VOL. 01 · KITCHEN PHYSICS
A KITCHEN PHYSICS NOTE

How water becomes ice.

A short walk through the strange five hours that pass between a cup of water and a cup of ice — including the case of a Tanzanian schoolboy who noticed something nobody believed.

01  /  SURFACE AREA

Why two cups beat one.

Pour a liter of water into one big cup, or split it into two smaller ones — same volume, same freezer. The two cups will freeze noticeably faster. The reason is geometry.

When you split a volume V into n equal pieces of similar shape, the total surface area scales as n^(1/3). For two cups, that's about 1.26×, or +26%.

More surface means more channels for heat to escape. It also means the warmest molecules — the ones in the center — sit closer to the cold edge. Both effects shorten the time to ice.

500ml × 2 surface ≈ 610 cm² +26% vs. 1L × 1 surface ≈ 484 cm² baseline
SAME VOLUME · DIFFERENT EXPOSURE
02  /  CALCULATION

The math of a frozen cup.

Imagine 500g of water at room temperature (20°C) placed in a freezer at −18°C. We need to figure out how much energy must leave the water before it becomes solid — and roughly how long that takes.

How much energy?

First we cool the water from room temperature down to the freezing point. That uses the standard heat-capacity equation: Q = m·c·ΔT.

Then comes the harder part — the phase change at 0°C. Water doesn't get colder during this step; instead, energy goes into rearranging molecules into a crystal. That's the latent heat of fusion, 334 J per gram.

Out of the total 209 kJ, 80% goes into the phase change, not the cooling. Freezing isn't slow because water is hard to cool — it's slow because crystallization is energetically expensive.

STEP 1 · COOLING20°C → 0°C
Q₁ = m · c · ΔT
   = 500 g × 4.18 J/g·K × 20 K
Q₁ = 41,800 J
STEP 2 · FREEZINGphase change at 0°C
Q₂ = m · L_f
   = 500 g × 334 J/g // latent heat
Q₂ = 167,000 J
TOTALQ₁ + Q₂
Q_total = 41,800 + 167,000
208,800 J ≈ 209 kJ
WHERE THE ENERGY GOES
20%
80% — phase change
cooling Q₁ freezing Q₂ (4× more)

Most of the wait isn't the cooling. It's the slow choreography of molecules locking into a crystal — at exactly 0°C, while nothing seems to be happening.

How long does it take?

To turn energy into time, we use Newton's law of cooling: P = h · A · ΔT. Power equals a heat-transfer coefficient times surface area times the temperature gap between water and air.

For a 500ml cup with natural convection (h ≈ 15 W/m²·K) and a freezer at −18°C, the cooling phase takes about 40 minutes. The freezing phase — same surface, smaller gap — takes another four-plus hours.

Total: roughly five hours. Real freezers do better, around 2–4 hours, because they have forced convection and better thermal contact through metal shelves.

ASSUMPTIONSfirst-order estimate
h ≈ 15 W/m²·K // nat. convection
A ≈ 0.04// 500ml cup
T_freezer = −18°C
PHASE 1 · COOLINGavg ΔT ≈ 28°C
P = 15 × 0.04 × 28 ≈ 16.8 W
t₁ = 41,800 / 16.8
t₁ ≈ ~40 minutes
PHASE 2 · FREEZINGΔT = 18°C
P = 15 × 0.04 × 18 ≈ 10.8 W
t₂ = 167,000 / 10.8
t₂ ≈ ~4 hr 17 min
THEORETICAL ESTIMATE
5 hours
REAL WORLD: 2–4 HOURS
CAVEAT

This is a back-of-the-envelope calculation. Real freezers have forced convection; cup material, shape, and air circulation matter a lot. Treat the number as a feel for the physics, not a stopwatch.

03  /  THE PLATEAU

The flat line at zero.

If you actually plotted the water's temperature over time, you'd see something strange: a long, flat plateau right at 0°C. The water stops cooling, even though it's still losing heat.

That heat is going into rearranging molecules into crystals — not into temperature. The thermometer reads zero for hours while the freezer is doing the bulk of its work, invisible.

This plateau is why a thermometer alone can't tell you how much ice has formed. The reading is the same at 5% frozen and 95% frozen.

20°C 0°C −18°C 0 ~40 min ~5 hr Cooling Phase change · 80% of total time Sub-zero time → temperature
TEMPERATURE vs. TIME · SCHEMATIC
04  /  TWO ΔT

Same symbol, two meanings.

A common confusion: "If water stays at 0°C while freezing, why do we use ΔT = 18°C in the heat-transfer formula?" The answer is that there are two different ΔTs in this problem, doing two different jobs.

ΔT · TYPE A

Water's own change

Used in Q = m·c·ΔT. During freezing this is zero — water sits at 0°C the whole time. That's why we switch to latent heat for that phase.

ΔT · TYPE B

The gap with the air

Used in P = h·A·ΔT. Sets the speed of heat flow. Water at 0°C facing air at −18°C still gives an 18°C gap. Without that gap, no heat moves, and ice never forms.

The water can stay at one temperature while heat keeps streaming out — because the gap with the freezer air is what drives the flow, not the change in the water itself.

05  /  FREEZER BUDGET

Like a microwave, but in reverse.

A microwave has a fixed wattage; load it with more food and each item gets a smaller share of energy. A freezer is similar — except instead of pumping energy in, it pumps energy out.

Most home freezers run on compressors rated around 100–250W. That's the upper limit on how fast heat can leave, no matter how many cups you stuff inside.

One or two cups? Barely matters. Five warm cups all at once? You'll feel it.

  • The internal air temperature rises temporarily — your −18°C freezer might briefly become a −10°C freezer.
  • That smaller ΔT means heat flows out of every cup more slowly.
  • If cups are packed tight, the cold air can't circulate, so h (the heat-transfer coefficient) also drops.
06  /  THE MPEMBA EFFECT

The case of the hot ice cream.

1963
Erasto B. Mpemba
MAGAMBA SECONDARY SCHOOL · TANZANIA

A thirteen-year-old boy in Tanzania was making ice cream in cooking class. The recipe said: boil milk and sugar, let it cool, then put it in the freezer. But on this day, the freezer was filling up fast. Mpemba skipped the cooling step and shoved his still-hot mixture in alongside everyone else's already-cooled ones.

Ninety minutes later, his was frozen. The cooled ones weren't.

He told his physics teacher. The teacher was unimpressed: "That's Mpemba's physics, not real physics." The classroom laughed. The boy didn't forget.

Years later, a visiting professor named Denis Osborne came to Mpemba's school. Mpemba asked him the question that had nagged him for years. Osborne, intrigued, ran the experiment back at his lab. The effect was real — under certain conditions, hot water did seem to freeze faster than cold. They published together in 1969.

The strangest part? Aristotle had noticed it. So had Francis Bacon and René Descartes. The phenomenon had been written about for two thousand years and quietly ignored.

"I have come, sir, to ask you a question about physics — but the boys are laughing at me."— MPEMBA TO DR. DENIS OSBORNE, 1969

Why does it happen?

Nobody knows for sure. Several mechanisms have been proposed, and they're probably all true in different situations.

  • Evaporation. Hot water loses some mass as steam.
  • Convection. Stronger internal currents distribute temperature more evenly.
  • Dissolved gases. Hot water has fewer dissolved gases, changing crystallization.
  • The frost layer. A hot container melts the frost beneath it.
  • Supercooling. Cold water can drop below 0°C without freezing; hot water tends to crystallize once it gets there.

A 2000-year timeline

  • ~350 BC
    Aristotle
    Notes that water previously warmed contributes to its freezing quickly. Files it away.
  • 1963
    Mpemba
    Notices it in cooking class. Gets laughed at.
  • 1969
    Mpemba & Osborne
    Publish formal results. The effect gets a name.
  • 2016
    Burridge & Linden
    Cannot reliably reproduce the effect. Suggest earlier studies hinged on imprecise definitions of "freezing time."
  • Today
    Open question
    Quantum analogues of Mpemba-like relaxation have been observed. The classical kitchen version remains contested.

So is it real? Sometimes, probably, under conditions that haven't been pinned down. It's the rare physics question where the right answer might still be: "It depends, and we're not sure on what."

DON'T TRY THIS AT HOME (FOR SPEED)

The Mpemba effect is fascinating, but it's not a reliable trick. If you want fast ice, use the geometry tricks below — they work every time.

07  /  OTHER STRANGENESS

Three more things water shouldn't do.

i

Stays liquid below zero

Pure water, cooled gently and undisturbed, doesn't freeze at 0°C. It can stay liquid down to roughly −38 to −42°C — the limit of homogeneous nucleation. Any small disturbance and the whole cup turns to slush in under a second. Search "supercooled water" on YouTube; it looks like a magic trick.

ii

Grows little spikes

Sometimes an ice cube has a thin spike rising from its top, like a tiny obelisk. Water expands by about 9% when it freezes. If the surface freezes first and the inside expands, liquid water gets squeezed up through a small hole, freezing as it goes and building a tube.

iii

Traps its own breath

Tap water has dissolved gases. As ice forms inward from the edges, those gases get pushed toward the center, ending up as tiny bubbles. That's why home ice is cloudy. Bartenders use directional freezing: insulate sides and bottom, freeze only from the top. The top half ends up glass-clear.

08  /  FOR THE FREEZER

How to actually freeze fast.

  • Spread thin and wide. A flat tray beats a deep cup every time. More surface, shorter distance to the center.
  • Use metal. Stainless steel and aluminum conduct heat hundreds of times better than plastic.
  • Leave space between cups. Cold air needs to circulate around every face.
  • Don't load too much warm stuff at once. The internal air warms up and slows everything else down.
  • Push it to the back. The door area swings most in temperature.