How much do clouds weigh?

How much does a cloud weigh? This interesting question crops up every now and then on the internet. If you Google it you’ll find a whole spectrum of answers from the absurd to the just plain wrong. (There are plenty of very bogus explanations about some of the science involved too!)

Image: pranav

One answer is that a cloud does not weigh anything! That’s why it floats.

This might seem like a facetious answer, but it seems to make some sense.

We’re taught in school about the difference between mass (the amount of ‘stuff’ in something), and weight (the force that gravity imposes of this ‘stuff’). A cloud, clearly, has mass. We know this because it contains water which falls out frequently as various forms of precipitation. So if it has mass, it must have a weight, so why doesn’t it fall out of the sky?

What else can you think of that has mass and just floats? Maybe a children’s Helium balloon with a small mass on the end, or a hot air balloon? Do these things have weight? If you floated either of these over to set of bathroom scales, they would not measure any weight. Could you describe a balloon as ‘weightless’? After all, it is not registering any weight on a scale. Hold onto that thought for just a moment …

What’s going on here? Well, yes, there is gravity acting on the balloon, creating a force pulling it down, but there is an equal and opposite force holding it up and this is called buoyancy.

Air, despite its transparency, is not a bunch of nothing, it’s a complex soup of gases and vapours, and actually has quite a bit of mass * In fact, there the approximately 5 quadrillion metric tonnes of air in our atmosphere! For more details on this, you can read this article about the atmosphere.

5,000,000,000,000,000,000 Kg

* Stop the madness

We’ll take a slight detour here to bring shame to some people who ought to know better. This is all related to the mass of air.

There’s a famous experiment, probably performed daily in some school somewhere on the planet, that tries to demonstrate to students that air has mass. It goes something like this:

You take two balloons, inflate them, and suspend them on either side of a finely balanced beam. The beam is initially level, as each side has equal forces acting on them. Then, you pop one of the balloons, and sure enough, if the balance is sensitive enough, the side with the full balloon drops.

The air inside the full balloon is small, but enough to tip the balance down; as this air has weight.

"Proof that air has mass?"

This is a 100% utterly bogus explanation.

Yes, the full balloon will drop, but for a different reason. Why should letting the air out of the balloon (transferring it to the other side of the rubber) make a difference? Imagine if the balloon were made out of a mesh stocking, or better still a paper lunch sack? If you put two identical paper lunch bags on the balance beam instead of two balloons, then crumpled one up, would you expect the crumpled side to rise as that bag no longer contained air and so weighed less? Of course not.

So what’s really going on, why does the side with the full balloon fall? The true explanation is that when you inflate a balloon you blow air into it under pressure . The tension of the rubber balloon skin keeps the air inside under pressure. As the air is under pressure there is more mass inside compared to the same volume of air under ambient conditions.

In inflated balloon weighs more than an open-ended (uninflated) balloon because the air inside is under more pressure (so there is more of it for the same volume) than air outside.

(The bogus explanation is analogous to simplifying 19/ 95 by cancelling the nines! You get the correct answer, but for the totally wrong reason!)

Returning to Helium balloons

The Helium in the child’s balloon has mass, but Helium is significantly less dense than the air surrounding it (less mass for the same volume). The Helium in the balloon is displacing the heavier air. This causes an upwards force equal to the volume of balloon multiplied by the difference in the densities. This is called Archimedes’ principal. It’s why boats float even when they are made from iron (which is denser than water). A simple lump of iron thrown into a pond would sink quickly to the bottom, but, if fashioned into a hull shape so that it can displace sufficient volume of water (the mass of which is equal to the iron), it will float. The Helium in the balloon is displacing air. This buoyancy results in lift. If you let go of an untethered Helium balloon, it will accelerate upwards, but, if you add a mass to the string to exactly balance this out it becomes ‘weightless’.

So clouds and balloons really are ‘weightless’ then? Well, no, they’re not, and this bit gets a little harder to explain, so hold onto your hats …

Further down the rabbit hole

When an object is floating neutrally in a fluid, it’s not really weightless, it’s actually distributed its weight throughout the rest of the supporting fluid (and eventually back into the ground!) Huh? Tell that again? What?

That’s right, when a balloon floats up in the air, it’s still pressing down on the ground with the same force it did when laying uninflated on the ground . It’s just that this force is distributed over such a wide area that it’s too small to measure.

Think about a kids bathing pool. Imagine you floated a heavy toy boat in that pool. The boat is neutrally buoyant and is displacing sufficient volume of water such that the mass of water displaced by the hull is equal to that of the boat. The boat does not sink. It floats.

Now imagine the kids bathing pool is on a set of scales. Before the boat was added it would weigh a certain amount. After the boat is added, the scales would increase to include that of the boat.

Even though the boat is floating ‘weightless’ in the water, what has happened is that, through buoyancy, the weight of the boat has been transferred to the water and this, in turn, is transferring this this force through the floor of the pool and into the ground.

It’s the same when a plane flies through the air! When a plane is flying it’s pushing down on the ground with just the same amount of force it did when sat on the runway, it’s just that when it’s in the air, this force is distributed through the air to the ground (via a tiny pressure increase in the fluid) over such a massive area that it’s just impossible to measure.

We're starting to get a few more clues towards our solution, but we still need more information …

What is a cloud?

We gracefully skipped past this at the start, but what exactly is a cloud? Obviously it's different from the air surrounding it (it looks different), but what is its composition? What are clouds made of? A cloud is a visible mass of condensed water vapour. As described before, our air is a complex soup of gases. Nitrogen and Oxygen make up the lion’s share, but there are also measurable concentrations of Carbon Dioxide, and smaller concentrations of Helium and the “Rare Earth Gases” such as Argon, Neon, Krypton and Xenon. Also present in various quantities is water vapour. Water vapour is practically always present in the air in various quantities depending on conditions. When water in the atmosphere condenses out of the air (changes from a vapour phase to a liquid phase), it either forms water droplets or ice crystals, depending on the local conditions. It is these small particles that scatter the sunlight passing through them (randomly across the spectrum), to make them appear white (or grey from shadowing and shading if they are dense). Pretty!

Return to the rabbit hole

There’s a bunch more pseudo-science typically taught that needs clarifying and correcting. You might have been told at school that warm air can ‘hold’ more moisture than cold air, and this is why clouds form. Sort of like equating air as a sponge that can absorb water proportional to temperature. You were probably told that warm air 'picks' up moisture, then precipitates this out when it cools down and can no longer 'hold as much'. This is garbage!

You might have been told that as warm ‘moist’ air cools down, as it drops below something called a 'dew point temperature' (the point that it can no longer ‘hold’ any more moisture), then the air becomes saturated and the vapour condenses out, forming clouds. This is also incorrect (though it certainly makes it easier to understand).

Science

Water molecules are present in air, and they are bouncing around as vapour (along with all the other molecules of gas). At any time there as some molecules that are traveling slowly, and some that are traveling quickly. In fact, there’s an entire spectrum of velocities. It is the average velocity of the molecules that actually gives us our definition about what temperature is (more strictly the definition of temperature is the average kinetic energy of the molecules).

This spectrum of energies explains how and why evaporation happens. If you pour water on the ground it slowly evaporates away. The more energetic molecules escape from the surface of the liquid, having sufficient energy to ‘boil’ away and turn to vapour; even at ambient temperatures. (The molecules left behind have a slower average speed, and this explains why evaporation cools things down).

Pools of water with a large surface areas evaporate quicker, as there is more surface area for molecules to escape from, than similar volumes of water with smaller surface areas. Pools of water at higher temperatures evaporate quicker because they already have molecules with higher average speeds.

We’re getting further away from clouds but this also explains why adding salt (or other substances) to water raises its boiling point. The presence of other particles in the fluid is a colligative property; these other particles obstruct the water molecules as they try to make their escapes. It also slows down evaporation.

Why did I mention this colligative property? Well, here is a thought experiment: Put out two beakers of water at the same temperature, in air of the same temperature/pressure in a closed region. One of the beakers should be filled with pure water, the other with strong saline (salt water). If the ‘carrying capacity’ of air is dependent on its temperature then we’d have expected no difference, but the water that gets in the air (at the same temperature) is dependent on liquid, not the air. The ‘carrying capacity’ of the air is not proportional to the temperature. In fact the air has nothing to do with it at all! Dalton published a paper about this in 1802, but it is still, often, taught incorrectly.

The reverse of evaporation is condensation. Slower moving molecules of water vapour that collide with liquid (or solid) phase water might decide it’s better to stay there and relinquish their flights. As the temperature (average kinetic energy) lowers, more molecules decide to stay put.

There is no magic threshold; there is a spectrum of kinetic energies. There is a constant dynamic equilibrium of molecules moving in-between states. All the time molecules are leaving and arriving. If there are, net, more molecules arriving than departing, there is some degree of condensation. If there are, net, more departing than arriving, there is some degree of evaporation. With me so far?

Microscopically small droplets of water/ice form and drift in and out of equilibrium all the time in the atmosphere.

What appears to be cloud free air contains water molecules as liquid drops, it’s just they are so tiny and so short lasting that they don’t get chance to coalesce with others!

As temperature decreases, we reach something called the ‘dew point’. At this temperature, the net rate of condensation equals the net rate of evaporation (This is true definition of what a dew point temperature is! It's not the temperature at which air becomes 'saturated'. It's the temperature at which evaporation and condensation are at perfect equilibrium).

At the dew point (or colder), the super tiny drops being created have chance to stay around, grow, and this is how clouds form!

One more puzzle piece to go

One more puzzle piece to go, and this one comes with a beauty of a pseudo-science bombshell:

Dry air weighs more than wet air!

Yes, you read that correctly, 'dry' air is more dense (at the same temperature and pressure), than 'wet' air. The more humid air is, the lighter it becomes! If you ever needed a little bit more convincing that air is not a temperature dependent sponge and does not pick up water, this is it.

If you dry air, it gets heavier! When you first hear this it sounds counter-intuitive.

More science

To understand this, we need to know a little bit more about of the physical properties of gases. For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume. This is called Avogadro’s Law after Amedeo Avogadro who discovered this. That’s pretty big statement, but explained in a slightly different way “equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties”. In our situation what it means is that if the air contains a water molecules, to have the same temperature and pressure, it needs less of other the gases constituents.

When air dries, you are not 'wringing' out water from the air to make it lighter, you are replacing the water molecules with heavier molecular mass gas molecules.

As a first order approximations, dry air contain approximately 80% Nitrogen gas (N 2 ), whose molecules have an molecular mass of about 28, and approximately 20% Oxygen (O 2 ), with atomic mass of 32, giving an average mass for dry air of 29 (the trace amounts of the other gases, whilst most are heavy, are so small in quantity that they make small difference to the value).

A water molecule (H 2 O) has a molecule weight of 18 (16 + 1 + 1).

So, when a water molecule replaces one of the dry air molecules to maintain the same temperature and pressure, the average weight of the molecules decreases. As density is mass per volume, the density of the air is lower. The more water present, the lower the density.

Latent heat

When air rises, it cools (and expands). As it cools there is a chance it will cool below the dew point and this will cause the condensation to become dominant and clouds will form. There is, however, and additional interesting twist in the story, and this is a dampening effect on condensation from the latent heat. Dry air rising cools quickly, but as soon as clouds are formed, the rising air cools more slowly.

Just as sweating and evaporation keep you cool by taking away heat, the inverse (adding heat) occurs when vapour condenses. This is called latent heat. The trading of energy backwards and forwards via the latent heat in water vapour is one of the fundamental ways the planet moves around energy and helps stay balanced.

Fun experiment

Here's a fun experiment you might want to try to see this effect. All you need a tight fitting (thin) latex glove, your hand, and the ability to blow.

The air in your lungs is moist and of constant temperature. Follow these steps:

Make a small hole with your lips, move your hand an few inches from your face, and blow quite quickly onto it. Notice your hand feels cool? Then, open your mouth wide, and breath slowly onto your hand. Notice your hand feels warm?

What's going on? We know the air coming from our lungs is the same temperature in both cases! When you blow quickly, the fast moving air is helping evaporate the water from your skin. The evaporation takes away heat. Your hand feels cool.

When you blow slowly, moisture condenses on your skin, warming it. The temperature is the same, but there is a different amount of heat transfered.

Next, put on the thin latex glove.

Now, blow onto your hand again strongly. This time, your hand feels warm not cold! Why? the latex glove is acting as a barrier and there is no evaporation happening from your skin, so no cooling effect. Open wide and wheeze slowly onto the glove as in the first experiment. As before, moisture will condense on the surface of the glove and your hand will feel warm. Now, if you're quick, try blowing on the glove strongly again. If you time it right you might get your hand to feel cool again. Why? Well your slow breathing had deposited a layer of moisture on the outside which you can evaporate off with your breath for a pleasant cooling effect.

Summary

Let's summarize what we've learned:

Clouds have mass (they contain stuff).

Air has mass too (and it's larger than you might think).

There's plenty of water vapour in the atmosphere, but we can't see it. We only see clouds because the water has condensed into stable enough droplets that diffract and disperse light.

Clouds float because they displace air to make them buoyant, but they are not 'weightless'.

The water stored in clouds weighs the same amount in the sky, and presses down on the planet with just the same force, as it does when it is sitting directly on the planet in seas, rivers and lakes.

The water vapour in the air in our atmosphere is in a constant state of dynamic equilibrium.

The more humid air gets, the lighter it becomes.

As condensation occurs, the water precipitates out (making the cloud denser that just the humid air). When it gets too dense, the precipitation falls. (How quickly this happens depends on the size of the water droplets. Smaller droplets have the ability to stay up longer, just like feathers and dust particles float down gradually, but if you made a compressed brick of dust or feathers they would drop quicker. This is due to different drag coefficients). Updrafts also contribute to keeping precipitation in the air in some conditions.

Because of the huge variability hinted at by the last point, there's actually quite a wide range of densities of condensed water in clouds. Roughly classified by type of cloud these densities range from about 0.05 g/m3 (grams of condensed water per cubic meter) to 3.0 g/m3.

Type Density (g/m3) Fog 0.05-0.5 Cumulus 0.2-1.0 Cumulonimbus 0.5-3.0 Altocumulus 0.2-0.5 Altostratus 0.2-0.5 Stratus 0.1-0.5 Stratocumulus 0.1-0.5 Nimbostratus 0.2-0.5 It's worth noting that, even in densest clouds, the weight of this condensed water inside it is thousands of times smaller than the weight of the air holding it!

Final Calculation

Clouds come in a wide variety of sizes, so let's just imagine one that is 1km cubed (not amazingly large, but not small), with a density of 1.0 g/m3 This works out at 1,000 Metric tonnes of water. That's about 700 Toyota Camrys! That sounds like a lot, and without context it is, but remember that whilst a cloud might contain thousands of tonnes of water, the air holding this will weighs millions and millions of tonnes.

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