Engineering task and calculation objective
This module calculates the thermophysical properties of nitrogen based on the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019) — either for the single-phase state or for boiling nitrogen along the vapor pressure curve. The outputs include density, specific heat capacity (isobaric and isochoric), thermal conductivity, dynamic and kinematic viscosity, Prandtl number, thermal diffusivity, enthalpy, entropy, compressibility factor, speed of sound, coefficient of thermal expansion, as well as fixed data such as molar mass, gas constant, standard density and the critical-point data.
Calculating nitrogen properties is an everyday task in process engineering: when sizing heat exchangers and piping for inert gas, in air separation plants, when handling liquid nitrogen in refrigeration and cryogenic engineering, for pressure tests and inerting, and as a reference substance for heat transfer and pressure drop calculations. The range of validity extends single-phase from −175 °C to 1000 °C at 1 bar to 1000 bar, and in the boiling state from −210 °C to −147 °C — so the module covers both cryogenic applications and high-temperature processes.
Standard and calculation basis: VDI Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Select the type of state: First it is specified whether the single-phase state (gas or liquid, defined by temperature and pressure) or the boiling state (saturation, defined by temperature alone) is to be calculated.
- Enter the state variables and check validity: Temperature and pressure are entered; the module checks whether the pair of values lies within the range of validity of the underlying correlations (single-phase −175 °C to 1000 °C, 1 bar to 1000 bar; boiling −210 °C to −147 °C).
- Calculate the thermal state properties: From the equation of state follow the density and the compressibility factor, as well as the caloric quantities specific enthalpy, entropy, isobaric and isochoric heat capacity, coefficient of thermal expansion and speed of sound.
- Determine the transport properties: Thermal conductivity and dynamic viscosity are determined from the property correlations of the VDI Heat Atlas; from these follow the kinematic viscosity, the thermal diffusivity and the Prandtl number — the parameters that enter Nusselt correlations directly.
- Report the fixed data: In addition, the module supplies the molar mass, the individual gas constant, the standard density as well as the critical temperature, critical pressure and critical density as reference quantities for further calculations.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature | ϑ | °C |
| Temperature | ϑ | °C |
| Pressure | p | Pa |
| Pressure | p | Pa |
| Density | ρ | kg/m³ |
| Density | ρ | kg/m³ |
| Specific heat capacity | cp | J/(kg·K) |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Thermal conductivity | λ | W/(m·K) |
| Dynamic viscosity | η | mPa·s |
| Dynamic viscosity | η | mPa·s |
| Kinematic viscosity | ν | m²/s |
| Kinematic viscosity | ν | m²/s |
| Prandtl number | Pr | - |
| Prandtl number | Pr | - |
| Specific enthalpy | h | J/kg |
| Specific enthalpy | h | J/kg |
| Specific entropy | s | J/(kg·K) |
| Specific entropy | s | J/(kg·K) |
| Compressibility factor | Z | - |
| Compressibility factor | Z | - |
| Speed of sound | w | m/s |
| Speed of sound | w | m/s |
Worked example
For an inerting line, the density of gaseous nitrogen at 20 °C and 1 bar (abs.) is to be estimated. At this state the compressibility factor is Z ≈ 1, so the thermal equation of state for ideal gases provides a good approximation — a simple worked example of a nitrogen property calculation.
Given values
| Temperature T | 20 °C = 293.15 K |
| Pressure p (abs.) | 1 bar = 100,000 Pa |
| Molar mass M | 28.013 kg/kmol |
| Individual gas constant R | 296.8 J/(kg·K) |
Solution
Individual gas constant
From the universal gas constant follows R = Rm/M = 8,314.46 / 28.013 = 296.8 J/(kg·K).
Density from the thermal equation of state
ρ = p / (R · T) = 100,000 / (296.8 · 293.15) = 1.149 kg/m³
For comparison: the standard density (0 °C, 1.01325 bar) is ρN = 101,325 / (296.8 · 273.15) = 1.250 kg/m³ — in good agreement with the tabulated value of 1.250 kg/m³ for nitrogen.
Result
| Density at 20 °C, 1 bar | ρ ≈ 1.149 kg/m³ |
| Standard density (0 °C, 1.01325 bar) | ρ_N ≈ 1.250 kg/m³ |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
When is the ideal gas equation sufficient for nitrogen, and when do I need real-gas properties?
At ambient temperature and pressures up to about 10 bar, the compressibility factor of nitrogen is very close to 1, so the ideal gas equation yields densities with deviations below roughly 1%. At high pressures (storage cylinders at 200–300 bar), near the saturation line and in the cryogenic range, the behavior deviates significantly — there the real-gas correlations of the VDI Heat Atlas are required, as they are for enthalpy and entropy differences in throttling and compression processes.
What does the boiling state mean for a pure substance like nitrogen?
In the boiling state, liquid and vapor are in equilibrium; pressure and temperature are coupled via the vapor pressure curve, so that one quantity determines the other. The module then delivers the properties of both phases on the saturation line (−210 °C to −147 °C, i.e. from the triple point to close to the critical point at about −147 °C and 34 bar). Above the critical point, no phase boundary exists any more.
Why are many quantities output twice?
In the saturation case, two values exist for each property — one for the boiling liquid and one for the saturated vapor (e.g. density, heat capacity, viscosity). For pool boiling, film condensation and two-phase flows, both values are needed, for instance in the correlations for boiling heat transfer.
What are typical sources of error when using the property data?
Common errors are confusing absolute pressure with gauge pressure, evaluating the properties at the wrong reference temperature (wall temperature instead of mean fluid temperature or vice versa), and extrapolating beyond the range of validity. Furthermore, enthalpy and entropy are defined only up to a reference-point convention — differences are reliable, absolute values are comparable only within the same property model.