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Quality

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Quick
Quality is defined as the mass of the vapor divided by the total mass. (m_vap/m)
Quality is useful because the specific volume, internal energy, enthalpy, and entropy will vary depending on whether a mass of interest is liquid, vapor, or a combination of both.


Equations

(Eq1)     x =  mvap m	quality
(Eq2)     v = vf + xvfg	average specific volume of the system, commonly used

Nomenclature

m	total mass
mvap	mass of the vapor
mliq	mass of the liquid
V	volume
v	specific volume
subscript f	saturated liquid
subscript g	saturated vapor
subscript fg	difference between g and f

Details

The mass is defined by a control volume, where the mass consists of either liquid, vapor, or a combination of both.

The fraction of mass that is vapor is given by:

mvap m

The fraction of mass that is liquid is given by:

mliq m

Because the fraction of mass that is vapor is quality:

(Eq1)

x =  mvap m

Also, because:

m = m_vap + m_liq

then:

mvap m

+

mliq m

= 1

Below are some equations that are commonly associated with and used in the determination of quality.

The total volume equals the sum of the volume that is liquid and the volume that is vapor.

V = V_liq + V_vap = m_liqv_f + m_vapv_g

The average specific volume of the system is:

v =

V m

=

mliq m

vf +

mvap m

vg = (1 – x)vf + xvg

v_fg is defined as v_fg = v_g – v_f

then using: v = (1 – x)v_f + xv_g and v_fg = v_g – v_f :

(Eq2)

v = vf + xvfg

therefore:

x =	v − vf vfg

Below is a T–v diagram for the two-phase liquid-vapor region to show the quality specific volume relation.