OPOpenPithMake curiosity visiblePhysics lab / Heat and state

About this lab

Six experiments, one question: where does the heat go?

Heat that goes into an object does one of two things: it raises the temperature or it changes the state. The first three experiments look at changes of state: hypo melts at a constant temperature, water boils at a constant temperature, and ice turned all the way into steam spends most of the heat on two flat parts. The fourth looks at temperature rise: the same heat warms different substances by different amounts. The last two look at how heat travels: along an object by conduction, or across the air as radiation.

Every reading, every curve and every falling matchstick comes from one physics model, not from a pre-drawn animation. Change one setting and all the data is recalculated together.

What each experiment shows

Six common ideas that the data overturns

  • “Keep heating and the temperature keeps rising” — hypo stays at 48 °C for about 9 minutes while still absorbing heat. Wax has no such flat part, so it is not a crystal.
  • “Water boils at 100 °C” — only at standard pressure. At 60 kPa it boils at about 86 °C; switch the hot plate off and boiling stops at once.
  • “All the heat raises the temperature” — boiling away 200 g of ice that starts at −20 °C spends about 85 % of the heat on the melting and boiling plateaus.
  • “A bigger rise means more heat” — heated for the same 4 minutes, both beakers absorb the same heat, yet kerosene rises twice as much as water, because water’s specific heat is twice kerosene’s.
  • “All metals conduct alike, glass not at all” — copper and aluminium drop their matchsticks within tens of seconds, iron several times later; the glass rod drops none, yet 4 cm from the hot end it still warms by about 2 °C.
  • “Black things absorb more, so they lose less” — the black can absorbs the most and also cools fastest; the shiny silver can absorbs the least and cools slowest.

Model and sources

Model and sources

  • Lumped heat capacity: the object has one temperature; Q = cmΔT when warming and Q = mL at constant temperature during a change of state. Heat flow = heater power + K(T(surroundings) − T); every stage has an exact solution.
  • Boiling point and pressure: the Clausius–Clapeyron equation anchored at 101.325 kPa and 100 °C; the check script compares it with the NIST Antoine equation and finds less than 0.6 °C difference from 50 to 101 kPa.
  • Conduction: the one-dimensional heat equation with heat loss from the sides and a fixed hot end, solved with the Crank–Nicolson method; the check script compares it with the erfc solution and the steady fin solution.
  • Radiation: absorbed = α·E·A, lost = convection + εσA(T⁴ − T₀⁴); fourth-order Runge–Kutta, one-second steps.

Specific heats are the textbook (PEP) values: water 4.2×10³, kerosene and ice 2.1×10³, castor oil 1.8×10³ J/(kg·°C). The latent heat of fusion of ice 3.34×10⁵ J/kg, the latent heat of vaporization of water 2.256×10⁶ J/kg, thermal conductivities and densities are from OpenStax. The melting point of hypo, 48 °C, is from the textbook table.

These are teaching assumptions, used only to compare sizes, not measured values: the specific heat and latent heat of hypo, the 42–62 °C softening range of wax, the heat-transfer coefficient between tube and water, the beaker’s heat loss, wax melting at 52 °C, heat loss from the rods, the lamp’s irradiance, and the absorptance and emissivity of the three can surfaces. Water and liquids are tinted only so they can be seen. The beaker and hot plate themselves store no heat in the model, so boiling stops the moment the plate switches off.

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