DIY · Card 02 · Physics
A salt shaker of hot red water, set down on the bottom of a jar of cold water. It erupts, curls into a mushroom and floats on top like oil. Nothing pushes it but the water around it.
01The brief
Make a volcano erupt inside a jar of water. No baking soda, no vinegar, no fizz. Only hot water and cold water.
1.4 %
lighter: hot tap water at 55 °C against cold water at 10 °C
g / 70
the net push on the hot water, seventy times weaker than gravity, and still enough
200×
faster: how much quicker heat spreads through water than red dye does
Most kitchen volcanoes are chemistry: baking soda, vinegar and a lot of foam. This one is physics, and it is quieter and stranger. A small shaker of hot, red water is lowered onto the floor of a big jar of cold water. For a second nothing happens. Then a red column climbs straight up out of it, widens, rolls over into curls and spreads across the surface like a cloud with a flat bottom.
The whole show runs on a difference you could never feel with your hand: hot water is about one and a half percent lighter than cold. The first card in this deck was about the air pushing an egg into a bottle. This one is about water pushing water.
02Kit
All of it is in a kitchen. The jar is the one thing worth choosing: clear glass, as big and tall as you have.
Tick off what you have
0 of 6 ready
03Method
Five minutes of setting up, a minute of eruption, and half an hour of slow aftermath that is worth watching too.
Step 1 of 8 · Minute 0
Cut about 60 cm of string. Tie one end round the neck of an empty salt shaker with a double knot, then tie the other end on the opposite side, so the string makes a loop you can lower it by.
The colour just leaks out and drifts.
Why
The temperature difference is too small, so the push is too weak to make a plume.
Fix
Use the hottest tap water for the shaker and chill the jar with ice for ten minutes first.
The jar goes cloudy red all at once.
Why
The water was still moving, or the shaker went in too fast and stirred it.
Fix
Let the jar settle for two minutes, and lower the shaker as slowly as you can.
A second eruption stops halfway up.
Why
The first run left a warm layer on top. The new plume cools as it rises and stops where its density matches the water around it.
Fix
That is a result, not a failure. For a full eruption again, start with fresh cold water.
04Physics
Water molecules are always jostling. Heat them and they jostle harder, and on average they sit a little further apart. The same number of molecules takes up a little more room, so a litre of hot water weighs a little less than a litre of cold. A litre of water at 10 °C weighs 999.7 g. At 55 °C the same litre weighs 985.7 g.
Fourteen grams in a litre is not much. But the cold water around the shaker does not care how small the difference is. It is heavier, gravity pulls it down harder, and it slides underneath the hot water and lifts it, exactly the way water lifts a cork. Archimedes worked out the rule more than two thousand years ago: anything immersed in a fluid is pushed up by the weight of the fluid it displaces.
Here is the curve the whole experiment lives on. Move the two temperatures and watch the gap between the dots.
The red water rises
It is 1.40 % lighter than the water around it. The net push is 0.140 m/s², about g / 70. On a shakerful of 100 ml, that is the weight of 1.4 g.
Notice the bump at the far left. Water is densest not at 0 °C but at about 4 °C, and below that it gets lighter again as its molecules begin to line up into the open, ice-like arrangement they take when they freeze. Almost every other liquid simply gets denser as it cools. Water does not, and that one bump explains why lakes freeze from the top down.
05The big idea
Heat doesn’t rise.
Hot water does.
“Heat rises” is one of those phrases everyone learns and almost nobody questions. It is not quite right. Heat on its own spreads in every direction, from warm to cold, sideways and downwards as happily as up. Touch the bottom of a hot pan and you will find out.
What rises is warm stuff: warm water, warm air, warm rock. It rises because it is lighter than what is around it, and it carries its heat along for the ride. That is convection. The red dye in the jar makes it visible, but it is happening right now in the room around you, wherever a lamp, a laptop or a person is warming the air.
06The math
1 · Buoyancy
F = (ρcold − ρhot) V g
The upward push on the hot water is the weight of the cold water it displaces, minus its own weight.
2 · Reduced gravity
g′ = g · Δρ / ρ
Divide by the hot water’s mass and you get the acceleration it feels: ordinary gravity, scaled down by the density gap.
3 · Diffusion
L ≈ √(D t)
How far something spreads by diffusion alone grows only with the square root of time. D is how quickly it diffuses.
Take a 100 ml shaker of water at 55 °C in a jar at 10 °C. The density gap is 14 kg/m³, so the push on the shaker’s worth of water is 14 × 0.0001 × 9.81 ≈ 0.014 N: the weight of about one and a half grams. Spread over the hot water’s own mass, that gives g′ ≈ 0.14 m/s², about a seventieth of ordinary gravity. It is a gentle push, which is why the plume rises at a few centimetres a second rather than shooting up like a fountain.
Gentle, but not timid. Physicists judge whether a fluid will start to churn with a single number, the Rayleigh number, which weighs buoyancy against the two things that resist it: the water’s stickiness and heat leaking away. Between two flat plates, convection starts once it passes about 1,700. For a jar 20 cm tall with a 45 °C difference, it comes out in the billions. That is why the plume does not rise as a neat column but tears at its edges and curls.
The third formula explains the slow part. Heat diffuses through water with D ≈ 1.4 × 10⁻⁷ m²/s; a red dye like amaranth manages about 6 × 10⁻¹⁰ m²/s, roughly two hundred times slower. In ten minutes, heat creeps about 9 mm on its own. The dye creeps about 0.6 mm. To cross a 15 cm jar by diffusion alone, the dye would need months. So the colour is a lagging witness: the heat has already gone, and the red is still showing where it went.
Now set it running. The simulation below is a toy, but its push comes from the real density curve.
It erupts upward
The shaker water is 1.40 % lighter than the jar. Time is sped up; a real plume moves a few centimetres a second.
07Real life
Once you have seen the plume in the jar, you start seeing it everywhere, at every scale.
The radiator that is badly named
A radiator gives off some heat as radiation, but most of its work is convection. Air touching it warms, rises to the ceiling, spreads, cools and sinks on the far side of the room. That loop is why radiators sit low, under windows, and air-conditioning units sit high.
Hot air balloons
Heat the air inside the envelope to around 100 °C and it becomes a quarter less dense than the air outside. The balloon is the shaker, the sky is the jar. The first crewed flight, over Paris in November 1783, ran on a straw fire.
Thermals
Sun-warmed ground heats the air above it, and bubbles of warm air break away and rise like the plume in the jar. Storks, vultures and glider pilots circle inside them to climb for free, sometimes thousands of metres.
Ice forms on top of lakes
Water is densest at 4 °C. In winter the coldest water, at 0 °C, is lighter and floats on top, where it freezes. The ice lid insulates the lake, and the bottom stays near 4 °C all winter. Fish survive because of one bump on a density curve.
The ocean’s deep water
In the North Atlantic and around Antarctica, surface water gets very cold and, as sea ice forms, very salty. It sinks to the sea floor and creeps along it for centuries. This is the backwards version of the experiment, and it helps move heat around the planet.
Real volcanoes
Hotspot volcanoes such as Hawaii are thought to sit above mantle plumes: columns of hot rock rising through the Earth’s mantle. The rock is solid, but over millions of years it flows, a few centimetres a year, by the same rule as the red water.
1979
The real underwater volcanoes were found in 1979. That April, the submersible Alvin was searching the East Pacific Rise, 2,600 metres down, when its pilot followed a trail of white clams to a chimney pouring out black, shimmering water. The temperature probe’s reading went off the scale, and back on deck the crew found its plastic tip had melted. A sturdier probe measured the fluid at about 350 °C, kept from boiling by the weight of the ocean above.
The black smoke is minerals dropping out as the hot water hits the near-freezing sea, and the plume above each chimney rises for hundreds of metres, curling exactly like the red water in the jar. Rising air bubbles ride the same push, and humpback whales use it to herd fish inside rising curtains of air.
08Is and isn’t
Heat rises.
Heat spreads in every direction. What rises is warm fluid, carried up by buoyancy, and it takes its heat with it. That is convection.
The food colouring makes the water rise.
A few drops change the density by almost nothing. Try it with plain hot water and a thermometer: the hot water still ends up on top. The colour only lets you see it.
Warmer water always floats on colder water.
Not below 4 °C. Water at 1 °C floats on water at 4 °C, even though it is colder. Set the density lab above to 1 °C and 4 °C and watch the verdict.
The colour spreads through the jar because it dissolves.
Diffusion is far too slow to do it. Over a jar’s height it would take months. The even colour you see after half an hour is the water stirring itself as the top layer cools.
09Go further
A
Run it backwards
Warm water in the jar, cold salty blue water in the shaker, held upside down under the surface. The blue cloud falls and pools on the bottom.
B
Two shakers at once
Hot red on the bottom, cold salty blue hung near the top. The two plumes pass each other, and the jar ends up in three layers: red, clear, blue.
C
A coloured ice cube
Freeze water with a drop of blue colouring and float the cube in a glass of warm water. Thin blue streams pour off it and sink, because the meltwater is colder than the glass.
D
Measure the layers
Right after the eruption, put a thermometer just under the surface and then at the bottom. The difference is the layer you can see, written as a number.
E
Stop it halfway on purpose
Erupt once, wait five minutes, erupt again. The second plume stops under the first layer, the way chimney smoke flattens out under a layer of warm air on a cold, still morning.
10Questions
Hot water takes up slightly more room than cold water, so it is less dense. When a shaker of hot, coloured water is set on the bottom of a jar of cold water, the cold water pushes the lighter hot water upward, and it rises in a plume until it reaches the surface.
Warm water molecules move faster and sit a little further apart, so a litre of hot water weighs less than a litre of cold. At 55 °C water is about 1.4 percent less dense than at 10 °C, and buoyancy lifts it the same way it lifts a cork.
Once it reaches the surface it is still the lightest water in the jar, so it spreads sideways into a layer and floats there. It only mixes down slowly, as the layer cools and sinks in thin fingers.
A convection current is a flow driven by differences in density, usually caused by temperature. Warm fluid rises, cool fluid sinks to take its place, and the loop carries heat from one place to another. It moves air in a room, water in the oceans and rock in the Earth’s mantle.
Not exactly. Heat spreads in every direction. What rises is warm fluid, because it is lighter than the cooler fluid around it, and it carries its heat along with it.
Safety · A grown-up should handle the scissors and the hot water. Hot tap water is enough; don’t use boiling water. Food colouring stains, so work on a tray.
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