.Annex60.Media.Air.specificEntropy

Information

This function computes the specific entropy.

The specific entropy of the mixture is obtained from

s = s_s + s_m,

where s_s is the entropy change due to the state change (relative to the reference temperature) and s_m is the entropy change due to mixing of the dry air and water vapor.

The entropy change due to change in state is obtained from

s_s = c_v ln(T/T₀) + R ln(v/v₀)
= c_v ln(T/T₀) + R ln(ρ₀/ρ)

If we assume ρ = p₀/(R T), and because c_p = c_v + R, we can write

s_s = c_v ln(T/T₀) + R ln(T/T₀)
=c_p ln(T/T₀).

Next, the entropy of mixing is obtained from a reversible isothermal expansion process. Hence,

s_m = -R ∑_i( X_i ⁄ M_i ln(Y_i p/p₀)),

where R is the gas constant, X is the mass fraction, M is the molar mass, and Y is the mole fraction.

To obtain the state for a given pressure, entropy and mass fraction, use Annex60.Media.Air.setState_psX.

Limitations

This function is only valid for a relative humidity below 100%.

Revisions

• November 27, 2013, by Michael Wetter:
  First implementation.