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Thermodynamics

Wet-steam quality and mixture enthalpy

Enthalpy of a liquid–vapour mixture from its dryness fraction.

Ref: THE-09
Rev: v1
Field: Thermodynamics
Result: h [kJ/kg]

x = \frac{m_{g}}{m_{f} + m_{g}}, h = h_{f} + x (h_{g} - h_{f})

Quality x is the vapour mass fraction. Use saturated liquid (f) and vapour (g) properties at the same pressure. The same interpolation works for u, v and s.

A wet mixture’s properties lie between the liquid and the vapour values, weighted by how much of it is vapour.

Calculator

Solve for

hMixture enthalpyComputed

kJ/kg

m_fMass of liquid

0.0110

m_gMass of vapour

0.0110

h_fLiquid enthalpy

kJ/kg

1001,500

h_gVapour enthalpy

kJ/kg

2,5002,900

Quality x0.2
Latent part x(hg − hf)440 kJ/kg

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Mixture enthalpy (kJ/kg) current value 940 kJ/kg

m_fMass of liquidKey driver

5432,600

m_gMass of vapour

5272,540

h_fLiquid enthalpy

6201,740

h_gVapour enthalpy

900980

The mixture lies between h_f and h_g; a quality of 0 is saturated liquid and 1 is saturated vapour.
Quality is a mass fraction, not a volume fraction.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (kJ/kg)	Local step	Change in result
m_f Mass of liquid	0.01 to 10 kg	543.1	2,595	2,052	+10%	−3.47 %
m_g Mass of vapour	0.01 to 10 kg	527.2	2,537	2,010	+10%	+3.67 %
h_f Liquid enthalpy	100 to 1,500 kJ/kg	620	1,740	1,120	+10%	+4.26 %
h_g Vapour enthalpy	2,500 to 2,900 kJ/kg	900	980	80	+10%	+5.74 %

Sweep of Mass of vapour

Mass of vapour (kg)	Mixture enthalpy (kJ/kg)
0.01	527.2
1.259	1,845
2.507	2,168
3.756	2,314
5.005	2,397
6.254	2,450
7.502	2,488
8.751	2,516
10	2,537

Sweep one variable

Vary

Mixture enthalpy (kJ/kg)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

Mixture enthalpy

Result · kJ/kg

What the equation gives you. Everything else feeds it.

m_f

Mass of liquid

kg · typical 0.01 to 10

Mass of saturated liquid. More liquid lowers the enthalpy.

m_g

Mass of vapour

kg · typical 0.01 to 10

Mass of saturated vapour. More vapour raises the enthalpy.

h_f

Liquid enthalpy

kJ/kg · typical 100 to 1,500

Saturated-liquid enthalpy at the pressure. Adds (1 − x) of its value.

h_g

Vapour enthalpy

kJ/kg · typical 2,500 to 2,900

Saturated-vapour enthalpy at the pressure. Adds x of its value.

Worked example with the values above

Quality: x = 0.2 / (0.8 + 0.2) = 0.2.
Latent part: x(h_g − h_f) = 440 kJ/kg.
h = 500 + 440 = 940 kJ/kg.

Assumptions and limits

Saturated mixture in equilibrium.
f and g properties at the same pressure.

Common mistakes

Using the volume fraction instead of the mass fraction.
Mixing properties from different pressures.

Statistics and uncertainty

Quality measured by throttling calorimeters is uncertain by about ±1–2% in x, which transfers directly to h.

Where it is used

Steam turbine exhaust conditions.
Boiler and condenser energy balances.

Maths you need

Steam tables: saturated properties
Mass fraction: part over whole

Related formulas

Practise this formula