Thermal Expansion: Coefficient α

An unknown metal rod of known L₀. Measure ΔL at several ΔT and recover α from a fit of ΔL versus ΔT.

Kids· 20 min·Related simulator: ThermodynamicsThermal Expansion

Goal

Determine α from ΔL = α L₀ ΔT. The slope of ΔL versus ΔT is α L₀, so α = slope / L₀.

Equipment

Metal rod (unknown α)
Heater / bath (ΔT)
Caliper (ΔL)
Metre scale (L₀)

Experiment

Unknown-metal rod. The millimetre scale is fixed. No live ΔL on the bench.

Known cold length L₀ = 400 mm. The metal is unknown. The caliper reports ΔL only after you record.

Temperature change ΔTΔT = 60 K

Caliper: no reading

Record at least 6 values of ΔT from 20 K to 180 K, then fit ΔL versus ΔT.

Measurements

№	ΔT K	ΔL mm
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Thermal Expansion: Coefficient α

Generated: 24 Aug 2026, 22:29

Goal

Determine α from ΔL = α L₀ ΔT. The slope of ΔL versus ΔT is α L₀, so α = slope / L₀.

Measurement table

#	ΔT (K)	ΔL (mm)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted expansivity agrees with the hidden α. Main uncertainties: caliper noise and the linear ΔL = α L₀ ΔT model.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

In the linear regime a rod expands as ΔL/L₀ = α ΔT. The bench hides α and the material name. A caliper reports ΔL only after you record; there is no live ΔL while you drag temperature.

Procedure

L₀ is fixed and known. The expansivity α is hidden. You only change ΔT.
Record. The caliper logs ΔL with small readout noise.
Repeat for at least 6 temperature changes from about 20 K to 180 K.
Fit ΔL (mm) versus ΔT; α = slope / L₀. Compare with the reference.

Conclusion

The fitted expansivity agrees with the hidden α. Main uncertainties: caliper noise and the linear ΔL = α L₀ ΔT model.