Heating curve

Heat ice at a steady rate and watch the temperature climb, stop while it melts, climb again and stop while it boils. See the heat and time for each stage, and use the mixer to find the final temperature when hot and cold things, or ice and water, are mixed.

Keep it one tap away for everyday use.

Bookmark Heating curve?

Press Ctrl + D now. Your browser opens its own bookmark box, where you choose the name and folder.

  1. Set heater
  2. Curve
  3. Mix
  4. Check
Nothing is uploadedWorks offline once open

Heat the ice

The heater is assumed to put all its heat into the ice, water or steam, with none lost to the air or the beaker, and the steam is kept in. Rounded school values: c of ice 2,100, of water 4,200 and of steam 2,000 J/(kg K); latent heat of melting 3.34 × 10⁵ J/kg and of boiling 2.26 × 10⁶ J/kg.

Mix and find the final temperature

Heat lost by the hot body = heat gained by the cold body (no heat lost to the cup or the air). The cup water must stay liquid, from 0 to 100 °C. Specific heats of the metals are rounded general values.

Try this

  • Watch the flat parts: the heater is still on, but the temperature does not move while ice melts or water boils.
  • Compare the lengths of the flat parts: boiling takes almost 7 times as long as melting, because L for boiling is much bigger.
  • Double the mass: every stage takes twice as long. Double the power: every stage takes half as long.
  • The water line is less steep than the ice and steam lines: water needs about twice as much heat for each degree.
  • In the mixer, drop 50 g of ice into 200 g of water at 50 °C, then 200 g of ice. Does it all melt?

Check yourself

What it does

Put ice from the freezer on a steady heater and measure its temperature. It rises, then stops at 0 °C for a long time while the ice melts, rises again, then stops at 100 °C for even longer while the water boils, and only then does the steam get hotter. The flat parts are where the heat goes into pulling the particles apart instead of making them move faster: that hidden heat is called latent heat. This page plays the whole heating curve, with a beaker that melts and boils as the graph is drawn, and a table of the heat and time for each stage. A second card is a mixer: drop hot water, a metal ball or ice into a cup of water and find the final temperature.

It follows the school topics on heat: Class 9 Science, Matter in Our Surroundings (change of state, latent heat of fusion and vaporisation), and Class 11 Physics, Thermal Properties of Matter (specific heat capacity, calorimetry, change of state, latent heat). Before this, try states of matter for the particle picture; afterwards, phase diagram shows melting and boiling at other pressures and heat engine cycles turns heat into work.

How to use it

  1. Set the mass of ice, the heater power and the starting temperature of the ice.
  2. Watch the curve draw itself (the whole heating plays in about 24 seconds). Pause to stop at a moment; Start again goes back to the start.
  3. Read the table: the heat each stage needs and how long it takes at your heater power, with the formula used.
  4. In the mixer, choose what you drop in, its mass and temperature, and the mass and temperature of the water in the cup. The final temperature is shown with the working.

Worked example

With the page as it opens: 0.5 kg of ice at −20 °C on a 500 W heater, heated to 120 °C.

  • Ice warms from −20 °C to 0 °C: Q = mcΔT = 0.5 × 2,100 × 20 = 21 kJ, taking 42 s.
  • Ice melts: Q = mL = 0.5 × 3.34 × 10⁵ = 167 kJ, taking 334 s (5.57 min).
  • Water warms from 0 °C to 100 °C: 0.5 × 4,200 × 100 = 210 kJ, 7 min.
  • Water boils: 0.5 × 2.26 × 10⁶ = 1,130 kJ, 37.7 min.
  • Steam warms to 120 °C: 0.5 × 2,000 × 20 = 20 kJ, 40 s.

In all, 1,548 kJ in 51.6 min. In the mixer, 0.2 kg of water at 80 °C and 0.3 kg at 20 °C end at (0.2 × 80 + 0.3 × 20) / 0.5 = 44.0 °C. Drop 50 g of ice into 0.2 kg of water at 50 °C: the water can give 42 kJ, melting needs 16.7 kJ, and the 25.3 kJ left warms all 0.25 kg to 24.1 °C.

Check yourself

Five questions with fresh numbers: heat to warm water, heat to melt ice, how long a heater takes to melt ice, the final temperature of a mixture, and what happens to the temperature while ice melts. Nothing is saved.

Tips

  • Steeper lines mean less heat per degree. Water’s line is the least steep: water has a large specific heat, which is why the sea warms up slowly.
  • Steam at 100 °C burns worse than water at 100 °C because it gives up its latent heat as it condenses on your skin.
  • Real experiments lose heat to the air and the container, so measured times are longer than the page shows.

FAQ

Why is boiling so much longer than melting? Turning liquid into gas pulls particles completely apart, which takes about 7 times as much energy per kilogram as loosening them from the solid.

Why does the mixer stop at 0 °C sometimes? If the warm water cannot supply enough heat to melt all the ice, the mixture stays at 0 °C with ice left over.

Is this from NCERT? No. It is an independent study aid that follows the same school topics, with its own pictures and numbers.

Where the numbers come from

  • Heat for a temperature change Q = mcΔT, latent heat Q = mL, power P = Q/t, and the principle of calorimetry (heat lost = heat gained): standard physics.
  • Rounded school values: specific heat of ice 2,100, water 4,200 and steam 2,000 J/(kg K); latent heat of fusion 3.34 × 10⁵ J/kg and of vaporisation 2.26 × 10⁶ J/kg; metals iron about 450, copper about 385 and aluminium about 900 J/(kg K).
  • Checked against hand working in Python written for the tests.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.

Change log for Heating curve

  1. Add #1065 Heating curve of water Details on GitHub

Every change to fibub

Related tools

Heat engine cycles #T652 Draw the air-standard Carnot, Otto, Diesel, Brayton and Stirling cycles on pressure-volume and temperature-entropy diagrams, with every state, the heat and work of each process, net work, mean effective pressure and efficiency against the Carnot limit. Phase diagram #T108 Draw the phase diagram of a two-component mixture from the melting points and enthalpies of fusion (complete solid solution like Cu–Ni, or a simple eutectic like Bi–Cd), find the phases, their compositions and amounts at any temperature, and use the lever rule on compositions read off any real diagram, in wt % or mol %. States of matter #L28 Heat or cool water, ethanol, oxygen or iron and watch the particles vibrate in place, slide past each other or fly apart. Stop at the melting and boiling points, change °C to kelvin, and race diffusion in liquids and gases. Kinetic theory #L30 Watch gas particles bounce around a box. The pressure is counted from their hits on the walls and compared with the gas law; a live histogram shows the speeds settle into the Maxwell shape. Then see the rms speed and average energy of real gases at any temperature. Measurement and parallax #L104 Read a ruler, a thermometer and a measuring cylinder, then move your eye off to one side and watch the reading change: parallax error. Type your reading to check it. Class 9 adds least count, uncertainty and percentage error. Barometer altitude #L110 Drag a climber up a mountain and watch the air thin out, the mercury barometer fall from 760 mm and water's boiling point drop to about 70 °C on Everest. Tick the pressure cooker to bring it back above 100 °C. Dissolving lab #L111 Spoon salt, sugar or potassium nitrate into water at any temperature and watch it stop dissolving at saturation. Your beaker is a dot on the solubility curve; cool it to grow crystals, and see why warm water holds less oxygen and fizz. Separation lab #L141 Pick a mixture such as sand and salt, oil and water or green ink, choose a lab method and see whether it separates them. Chain steps into a plan, watch the thermometer during distillation and fractional distillation, and see which property each method uses. Temperature scales #L208 Drag one thermometer and read Celsius, Fahrenheit and kelvin side by side, with the conversion worked out. See a gas thermometer's straight lines all reach zero pressure at −273.15 °C, and at Class 11 add Rankine and make a scale of your own. Thermal expansion #L209 Warm a railway track or a bridge and watch the gaps between the pieces shrink, then close and make the rail bow. See ΔL = α L ΔT with your numbers, the gap to leave, and at Class 11 the stress in a welded rail and how area and volume grow. Carnot engine #L210 Set the hot and cold temperatures and see the best possible engine's efficiency, with heat and work arrows drawn to scale. Run it backwards as a refrigerator or heat pump for the COP, watch the cycle go round on a p–V diagram, and test an inventor's claim against the second law. Gibbs explorer #L221 Slide ΔH, ΔS and the temperature and watch ΔG = ΔH − TΔS change as a straight line against temperature, with the spontaneous region shaded, the turn-over temperature T = ΔH/ΔS marked and the four sign cases sorted. A Class 12 level adds K = e^(−ΔG°/RT) and E° = −ΔG°/nF.

Also related: Bond enthalpy estimator, Bomb calorimeter, Hydrogen bonding