Thermal expansion sim

What the sim shows

Model. Every length grows as L = L₀ (1 + α (θ − 20)) (beyond the syllabus), with α = 19 × 10⁻⁶ per °C for brass, 1.2 × 10⁻⁶ for invar, 12 × 10⁻⁶ for steel and 3.3 × 10⁻⁶ for borosilicate glass (handbook values from memory). Ball 25.40 mm and hole 25.45 mm across at 20 °C: the ball sticks once it is about 104 °C hotter than the ring. In the flame a part heats toward 700 °C (time constant 100 s for the ball, 120 s for the ring); in the air it cools toward 20 °C (400 s and 450 s). These are chosen values. The strip: two 0.5 mm layers, 90 mm long. Its curvature comes from Timoshenko's bimetal formula, with Young's moduli 100, 141 and 200 GPa (beyond the syllabus): the free tip moves 10.7 mm (brass–invar) or 4.1 mm (brass–steel) for a 100 °C rise. The layers are drawn three times thicker than they are; the bend is drawn true. The burner brings the strip toward 250 °C (time constant 40 s) and it cools with 90 s (chosen). The bath: two 100 cm³ flasks; the water's density from the Tanaka (2001) formula; the air an ideal gas at constant pressure, and the air pushed into the syringe cools to 20 °C; the glass flask's own growth is taken off both. The bath heats toward its dial with a time constant of 120 s and cools with 900 s (chosen); the flasks are taken to be at the bath's temperature at each reading. Readings carry seeded scatter and are read to the instrument: thermometer 0.5 °C, thermocouple 0.1 °C, mm scale 0.5 mm, tube 0.05 cm³, syringe 0.5 cm³. Time moves only when you press a heat or wait button.

• The part to watch: the brass ball, the bimetallic strip, or the graduated tube with its column of coloured water
• Retort stands, Bunsen burners, brass ring, contact screw, mm scale, lamp, battery, thermocouple meter, water bath, flasks, gas syringe, stopwatch

Use it in your lessons

• Try it here: anyone can unlock 2 figures free, and a free account unlocks up to 5. Runs on a laptop, a Chromebook or a phone; nothing to install.
• Present it and share student links with the teacher plan, from US$5 a month, billed yearly.
• Put it on your own website or LMS for US$9, paid once, or every sim from US$29 a month.

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