PHY031 · Thermodynamics · Classes 11–12
Linear thermal expansion
Objective: To measure the linear expansion of a metal rod and find its coefficient of linear expansion α.
🧰 Apparatus
- Metal rod in a steam jacket
- Dial gauge (0.01 mm)
- Steam generator
- Thermometer
- Metre scale
📐 Formulas and SI units
ΔL = α L₀ ΔT (m)
α in /K (about 10⁻⁵ for metals)
💡 Theory
Solids expand when heated because their atoms vibrate more and sit further apart. The increase in length is ΔL = αL₀ΔT, where α is the coefficient of linear expansion, a property of the material. Bridges and rails have gaps to allow for this.
🪜 Procedure
- Measure the rod length L₀ and the room temperature.
- Fit the rod in the jacket against the fixed end and set the dial gauge to zero.
- Pass steam through the jacket until the reading is steady.
- Record the steam temperature and ΔL.
- Calculate α = ΔL/(L₀ΔT).
- Repeat for another metal.
📋 Observations Simulated values
✅ Result and conclusion
A 1 m steel rod (α = 12 × 10⁻⁶ /K) heated by 50 K grows 0.6 mm; aluminium grows about twice as much.
🔬 In a real lab
The rod's ends may not reach steam temperature and the jacket also expands, so α is slightly underestimated.
⚠️ Safety
Steam scalds: let the apparatus cool, use heat-proof gloves and point steam outlets away from people.
❓ Quick check
1. Why do railway tracks have small gaps?
2. Doubling ΔT makes ΔL…
3. Invar is used in clocks because…
🏋️ Practice
EasyCopper (17 × 10⁻⁶ /K), 2 m, ΔT 40 K. ΔL?
Answer: 1.36 mm
MediumΔL = 0.46 mm for 1 m, 20 K. α?
Answer: 23 × 10⁻⁶ /K (aluminium)
ChallengeWhy are power lines slack in summer?
Answer: The wires expand