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Chapter 4: Problem 15

The concentration of carbon in an ironcarbon alloy is \(0.15 \mathrm{wt} \%\). What is the concentration in kilograms of carbon per cubic meter of alloy?

Short Answer

Expert verified
Answer: The concentration of carbon in the iron-carbon alloy is 11.775 kg of carbon per cubic meter of alloy.

Step by step solution

01

Find the density of the iron-carbon alloy

We need to find the density of the iron-carbon alloy in order to convert the concentration from wt% to kilograms per cubic meter. The density will depend on the composition of the alloy, but a typical value for steel (an iron-carbon alloy) ranges between 7,750 - 8,050 kg/m³. In this step, let's assume a density of 7,850 kg/m³ for the iron-carbon alloy.
02

Calculate the mass of the alloy in one cubic meter

Now that we have the density of the iron-carbon alloy, we can calculate the total mass of the alloy in one cubic meter. To do this, we simply multiply the density by the volume (in this case, 1 cubic meter). Mass of alloy = density × volume = 7,850 kg/m³ × 1 m³ = 7,850 kg
03

Calculate the mass of carbon in one cubic meter alloy

We are given the concentration of carbon as 0.15 wt% in the iron-carbon alloy. Now, we can calculate the mass of carbon in one cubic meter of the alloy. Mass of carbon = (Mass of alloy × concentration of carbon) / 100 Mass of carbon = (7,850 kg × 0.15) / 100 = 11.775 kg
04

Express the concentration of carbon in kilograms per cubic meter

Now that we have the mass of carbon in one cubic meter of alloy, we can simply express it as the concentration in kilograms per cubic meter. Since we already calculated the mass of carbon in one cubic meter of alloy, we have our answer: Concentration of carbon = 11.775 kg of carbon per cubic meter of alloy

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Most popular questions from this chapter

For each of the following stacking sequences found in FCC metals, cite the type of planar defect that exists: (a) ... \(A B C A B C B A C B A \ldots\) (b) ... \(A B C A B C B C A B C \ldots\) Now, copy the stacking sequences and indicate the position(s) of planar defect(s) with a vertical dashed line.

For an FCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (111) plane? Why? (Note: You may want to consult the solution to Problem \(3.54\) at the end of Chapter 3.)

Cite the relative Burgers vector-dislocation line orientations for edge, screw, and mixed dislocations.

Calculate the composition, in weight percent, of an alloy that contains \(218.0 \mathrm{~kg}\) titanium, 14.6 kg aluminum, and \(9.7 \mathrm{~kg}\) vanadium.

(a) For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why? (b) The grain boundary energy of a smallangle grain boundary is less than for a highangle one. Why is this so?
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