Why does the metal ball get stuck?
A metal ball just fits through a ring. Heat only the ball and try again: it gets stuck. It has not melted and is still round; it has grown a little. This is thermal expansion.
Look inside: atoms are always vibrating. Heating usually raises their average vibration energy and increases their average separation. Many tiny increases add up to a slightly larger ball.
Now watch the thermometer and two-layer strip. Expanding liquid rises in a thin tube; two metals that expand by different amounts make the strip bend. Follow the changing shape first; open the calculations below if you want more.
Two experiments to try at home
- The bottle that inflates a balloon. Stretch a deflated balloon over the mouth of an empty plastic bottle, then stand the bottle in hot water: the balloon puffs up. Move it into cold water and the balloon deflates again, sometimes sucked right into the bottle. Both the air inside and the bottle’s walls expand and contract; you are watching their combined result.
- A ping-pong ball in warm water. Place a dented ping-pong ball in hot water (about 60 ℃) and watch the dent swell back out—the air inside expands and pushes the shell from within. Skip boiling water: overheating warps the plastic.
Predict first: two bottles in the same hot bath, one filled with water and one empty—which balloon inflates faster? Then test it. Liquids and gases expand more than solids, but heat still needs time to travel.
How wide should the gap be? The formula decides
More: a closer explanation
A metal ball just passes through its ring. Heat the ball for half a minute and try again—it sticks. The ball has not melted or bent; it has simply grown a little.
Zoom into the metal for the reason: atoms hold their places yet vibrate gently all the time. At a higher temperature, atoms generally have more average vibrational energy and larger vibration amplitudes. Heating transfers energy into the metal; heat transferred and temperature are different quantities.
The key is that the push and pull between atoms is asymmetric: crowding is punished sharply, while separation is only gently recalled. As vibration grows, atoms yield more room outward than inward, so their average spacing grows—stack up billions of those spacings and, macroscopically, you have expansion. The experiment’s chain model computes exactly this with an asymmetric “softening spring”: the higher the vibration energy, the larger the mean spacing it derives. That single fact is why the ball jams and why rails need gaps.
Open: ΔL = αL₀ΔT
Linear expansion has a very short rule: the growth equals the coefficient α, times the original length L₀, times the temperature rise ΔT.
Teaching values: iron α ≈ 1.2×10⁻⁵/℃, copper ≈ 1.7×10⁻⁵/℃, aluminum ≈ 2.3×10⁻⁵/℃; alcohol’s volumetric coefficient β ≈ 1.1×10⁻³/℃—dozens of times larger than a metal’s α, which is why thermometers hold dyed alcohol. Check a rail: 100 m of track warming by 40 ℃ grows about 1.2×10⁻⁵ × 100 × 40 = 0.048 m—under five centimetres. This does not mean a long welded track freely extends at its ends. Jointed rails use gaps; continuous welded rails manage temperature stress with a chosen neutral temperature, fasteners and ballast. Bridges may use expansion joints. In the experiment, swap in a copper rail or an aluminum rod: at the same ΔT, the growth scales with α.
Open: why a bimetal strip bends
Forge a high-expansion copper layer onto a low-expansion iron layer. Heated, both layers want to lengthen but must curve together: copper rides the outer, longer arc, so the strip bends toward the iron side. For equal-thickness layers, also approximating their elastic moduli as equal, the curvature is roughly
with t the combined thickness. Real copper and iron have different moduli, which an accurate curvature calculation must include. The thermostat in an iron or an oven uses precisely this: hot enough, the strip bends off the contact and cuts the circuit; cooling lets it bend back and reconnect. The “bend exaggerated 25×” label in the experiment only makes this formula’s angle visible.
Limits: water’s odd expansion below 4 ℃
Most liquids expand when warmed; below 4 ℃ water does the opposite—cooling expands it, and its density peaks at 4 ℃. Ice therefore floats, lake beds hold near-4 ℃ water through winter, and life below survives. That hydrogen-bond exception lies outside ΔL = αL₀ΔT; likewise, this topic’s atomic chain is a one-dimensional teaching potential, the α values are teaching values, and the spacing, ball-diameter and bending changes in the pictures are exaggerated by their labelled factors. For data see OpenStax College Physics 13.2 Thermal Expansion, OpenStax Physics 13.2, and NIST thermal expansion measurements.