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The volumetric thermal expansion coefficient β describes how much a fluid expands per degree of temperature rise at constant pressure:
β = −(1/ρ)(dρ/dT)
Because MIL-PRF-23699 density decreases linearly with temperature (slope −0.754 kg·m⁻³·K⁻¹ from NIST IR 8263), β increases slowly with temperature as density decreases. At room temperature (68 °F / 20 °C) β ≈ 7.60 × 10⁻⁴ 1/K, rising to about 8.80 × 10⁻⁴ 1/K at 392 °F (200 °C). This is typical for polyol ester (POE) synthetic lubricants.
For a fixed mass of oil, volume is inversely proportional to density. The percent volume change relative to room temperature (68 °F, ρ₀ = 992.12 kg/m³) is:
ΔV/V₀ = (ρ₀ − ρ(T)) / ρ(T) × 100%
Negative values indicate that the oil is denser than at room temperature (volume contracted). At −40 °F the oil occupies about 4.4% less volume than at room temperature; at 392 °F it occupies about 15.8% more. These values are important for sizing oil tanks, reservoirs, and expansion chambers in turbine engine lubrication systems.
β and ΔV/V₀ are derived from the NIST IR 8263 density dataset (Table 23), which covers 5–70 °C (41–158 °F) at ambient pressure (~83 kPa). Values outside this range are extrapolated using the linear density slope. The high-temperature end is capped at 200 °C (392 °F), near MIL-PRF-23699's own 204 °C corrosion/oxidation stability test temperature; no published density measurements exist above the NIST-measured range, so all extrapolated values should be treated as rough estimates only.