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Air properties calculator

1) k = ... W/(m·K)

2) µ = ... kg/(m·s)

3) c_{p} = ... J/(kg·K)

4) c_{v} = ... J/(kg·K)

5) γ = c_{p}/c_{v} = ...

6) Pr = c_{p}µ/k = ...

7) c_{p}/k = ... (m·s)/kg

8) h = ... J/kg

9) ρ = ... kg/m^{3}

10) α = ... m^{2}/s

11) ν = ... m^{2}/s

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 [1]. It is used to compute thermal conductivity and dynamic viscosity.

2. Daubert and Danner correlations, recommended to academic libraries serving students in engineering [2]. 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

c_{p}: specific heat at constant pressure

Units: [c_{p}] = 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

c_{v}: specific heat at constant volume

Units: [c_{v}] = 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 h_{R}, i.e., change in enthalpy that occurs when air is taken from T_{R} to T

Units: [h] = J/kg

h_{R}: reference specific enthalpy at T_{R}

Units: [h_{R}] = 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 [4]. 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 [5]

T: air temperature

T_{R}: 0 °C

Greek

α: thermal diffusivity

α = k/(ρ·c_{p})

Units: [α] = m^{2}/s = (J/kg)·s. Specific energy multiplied by time.

γ: specific heat capacity

γ = c_{p}/c_{v}

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] = m^{2}/s = (J/kg)·s. Specific energy multiplied by time.

ρ: density, mass per unit volume

ρ = p/(R·T)

Units: [ρ] = kg/m^{3}

References

[1] Sutherland W. (1893). The viscosity of gases and molecular force. [2] Daubert, T.E. (1989). Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation. [3] White F.M. (1974). Viscous fluid flow. [4] Ratna D. (2012). Thermosets Structure, Properties and Applications. [5] Houghton E.L., Carpenter P.W., Collicott S.H., Valentine D.T. (2017). Aerodynamics for Engineering Students.