Kettle on a balance: latent heat of vaporization from mass loss
SPH3U Grade 11 Physics · Energy and Society
A student sets an open-lidded kettle on a kitchen balance, brings it to a full rolling boil, and only then starts the measurement: a plug-in power meter at the wall reads a steady 1440 W, and over exactly 4.00 min of hard boil the balance falls from 1462.0 g to 1312.0 g — 150.0 g gone as steam. The handbook latent heat of vaporization of water, for the audit, is 2257 kJ/kg.
- P = 1440 W — Metered power at the wall
- t = 4 min — Timed interval at full boil
- Δm = 150 g — Mass lost to steam (1462.0 − 1312.0 g)
- L_v = 2257 kJ/kg — Handbook latent heat of vaporization
- (a)the energy the kettle delivers during the timed boil
- (b)the latent heat of vaporization these readings imply
- (c)the mass a perfectly insulated kettle would have boiled off with the same energy
E = Pt with the METERED 1440 W, not the 1500 W on the rating plate — nameplates are maxima at nominal voltage, and the wall meter is the truth. Starting the clock only after the boil is established is the other half of the design: from then on, no joule goes into raising temperature.
Carried onward at full precision, not this rounded figure.
At a rolling boil the thermometer is parked at 100 °C, so every joule buys phase change: L = Q/m. The result reads about 2% above the handbook 2257 kJ/kg, and high is the only direction it can miss — the kettle's walls shed some heat to the room, so the metered E overstates what the steam actually received.
Carried onward at full precision, not this rounded figure.
The audit, run the other way: a lossless kettle spending all 345.6 kJ at the handbook rate would have boiled off 153.1 g. The balance saw 150.0 g. The 3.1 g gap is the wall losses and the fine spray that escapes as droplets rather than vapour — about 2% of the water, and the whole error budget of the lab.
Carried onward at full precision, not this rounded figure.
Therefore the kettle metered 345.6 kJ into the water, the balance's 150.0 g of lost steam prices vaporization at 2304 kJ/kg — 2.1% over the handbook 2257 — and a perfect kettle would have boiled off 153.1 g, the 3.1 g shortfall being the loss the foam and spray claimed.
Why this order
The elegance of this lab is what it does NOT need: no thermometer, no calorimeter constant, no mixing. Once the boil is rolling, temperature is pinned at the boiling point and the first law collapses to E = mL — so the chain needs only a wall meter, a clock and a balance, in that order. Part (a) must come first because the energy is the only thing being metered; part (b) divides it by the balance's verdict; part (c) reruns the division with the handbook L to expose the difference as grams rather than percent. The two design decisions in the scenario are the actual physics content: start timing AFTER the boil (or sensible heating contaminates E with joules that moved no mass), and read the wall meter, not the rating plate (or the error is built in before the water is).
The number itself deserves awe: 2257 kJ/kg is nearly seven times the 334 kJ/kg that melting cost in the ice-cube chain, and five times the energy needed to heat the same water from 0 to 100 °C. That enormity is why a kettle takes seconds to climb the last degree and minutes to boil dry, why sweating is the body's most powerful cooling instrument, and why a steam burn injures so much worse than boiling water — every condensing gram hands back its 2.26 kJ on contact. It is also why the measured value always errs high in this lab and how to shrink the error: lag the kettle, shield the spray, lengthen the run so the fixed losses dilute. Doubling the timed interval roughly halves the percentage miss — the cheapest precision upgrade in experimental physics.
Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.