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

Last Updated on January 16, 2023

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.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the conversion of volume fraction to mass fraction.

To get the answer and workings of the conversion of volume fraction to mass fraction using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

You can also try the demo version via https://www.nickzom.org/calculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Phase Transformation under Materials and Metallurgical

Now, Click on Conversion of Volume Fraction to Mass Fraction under Phase Transformation

The screenshot below displays the page or activity to enter your values, to get the answer for the conversion of volume fraction to mass fraction according to the respective parameter which is the α-phase Volume Fraction (Vα), β-phase Volume Fraction (Vβ), α-phase Density (ρα) and β-phase Density (ρβ).

Now, enter the values appropriately and accordingly for the parameters as required by the α-phase Volume Fraction (Vα) is 4, β-phase Volume Fraction (Vβ) is 7, α-phase Density (ρα) is 11 and β-phase Density (ρβ) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the conversion of volume fraction to mass fraction and presents the formula, workings and steps too.