Motion lab · heat

Heat Conduction Lab

Two insulated beakers are joined by a rod. Pick what the rod is made of, and see how fast heat moves from the hot water to the cold water.

Time
(seconds)
T (°C)
(Beaker A)
T (°C)
(Beaker B)
Controls:
How to use this simulation
  1. Choose the Rod material from the menu above the beakers: aluminum, copper, steel, glass or plastic. The rod carries heat from Beaker A to Beaker B.
  2. Press Play (the triangle). Beaker A starts at 95 °C and Beaker B starts at 5 °C. Watch the thermometers and the T = readings above them.
  3. The Minutes and Seconds boxes show how much time has passed. The simulation runs much faster than real time.
  4. Open Table to see both temperatures every 5 seconds. Use Copy table or Save as a CSV file to put the data in a spreadsheet.
  5. Open Bar chart to compare the two temperatures right now. Check Show numerical values to see the numbers on the bars.
  6. Open Graph to see how each temperature changes over time. Use Zoom out to see a longer time, or Zoom in to see the start up close.
  7. Press Pause to freeze the clock. Press Reset to start over. You must reset before you can pick a new rod.
Conductors and insulators

Conduction is heat moving through a material when its particles bump into each other. Fast particles in the hot water bump the rod's particles. Those bump the next ones, all the way to the cold water.

A thermal conductor lets heat move through it easily. Metals like copper and aluminum are good conductors. A thermal insulator slows heat down. Glass and plastic are insulators.

Scientists rate this with a number called thermal conductivity. A bigger number means heat moves through faster.

Rod materialThermal conductivity (W/m·K)
Copper385
Aluminum205
Steel45
Glassabout 0.8
Plasticabout 0.2
Thermal equilibrium

Heat always moves from the hotter object to the colder one. It never goes the other way by itself.

The beakers are sealed and insulated, so no heat gets out to the room. Every bit of heat Beaker A loses, Beaker B gains. Add the two temperatures at any time and you get 100 °C.

Heat moves fastest when the temperature gap is big. As the beakers get closer in temperature, heat moves more slowly. That is why the graph lines are steep at first and then flatten out.

In the end, both beakers reach the same temperature, 50 °C. Then heat stops moving between them. This is called thermal equilibrium.

The math the simulation uses
  • The temperature gap starts at 95 − 5 = 90 °C and shrinks over time: gap = 90 × e−rt
  • The beakers always stay the same distance from 50 °C: TA = 50 + gap ÷ 2 and TB = 50 − gap ÷ 2
  • The rate r depends on the rod. It is bigger for a better conductor: r = thermal conductivity × 0.0000244 per second.
  • With aluminum, r = 0.005 per second, so the gap halves about every 139 seconds. With copper it halves about every 74 seconds. With glass it takes almost 10 hours.