Quality Explained: What x Really Means

Inside the saturation dome, liquid and vapour coexist. Quality x is the mass fraction that is vapour:

x = mass of vapour / total mass        (0 ≤ x ≤ 1)

x = 0 is saturated liquid (all liquid). x = 1 is saturated vapour (all vapour). In between, you have a mixture.

The quality formula

Every intensive property inside the dome is a weighted average of the liquid value (subscript f) and the vapour value (subscript g):

y = (1 − x)·yf + x·yg
  = yf + x·(yg − yf)
  = yf + x·yfg

where yfg = yg − yf is tabulated directly (hfg, ufg, sfg, vfg).

Worked example

P = 100 kPa, x = 0.5. From the saturation table at 100 kPa: hf = 417.53, hfg = 2257.5, sf = 1.3028, sfg = 6.0562.

Enthalpy:

h = hf + x·hfg = 417.53 + 0.5·2257.5 = 1546.3 kJ/kg

Entropy:

s = sf + x·sfg = 1.3028 + 0.5·6.0562 = 4.3309 kJ/kg·K

Specific volume:

v = vf + x·vfg = 0.001043 + 0.5·(1.6941 − 0.001043) = 0.8476 m³/kg

Enter P = 100 and x = 0.5 in the property lookup calculator and you get exactly these numbers.

Why quality only exists inside the dome

Quality is a mixture concept. A compressed liquid has no vapour fraction to speak of (x is undefined), and a superheated vapour is all vapour past the x = 1 line. That’s why the calculator only accepts x when the state is saturated — and why, if you give it P and T that land in the superheated region, it ignores quality and switches tables.

The trap

Students often reach for x when they only have P and T. You can’t use quality to find the region — you need to know the region first. Compare T to Tsat (see How to read steam tables), and only use x once you’ve confirmed you’re inside the dome.