Warming a lake with a person

Worked Example · Physics

A 70 kg person falls 10 m from a bridge into a lake the size of a football pitch and 2 m deep. Assume every joule of their fall ends up as heat in the water. How much warmer is the lake afterwards? This is a Fermi estimate: we want the order of magnitude, not the decimal.

1.
Energy of the fall: mass × gravity × height = 70 × 10 × 10 ≈ 7,000 joules.
—Round g to 10. Fermi estimates round everything; the answer will be dominated by the lake, not by the second decimal of gravity.
2.
Volume of the lake: a football pitch is roughly 100 m × 70 m, so 7,000 m² × 2 m deep = 14,000 m³ of water.
—You do not need the exact pitch. You need a number within a factor of two.
3.
Mass of that water: 14,000 m³ × 1,000 kg/m³ = 14 million kg.
—This is the step where the answer is decided. The person is 70 kg; the lake is 200,000 times heavier.
4.
Heat needed to warm water: about 4,200 joules per kilogram per degree. So warming the whole lake by 1 °C would take 14,000,000 × 4,200 ≈ 6 × 10¹⁰ joules.
—The specific heat of water is the one constant worth remembering; it is unusually high, which is why oceans moderate climate.
5.
Temperature rise: 7,000 J ÷ 6 × 10¹⁰ J/°C ≈ 1 × 10⁻⁷ °C. A ten-millionth of a degree.
—No thermometer on Earth can see this. The lake does not notice you.

The move is step 3: find the big number first, because it decides the answer, and everything else is a rounding error next to it.

Pass it alonga thing worth keeping

Save imageX wa in f @

Where this came from

Somebody asked poisonal teach me a little bit about everything

It made 198 things out of that question. This is number 125.

See the other 197

Made 9 October 2026. Written by poisonal ai.

↓ learn more

Your turn

Name a topic and poisonal makes you a whole spread of pieces like this one.