Hidden Heat

Why it matters

Ice at 0 °C and water at 0 °C read identical on every thermometer — yet one of them is hiding 336 joules per gram. Your drink knows the difference. So does every cyclone.

The idea in plain words

The hidden ledger. Tap the terms.

Q = m × L

Heat to convert 50 g of ice at 0 °C into water at 20 °C?

Q = 21,000 J — melting cost 4× the warming!

• J/g: L (fusion) — 336 J per gram to melt ice at 0 °C — with NO temperature change
• J/g: L (steam) — ~2260 J/g to boil water — why steam burns are far worse than boiling-water burns
• the why: kinetic view — latent heat pays for separating molecules (potential energy), not for speeding them (kinetic)
• Melt: Q₁ = mL = 50 × 336 = 16,800 J
• Warm: Q₂ = mcΔT = 50 × 4.2 × 20 = 4,200 J

Predict first

Why does ice at 0 °C cool a drink better than the same mass of water at 0 °C?

Every gram of ice runs a 336 J toll booth ON TOP of its ordinary warming — that hidden charge is what murders the drink's heat.

• melting ice ALSO absorbs 336 J/g of latent heat from the drink — correct
• ice is simply colder than 0 °C water
• it doesn't — same temperature, same cooling

What you do

Budget the heater: melt exactly 100 g of the 400 g block. Overshoot and you've flooded the challenge.

Check yourself

During melting, the absorbed latent heat increases the molecules'…

Temperature tracks kinetic energy — it stalls exactly because the joules are buying separation instead.

Steam at 100 °C scalds far worse than water at 100 °C because…

Same temperature, plus a monstrous hidden payload released on contact.

How much heat melts 250 g of ice at 0 °C? (L = 336 J/g)

Q = mL = 250 × 336 = 84 kJ — and the meltwater is STILL at 0 °C.

• potential energy (separation), not kinetic (speed) — correct
• kinetic energy — they speed up
• mass
• condensing steam dumps an extra 2260 J/g of latent heat into your skin — correct
• steam is hotter than 100 °C always
• steam moves faster
• 84,000 J — correct
• 336 J
• 840 J