Real Gases

Real fluids (gas, liquids or solids)

Molecules have finite volume (and cannot occupy the same space)

Molecules attract each other

This influences the compressibility and the internal energy of the substance:

Change in internal energy at constant T is given by:

“ideal” liquid

Molecules have finite mass and finite volume

Packing density depends little bit on temperature but independent from external forces

Incompressible fluid: V= V(T) ≠ V(P)

Constant T:

Remember this equation: it also
works quite well for real liquids!

ideal gas

Molecules have finite mass but NO finite volume

No intermolecular forces

PV=RT

h=u+PV ->enthalpy is a function of temperature only

Intermolecular forces in a real gas

Constant temperature
Compression:

In a real gas, internal energy is also a function of specific
volume (and thus pressure)

Molecules attract each other: internal energy and enthalpy are low when the
molecules are close together (high pressure, low density)

Because the molecules attract each other, they “want” to be close together:
density at given P and T will be higher in a real gas than in an ideal gas

However, attraction only present on short distances: <3x diameter of the molecule

Molecules have finite volume

Finite volume impacts ideal gas law

At high pressures, density will be higher than ideal gas density because of the
intermolecular attraction

At VERY high pressures, a gas cannot be compressed any further due to the finite
volume of the molecules and the density will be lower than the ideal gas density

The finite volume of the molecules has no influence on internal energy

Real gases

Normally properties properties of real gases “in between” those of gases and liquids

Compared to ideal gas:

Lower internal energy (somewhere in between values for ideal gas and liquid)

Lower enthalpy

high densities than an ideal gas at same P and T

Lower entropy

Which relationships do NOT work any more for a real gas:

PV=RT

Polytropic relationships

u=u(T), h=h(T)

Q (or W) =CpΔT

Limited accuracy

Typical errors

Many ways to describe a real gas

compressibility factors (reduced coordinates)

van der Waals

Tables (graphs) of measured data

You need correction when H, S and PVT-correlations deviate significantly from ideal
gas correlations

IF one of these quantities deviates, usually all three do.

Method: check PVT (because that is simple)
If PVT data follows ideal gas laws, you can assume that enthalpy and entropy also will follow ideal gas correlations

Real gases are actually not that common: don’t waste time on real gas calculations
when it is not necessary

Method 0

Low pressure, low density and high temperature gases are always ideal

ρ < 10 kg/m³

T > 1000°C

P < 5bar

Method 1

use the reduced temperature and the reduced pressure