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For dry air at 20 °C and 1 atm, β = 3.421×10⁻₃ 1/K (1.901×10⁻₃ 1/°F). The ideal gas value 1/T is 3.411×10⁻₃ 1/K, only -0.29 % different. This page is for dry air.
For most gas work at 1 atm, use β = 1/T with T in kelvin. The real-gas value matters at high pressure and low temperature.
β is the fractional change in volume per degree at constant pressure:
β = (1/v) (∂v/∂T)P = −(1/ρ) (∂ρ/∂T)P
For an ideal gas v = RT/P, so β = 1/T exactly. A hotter gas has a smaller β. β sets the buoyancy force in natural convection, through the Grashof and Rayleigh numbers:
Gr = g β ΔT L³ / ν²
At 100 bar and −100 °C the real β is 17.5×10⁻₃ 1/K, against 1/T = 5.78×10⁻₃ 1/K. Density comes from the air density page and ν from the viscosity page.
Accuracy. Lemmon et al. (2000) state an uncertainty of about 0.1 % in density, 0.2 % in speed of sound and 1 % in heat capacity from the solidification point to 873 K (600 °C) and up to 70 MPa. Above 873 K there were no reliable air data, so nitrogen data were used and the paper gives about 0.5 % for density. Lemmon & Jacobsen (2004) state about 5 % for the viscosity and thermal conductivity of air, and more near the critical point. Viscosity and conductivity above about 600 °C, and the 1000 °C end of the range, are less certain than that. CoolProp uses a molar mass of 28.96546 g/mol, the U.S. Standard Atmosphere uses 28.9644 g/mol. That is the main reason CoolProp density at 15 °C and 1 atm is 0.04 % above the Standard Atmosphere value.