# Online calculator

## Air properties calculator

This online calculator has been designed to simplify the task of computing the thermal properties of air at a given temperature and pressure.

The correlations are defined in the temperature range of 160–1000 K.

## How it Works

Our calculator uses:

1. Sutherland law, which results from a kinetic theory that uses an idealized intermolecular-force potential . It is used to compute thermal conductivity and dynamic viscosity.

k = k_{0} \cdot \left( \frac{T_\mathrm{0_{input}}}{T_{0}} \right)^{3/2} \cdot \frac{T_{0} + S_\mathrm{k}}{T_{0_\mathrm{input}} + S_\mathrm{k}}  \left( 1 \right)
\mu = \mu_{0} \cdot \left( \frac{T_{0_{input}}}{T_{0}} \right)^{3/2} \cdot \frac{T_{0} + S_\mathrm{\mu}}{T_{0_{input}} + S_\mathrm{\mu}}  \left( 2 \right)

where:

k_{0} = 2.404\cdot10^{-2}\ \mathrm{W/(m·K)}
S_\mathrm{k} = 202.2\  \mathrm{K}
S_\mathrm{\mu} = 111.8\  \mathrm{K}
T_{0} = 273\  \mathrm{K}
\mu_{0} = 1.721\cdot10^{-5}\ \mathrm{kg/(m\cdot s)}

2. Daubert and Danner correlations, recommended to academic libraries serving students in engineering . They are used to compute specific heat at constant pressure and specific heat at constant volume.

c_\mathrm{p} = \frac{A + B \cdot \left( \frac{\frac{C}{T_{0_{input}}}}{\sinh\left(\frac{C}{T_{0_{input}}}\right)} \right)^{2} + D \cdot \left( \frac{\frac{E}{T_{0_{input}}}}{\cosh\left(\frac{E}{T_{0_{input}}}\right)} \right)^{2}}{MW}\ (3)

c_\mathrm{v}=c_\mathrm{p}-R\ (4)

where:

A = 28958
B = 9390
C = 3012
D = 7580
E = 1484
MW =  28.951\ \mathrm{kg/kmol}
R = 287\  \mathrm{J/(kg·K)}

## Nomenclature

Roman

• cp: specific heat at constant pressure
• Units: [cp] = J/(kg·K)
• Interpretation: the quantity of heat required to raise the temperature of unit mass of the gas by 1 degree, the pressure remaining constant during heating
• cv: specific heat at constant volume
• Units: [cv] = J/(kg·K)
• Interpretation: the quantity of heat required to raise the temperature of unit mass of the gas by 1 degree, the volume remaining constant during heating
• h: specific enthalpy evaluated relative to hR, i.e., change in enthalpy that occurs when air is taken from TR to T
• Units: [h] = J/kg
• hR: reference specific enthalpy at TR
• Units: [hR] = J/kg
• k: thermal conductivity
• Units: [k] = W/(m·K)
• Interpretation: rate at which heat is transferred by conduction through a unit cross-section area of a material, when a temperature gradient exits perpendicular to the area . For a fixed temperature gradient, conduction increases with increasing thermal conductivity.
• p: air pressure
• Units: [p] = Pa
• Pr: Prandtl number
• Units: Pr has no units, it is nondimensional (dimensionless).
• R: Specific gas constant
• Units: [R] = J/(kg·K)
• Interpretation: amount of mechanical work obtained by heating the unit mass of a gas through a unit temperature rise at constant pressure 
• T: air temperature
• TR: 0 °C

Greek

• α: thermal diffusivity
• α = k/(ρ·cp)
• Units: [α] = m2/s = (J/kg)·s. Specific energy multiplied by time.
• γ: specific heat capacity
• γ = cp/cv
• Units: γ has no units, it is nondimensional (dimensionless).
• µ: dynamic viscosity
• Units: [µ] = kg/(m·s) = Pa/s. Pressure multiplied by time.
• ν: kinematic viscosity
• ν = µ/ρ
• Units: [ν] = m2/s = (J/kg)·s. Specific energy multiplied by time.
• ρ: density, mass per unit volume
• ρ = p/(R·T)
• Units: [ρ] = kg/m3

## References

 Sutherland W. (1893). The viscosity of gases and molecular force.
 Daubert, T.E. (1989). Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation.
 White F.M. (1974). Viscous fluid flow.
 Ratna D. (2012). Thermosets Structure, Properties and Applications.
 Houghton E.L., Carpenter P.W., Collicott S.H., Valentine D.T. (2017). Aerodynamics for Engineering Students.