Volume Thermal Expansion Calculator
First-order volume expansion for solids and liquids: V=V₀(1+β·ΔT). Common β: ethanol 1.12e-3/°C, water 0.21e-3/°C, steel 35.7e-6/°C, aluminum 69e-6/°C.
Input Data
Results
At a glance:First-order volume expansion of solids and liquids with temperature: V=V₀·(1+β·ΔT), where β is the volume expansion coefficient. For an isotropic solid β≈3α (three times the linear coefficient). This free tool is based on standard textbook physics and suits DSE/GCE/IB Physics exams and engineering calculations. Notes: (1) β is material- and phase-dependent; liquids generally have much larger β than solids (water 0.21e-3/°C at 20°C, ethanol 1.12e-3/°C); (2) for solids β≈3α (steel α≈11.9e-6 → β≈35.7e-6/°C; aluminum α≈23e-6 → β≈69e-6/°C); (3) water is anomalous near 4°C (density maximum), so this linear form is only an approximation away from that range; (4) the first-order formula is accurate for small ΔT; for large changes use the integrated form if β varies with T.
Formula
Volume: V = V₀·(1 + β·ΔT)
Volume change: ΔV = V₀·β·ΔT
Percent change: (ΔV / V₀)·100%
Relative volume: V/V₀ = 1 + β·ΔT
For solids: β ≈ 3α
$$V = V_0(1 + \beta \Delta T), \quad \Delta V = V_0 \beta \Delta T$$How to Use
- Enter initial volume V₀ (L).
- Enter volume coefficient β (1/°C); pick a common substance or type your own.
- Enter temperature change ΔT (°C).
- The tool outputs final volume, ΔV, percent change and V/V₀.
Case Studies
Ethanol in a thermometer
V₀=1 L ethanol, β=1.12e-3/°C, ΔT=20°C.
V = 1×(1+1.12e-3×20) = 1.0224 L.
ΔV = 0.0224 L (2.24% expansion) — the basis of alcohol thermometers.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.