Materials Question - Calculating Percent Carbon ?

[Seraph042]

Homework Statement

Calculate the percent carbon in an iron-carbon alloy that will give no volume change when liquid transforms to austenite plus graphite during solidification.

Homework Equations

Density of liquid = 7.0 g/cc
Density of austenite = 7.69 g/cc
Density of graphite = 1.5 g/cc

The Attempt at a Solution

For constant volume, let's say the area is 1 cubic centimeter

x*(1.5 g/cc)+y*(7.69 g/cc) = (1 cc)*(7.0 g/cc)

Since the volume is constant, x+y = 1 cc, and thus
y = 1-x

Putting it into the original equation yields:
x*(1.5 g/cc) + (1-x)*(7.69 g/cc) = (1 cc)*(7.0 g/cc)

Thus, x=0.111 cc, y=0.889 cc

Now at this point I am confused. Since the graphite is 100% carbon, there will be 1*.111 % carbon, but what will it be for the austenite as we are not given what temperature this occurs at so that we may not see the iron-cementite phase diagram

Any ideas?

 

[KataKoniK]

Thank you for your post. In order to calculate the percent carbon in the iron-carbon alloy, we need to first determine the composition of the alloy that will result in no volume change during solidification. This can be done by using the lever rule, which states that the fraction of a phase in a two-phase system is equal to the ratio of the distance of that phase from the opposite side of the phase diagram to the total distance across the phase diagram. In this case, we can use the lever rule to determine the fraction of carbon in the alloy that will result in no volume change.

The phase diagram for iron-carbon alloys shows that at a eutectic composition of 4.3% carbon, the alloy will transform into austenite and graphite without any change in volume. This means that we need to have a carbon content of 4.3% in our alloy in order to achieve no volume change during solidification.

Now, to calculate the percent carbon in the alloy, we can use the weight fraction formula:

% carbon = (mass of carbon / total mass of alloy) * 100

Since we have a constant volume of 1 cc, we can assume that the total mass of the alloy is equal to the density of the alloy, which is given by the sum of the densities of the liquid, austenite, and graphite. Therefore, the total mass of the alloy is:

(1 cc)*(7.0 g/cc) = 7.0 g

Now, to determine the mass of carbon in the alloy, we can use the lever rule again. Since we know that the eutectic composition is 4.3% carbon, the fraction of carbon in the alloy will be:

% carbon = (distance of austenite from graphite / total distance across phase diagram) * 100

= (7.69 g/cc - 1.5 g/cc) / (7.69 g/cc - 1.5 g/cc) * 100

= 6.19 g/cc / 6.19 g/cc * 100

= 100%

Therefore, the mass of carbon in the alloy is:

mass of carbon = (100% / 100%) * 7.0 g = 7.0 g

Now, using the weight fraction formula, we can calculate the percent carbon in the alloy:

% carbon = (7.0 g / 7.0

 

[Mene]

it is important to have all the necessary information in order to accurately calculate the percent carbon in this iron-carbon alloy. Without knowing the temperature at which the liquid transforms to austenite plus graphite, it is not possible to accurately determine the percent carbon. The iron-cementite phase diagram is essential in understanding the transformation of iron and carbon at different temperatures and compositions. Therefore, it is important to obtain this information before attempting to calculate the percent carbon in this alloy.