an instant?
― It doesn't happen with cold water. Only hot water can give off steam
In inland Hokkaido, Siberia and Canada in winter, you can toss a cup of hot water into the sky and watch the spray turn into white smoke and vanish before it hits the ground. The stars of the show are the huge amount of steam the hot water gives off, and the frozen air that cannot hold that steam.
It is an early morning in midwinter, and the temperature is −30°C. Your eyelashes freeze and the inside of your nose crackles.
You swing your arm and fling hot water from a thermos into the sky. The spray draws an arc, then turns into a white cloud with a "shwoosh". Almost nothing falls to the ground.
But do the same with cold water and the spray just patters down onto the snow. You would expect the colder water to freeze faster, so why does only the hot water become a cloud?
Just two reasons
Hot water is thin and runny, and it breaks into tiny droplets in mid-air. The smaller the droplets, the more surface touches the air, and hot water gives off a large amount of steam in an instant.
Air at −30°C can hold only about one fiftieth as much water vapour as air at 20°C. With nowhere to go, the steam quickly turns into tiny ice grains.
What looks white is not just hot water that froze as it was. Most of it is steam from the hot water turning into ice grains all at once in the surrounding air: a cloud made on the spot. Let's take it step by step.
Air has a "limit" on how much steam it can hold
Air can hold an invisible gas, water vapour, up to a certain amount. In science class this limit is called the "saturation vapour content". The limit changes a lot with temperature, and it shrinks sharply as air gets colder.
Move the slider in Figure 1 to change the temperature. At 20°C, one cubic metre of air can hold about 17 grams of water vapour. At −30°C, it can hold only 0.34 grams. Left of 0°C, the line of the graph almost hugs the floor.
When 200 grams of 90°C hot water (one cup) cools, it can give off at most about 34 grams of steam (the calculation is in the fold-out at the end). Air at 20°C could take that up in about 2 cubic metres. At −30°C you would need about 100 cubic metres, roughly half a classroom of air.
The thin layer of air around the hot water passes its limit in no time. The overflowing vapour quickly turns back into tiny water droplets or ice grains, using dust and the like as seeds. Those grains scatter light in every direction, so we see a white cloud.
Hot water "breaks up easily" and "gives off steam easily"
The other key is the nature of hot water itself. Look at Figure 2 from left to right.
Hot water is thinner and runnier than cold water. Its stickiness (viscosity) is about a third lower, and the force that pulls its surface into a round shape (surface tension) is said to be over 10% weaker. So when you swing your arm and fling it, it breaks easily into fine droplets.
Suppose a cup of water broke up entirely into droplets 0.1 millimetre across. Their total surface area would be about seven tatami mats, roughly 3,000 times the surface of the water in the cup. Every droplet starts giving off steam at once, over a wide surface.
On top of that, hot water gives off steam at a vastly higher rate. The urge of 90°C water to escape as vapour is about 30 times that of 20°C water. Cold water, even when broken up, gives off hardly any steam and just falls as plain droplets.
When water turns to steam, it takes a lot of heat from its surroundings. Small droplets hold little heat, so they cool quickly as they give off steam. As a result, some of the broken-up droplets freeze before they fall and become a fine ice powder. That powder is mixed into the cloud too.
Abroad, there have been reports of people burned when the thrown water blew back or fell from overhead. Use water that has cooled a little rather than boiling water, always throw it downwind, and make sure nobody is nearby. Wet gloves can cause frostbite. When the air is warmer than about −20°C, the water tends to fall back down instead of becoming a full cloud.
Summary
Hot water turns into a white cloud in an instant because it breaks into fine droplets and gives off a lot of steam. And air at −30°C can hold almost none of that steam. The overflowing steam becomes a cloud of ice grains on the spot. Cold water gives off no steam to speak of, so it makes no cloud.
The cold did not make the cloud; the steam from the hot water did.
The freezing air simply cannot hold it.
The white breath you exhale in winter is a small version of the same mechanism. See also Why does your breath look white in winter? A different story, "hot water freezes faster", is covered in Does hot water really freeze faster than cold water?
- On a cold winter morning, open a kitchen window and watch the steam from a kettle. The white steam should look clearer and longer near the window than inside the warm room.
- Open the freezer door just a crack and hold a cup of hot water near it. Where it meets the cold air, you will see the white steam suddenly thicken.
- Do the same with cold water. Almost no white steam appears. The difference is the amount of vapour it can give off.
An adult should handle the hot water, using a shallow container so it doesn't spill. Throw-outdoors experiments should be done only in places colder than −20°C, with an adult checking the wind direction.
For those who want to know more ― terms, formulas, and links to textbooksEach part is marked with its level, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school physics and earth science
- High school+Advanced high-school material, or textbook sidebars
- UniversityUniversity-level topics (thermodynamics, cloud physics) not taught in high school
- ResearchNot yet settled even at university; researchers are still studying it
Middle schoolTerms: this phenomenon has names
- Saturation vapour content: the maximum amount of water vapour one cubic metre of air can hold. It shrinks sharply as the temperature falls.
- Heat of vaporisation (latent heat): the heat water takes away when it becomes vapour. About 2260 joules per gram, roughly 540 times the heat needed to warm water by 1°C.
- Hot-water fireworks (o-yu hanabi): one Japanese name for the game of throwing hot water in extreme cold to make a white cloud.
Middle schoolHigh schoolChecking with a formula: how much air does one cup's steam need?
Assume all the heat released as 200 grams of 90°C hot water cools to 0°C goes into evaporation. In reality some heat goes straight into the air, so this is an upper estimate of the amount of steam.
| In symbols | m ＝ M × c × ΔT ÷ L , V ＝ m ÷ ρs |
| In words | Steam amount ＝ water amount × specific heat × temperature drop ÷ heat of vaporisation , air needed ＝ steam amount ÷ saturation vapour content |
| Where they come from | The first is conservation of heat (heat lost by the hot water ＝ heat taken by evaporation); the second is the definition of saturation vapour content (the limit one cubic metre of air can hold) |
| Symbol | Meaning and unit |
|---|---|
| M | Amount of hot water (grams) |
| c | Specific heat of water (joules per gram per degree) |
| ΔT | Temperature drop (°C) |
| L | Heat of vaporisation (joules per gram) |
| m | Amount of steam produced (grams) |
| ρs | Saturation vapour content (grams per cubic metre) |
| V | Air needed to hold the steam (cubic metres) |
| Amount of hot water M | 200 g |
| Specific heat of water c | 4.2 J/(g・℃) |
| Temperature drop ΔT (90°C→0°C) | 90 ℃ |
| Heat of vaporisation L | about 2260 J/g |
| Saturation vapour content (−30°C, over ice) | about 0.34 g/m³ |
| Saturation vapour content (20°C) | about 17 g/m³ |
| Heat released when 1 gram drops 90°C | 4.2 × 90 ＝ 378 J |
| Fraction going to evaporation | 378 ÷ 2260 ≒ 0.17 |
| Steam from one cup m | 200 × 0.17 ＝ 34 g |
| Air needed at −30°C V | 34 ÷ 0.34 ＝ 100 m³ |
| Air needed at 20°C V | 34 ÷ 17 ＝ 2 m³ |
| How many times different | 100 ÷ 2 ＝ 50 times |
At −30°C, holding one cup's steam takes about 100 cubic metres of air, roughly half a classroom. The air around the spray passes its limit at once, and the overflowing vapour becomes cloud. This also shows that about one sixth of the hot water can turn to steam.
High schoolHigh school+Why saturation vapour content changes so sharply with temperature
High schoolThe only water molecules that leave the surface are those that have gained energy from their surroundings. When the temperature drops, the number of such molecules falls sharply. So saturation vapour pressure changes almost exponentially with temperature. As a rule of thumb, it roughly halves for every 10°C drop.
High school+In air below 0°C, the saturation vapour pressure over ice is lower than over chilled liquid water (supercooled water). So when chilled droplets and ice grains mix, vapour gathers onto the ice. This is called the Bergeron process, the same mechanism by which snow grows inside clouds.
UniversityThe Clausius–Clapeyron equation and homogeneous nucleation
How saturation vapour pressure changes with temperature is described by the Clausius–Clapeyron equation of thermodynamics. The larger the heat of vaporisation, the steeper the change with temperature. The script in Figure 1 uses the Magnus formula, an approximation of it. Also, pure water droplets with no dust or other seeds are known to stay unfrozen down to around −38°C (homogeneous freezing). Clouds formed at −30°C are thought to contain supercooled droplets that have not yet frozen.
📖 Derivations and further reading: Clausius–Clapeyron equation (Wikipedia) ／ Saturation vapour content (Wikipedia)
ResearchWhat is still not well understood
- What the cloud is made of How much of the white cloud is grains formed from steam, and how much is broken-up hot water frozen as it was, probably varies a lot with conditions.
- How droplet sizes are distributed How much water splits into droplets of each size when thrown by arm depends on the speed of the throw and the shape of the container, and is hard to predict.
- Likeness to artificial clouds The mechanism is said to be close to that of contrails and of factory steam turning into ice fog in cold regions. Research on "ice fog" in extremely cold cities continues today.
In other words, this article too is "an explanation within what is known now". The temperature at which a cloud forms also shifts with wind, humidity and the water's temperature.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Grade 8 science, "Weather and its changes" (saturation vapour content, dew point) | Figure 1, the limit of steam air can hold |
| High school | Physics "Heat and temperature", Earth science "Water in the atmosphere" | Heat of vaporisation calculation, temperature dependence of saturation vapour pressure |
| High school+ | Advanced earth science (how snow grows in clouds) | Bergeron process |
| University | Thermodynamics, cloud physics | Clausius–Clapeyron equation, homogeneous freezing |
| Research | Studies of ice fog and fog droplets | What the cloud is made of, droplet sizes |
| ― | Links to daily life | Winter breath, kettle steam, ice fog in cold regions |
- Murphy, D. M. & Koop, T. (2005) Review of the vapour pressures of ice and supercooled water for atmospheric applications. Quarterly Journal of the Royal Meteorological Society
- Saturation vapour content (Wikipedia, Japanese)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing (tables of saturation vapour pressure, viscosity and surface tension of water)
- Yoshimitsu Ogura (小倉義光), Ippan Kishōgaku (一般気象学, General Meteorology), University of Tokyo Press (formation of cloud droplets and growth of ice crystals)
* This article is a popular-science explanation. The figures given are rough guides to help you understand the mechanism. If you throw hot water outdoors, take great care to avoid burns and frostbite, and have an adult present.