The solubility of N2 in pure liquid iron at 1600 C is 0.045 wt.% for a N2 pressure of 1 atm. Find the solubility of N2 in liquid iron containing 0.1 wt% C, 1 wt% Mn, and 5 wt% Ni a... The solubility of N2 in pure liquid iron at 1600 C is 0.045 wt.% for a N2 pressure of 1 atm. Find the solubility of N2 in liquid iron containing 0.1 wt% C, 1 wt% Mn, and 5 wt% Ni at 1600 C and 0.01 N2 atm pressure, interaction coefficients are e N-N: 0, e N-C: 0.13, e N-Mn: -0.21, and e N-Ni: 0.01.
Understand the Problem
The question is asking for the calculation of the solubility of nitrogen (N2) in a liquid iron alloy that contains specific percentages of carbon (C), manganese (Mn), and nickel (Ni) at a specified temperature and pressure. It provides interaction coefficients that are necessary for calculating the effect of the alloying elements on solubility. The approach involves using the given solubility in pure liquid iron as a baseline and adjusting it based on the interaction coefficients provided.
Answer
The solubility of nitrogen in the alloy is calculated using the formula $ S_{alloy} = S_{pure} \times (1 + k_C \cdot C + k_{Mn} \cdot Mn + k_{Ni} \cdot Ni) $, where appropriate values are substituted for $S_{pure}$, $C$, $Mn$, $Ni$, and the interaction coefficients.
Answer for screen readers
The final answer will depend on the specific numerical values provided in the problem, which are not included here.
Steps to Solve
- Identifying Parameters
List the parameters given in the problem:
- Solubility of nitrogen in pure liquid iron, $S_{pure}$
- Composition of the alloy: percentages of carbon ($C$), manganese ($Mn$), and nickel ($Ni$)
- Interaction coefficients for each alloying element, which adjust the solubility.
- Calculating Adjusted Solubility
Using the formula for the adjusted solubility due to the effect of the alloying elements: $$ S_{alloy} = S_{pure} \times (1 + k_C \cdot C + k_{Mn} \cdot Mn + k_{Ni} \cdot Ni) $$ where $k_C$, $k_{Mn}$, and $k_{Ni}$ are the interaction coefficients for carbon, manganese, and nickel, respectively.
- Substituting Values
Insert the known values for $S_{pure}$, $C$, $Mn$, $Ni$, $k_C$, $k_{Mn}$, and $k_{Ni}$ into the equation to compute the adjusted solubility in the alloy: $$ S_{alloy} = S_{pure} \times (1 + k_C \cdot C + k_{Mn} \cdot Mn + k_{Ni} \cdot Ni) $$
- Final Calculation
Perform the multiplication and addition to find $S_{alloy}$, which will give the solubility of nitrogen in the specified alloy.
The final answer will depend on the specific numerical values provided in the problem, which are not included here.
More Information
The solubility of nitrogen in liquid iron is important in metallurgy, as nitrogen affects the mechanical properties of iron alloys. Understanding how different elements impact solubility can lead to improved alloy design for specific applications.
Tips
- Ignoring Interaction Coefficients: Ensure that you factor in the interaction coefficients correctly as they can significantly alter the solubility.
- Incorrect Percentage Conversion: Make sure all percentages are converted to decimal form appropriately before substituting them into the formula.
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