## How to Calculate and Solve for Conversion of Volume Fraction to Mass Fraction | Phase Transformation The image above represents the conversion of volume fraction to mass fraction.

To compute for volume fraction to mass fraction, four essential parameters are needed and these parameters are α-phase Volume Fraction (Vα), β-phase Volume Fraction (Vβ), α-phase Density (ρα) and β-phase Density (ρβ).

The formula for calculating volume fraction to mass fraction:

Wα = Vαρα/(Vαρα) + (Vβρβ)

Wβ = Vβρβ/(Vαρα) + (Vβρβ)

Where:

Wα = α-phase Weight/Mass Fraction
Wβ = β-phase Weight/Mass Fraction
Vα = α-phase Volume Fraction
Vβ = β-phase Volume Fraction
ρα = α-phase Density
ρβ = β-phase Density

Let’s solve an example;
Find the conversion of volume fraction to mass fraction when the α-phase volume fraction is 4, the β-phase volume fraction is 7, the α-phase density is 11 and the β-phase density is 10.

This implies that;

Vα = α-phase Volume Fraction = 4
Vβ = β-phase Volume Fraction = 7
ρα = α-phase Density = 11
ρβ = β-phase Density = 10

Wα = (4)(11)/((4)(11)) + ((7)(10))
Wα = (44)/(44) + (70)
Wα = (44)/(114)
Wα = 0.38

Therefore, the α-phase mass fraction, Wα is 0.38.

Wβ = (7)(10)/((4)(11)) + ((7)(10))
Wβ = (70)/(44) + (70)
Wβ = (70)/(114)
Wβ = 0.614

Therefore, the β-phase mass fraction, Wβ is 0.614.

## How to Calculate and Solve for Conversion of Mass Fraction to Volume Fraction | Phase Transformation

The image of conversion of mass fraction to volume fraction is represented below. To compute for conversion of mass fraction to volume fraction, four essential parameters are needed and these parameters are α-phase Weight/Mass Fraction (Wα), β-phase Weight/Mass Fraction (Wβ), α-phase Density (ρα) and β-phase Density (ρβ).

The formula for calculating conversion of mass fraction to volume fraction:

Vα = Wαα/(Wα/ρα) + (Wβ/ρβ)

Vβ = Wββ/(Wα/ρα) + (Wβ/ρβ)

Where:

Vα = α-phase Volume Fraction
Vβ = β-phase Volume Fraction
Wα = α-phase Weight/Mass Fraction
Wβ = β-phase Weight/Mass Fraction
ρα = α-phase Density
ρβ = β-phase Density

Given an example;
Find the conversion of mass fraction to volume fraction when the α-phase Weight/Mass Fraction is 2, the β-phase Weight/Mass Fraction is 4, the α-phase Density is 6 and the β-phase Density is 8.

This implies that;

Wα = α-phase Weight/Mass Fraction = 2
Wβ = β-phase Weight/Mass Fraction = 4
ρα = α-phase Density = 6
ρβ = β-phase Density = 8

Vα = (2/6)/(2/6) + (4/8)
Vα = (0.333)/(0.333) + (0.5)
Vα = (0.333)/(0.833)
Vα = 0.4

Therefore, the α-phase volume fraction, Vα is 0.4.

Vβ = (4/8)/(2/6) + (4/8)
Vβ = (0.5)/(0.333) + (0.5)
Vβ = (0.5)/(0.833)
Vβ = 0.600

Therefore, the β-phase volume fraction, Vβ is 0.60.