1. Suppose that liquid nickel is undercooled until homogeneous nucleation occurs. Calculate (a) the critical radius of the nucleus required and (b) the number of nickel atoms in the nucleus. Assume that the lattice parameter of the solid FCC nickel is 0.356nm. Suppose that liquid iron is undercooled until homogeneous nucleation occurs. Calculate (a) the critical radius of the nucleus required and (b) the number of iron atoms in the nucleus. Assume that the lattice parameter of the solid BCC iron is 2.92 Å. Suppose that solid nickel was able to nucleate homogeneously with an undercooling of only 22°C. How many atoms would have to group together spontaneously for this occur? Assume that the lattice parameter of the solid FCC nickel is 0.356 nm. Suppose that solid iron was able to nucleate homogeneously with an undercooling of only 15°C. How many atoms would have to group together spontaneously for this to occur? Assume that the lattice parameter of the solid BCC iron is 2.92 Å. Use the data in Table 9-1 and the specific heat data given below to calculate the undercooling required to keep the dendritic fraction at 0.5 for each metal. (Data given in the book. You can also find it out in other literature.) Calculate the fraction of solidification that occurs dendritically when silver nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously. Calculate the fraction of solidification that occurs dendritically when iron nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously. 8. Analysis of a nickel casting suggests that 28% of the solidification process occurred in a dendritic manner. Calculate the temperature at which nucleation occurred. Find the mold constant B and exponent n in Chvorinov’s rule using the following data and a log–log plot: Use data given in problem 9.33 A 2 in cube solidifies in 4.6 min. Assume n = 2. Calculate (a) the mold constant in Chvorinov’s rule and (b) the solidification time for a 0.5 in. x0.5 in.x 6 in. bar cast under the same conditions. A 5-cm-diameter sphere solidifies in 1050 s. Calculate the solidification time for a 0.3cm x 10 cm x 20 cm plate cast under the same conditions. Assume that n = 2. Find the constants B and n in Chvorinov’s rule by plotting the following data on a log-log plot: A 3-in.-diameter casting was produced. The times required for the solid-liquid interface to reach different distances beneath the casting surface were measured and are shown in the following table (SEE QUESTIONS IN THE EXERCISE) An aluminum alloy plate with dimensions 20 cm x 10 cm x 2 cm needs to be cast with a secondary dendrite arm spacing of 10-2 cm (refer to Figure 9-6). What mold constant B is required (assume n = 2)? Figure 9-5(b) shows a micrograph of an aluminum alloy. Estimate (a) the secondary dendrite arm spacing and (b) the local solidification time for that area of the casting. Find the constants k and m relating the secondary dendrite arm spacing to the local solidification time by plotting the following data on a log-log plot: Data problem 9.42 Assume that instead of a spherical nucleus, we had a nucleus in the form of a cube of length (x). Calculate the critical dimension x* of the cube necessary for nucleation. Write down an equation similar to Equation 9-1 for a cubical nucleus, and derive an expression for x* similar to Equation 9-2.

1. Suppose that liquid nickel is undercooled until homogeneous nucleation occurs. Calculate (a) the critical radius of the nucleus required and (b) the number of nickel atoms in the nucleus. Assume that the lattice parameter of the solid FCC nickel is 0.356nm. Suppose that liquid iron is undercooled until homogeneous nucleation occurs. Calculate (a) the critical radius of the nucleus required and (b) the number of iron atoms in the nucleus. Assume that the lattice parameter of the solid BCC iron is 2.92 Å. Suppose that solid nickel was able to nucleate homogeneously with an undercooling of only 22°C. How many atoms would have to group together spontaneously for this occur? Assume that the lattice parameter of the solid FCC nickel is 0.356 nm. Suppose that solid iron was able to nucleate homogeneously with an undercooling of only 15°C. How many atoms would have to group together spontaneously for this to occur? Assume that the lattice parameter of the solid BCC iron is 2.92 Å. Use the data in Table 9-1 and the specific heat data given below to calculate the undercooling required to keep the dendritic fraction at 0.5 for each metal. (Data given in the book. You can also find it out in other literature.) Calculate the fraction of solidification that occurs dendritically when silver nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously. Calculate the fraction of solidification that occurs dendritically when iron nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously. 8. Analysis of a nickel casting suggests that 28% of the solidification process occurred in a dendritic manner. Calculate the temperature at which nucleation occurred. Find the mold constant B and exponent n in Chvorinov’s rule using the following data and a log–log plot: Use data given in problem 9.33 A 2 in cube solidifies in 4.6 min. Assume n = 2. Calculate (a) the mold constant in Chvorinov’s rule and (b) the solidification time for a 0.5 in. x0.5 in.x 6 in. bar cast under the same conditions. A 5-cm-diameter sphere solidifies in 1050 s. Calculate the solidification time for a 0.3cm x 10 cm x 20 cm plate cast under the same conditions. Assume that n = 2. Find the constants B and n in Chvorinov’s rule by plotting the following data on a log-log plot: A 3-in.-diameter casting was produced. The times required for the solid-liquid interface to reach different distances beneath the casting surface were measured and are shown in the following table (SEE QUESTIONS IN THE EXERCISE) An aluminum alloy plate with dimensions 20 cm x 10 cm x 2 cm needs to be cast with a secondary dendrite arm spacing of 10-2 cm (refer to Figure 9-6). What mold constant B is required (assume n = 2)? Figure 9-5(b) shows a micrograph of an aluminum alloy. Estimate (a) the secondary dendrite arm spacing and (b) the local solidification time for that area of the casting. Find the constants k and m relating the secondary dendrite arm spacing to the local solidification time by plotting the following data on a log-log plot: Data problem 9.42 Assume that instead of a spherical nucleus, we had a nucleus in the form of a cube of length (x). Calculate the critical dimension x* of the cube necessary for nucleation. Write down an equation similar to Equation 9-1 for a cubical nucleus, and derive an expression for x* similar to Equation 9-2.

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

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Suppose that liquid iron is undercooled until homogeneous nucleation occurs. Calculate (a) the critical radius of the nucleus required and (b) the number of iron atoms in the nucleus. Assume that the lattice parameter of the solid BCC iron is 2.92 Å.
Suppose that solid nickel was able to nucleate homogeneously with an undercooling of only 22°C. How many atoms would have to group together spontaneously for this occur? Assume that the lattice parameter of the solid FCC nickel is 0.356 nm.
Suppose that solid iron was able to nucleate homogeneously with an undercooling of only 15°C. How many atoms would have to group together spontaneously for this to occur? Assume that the lattice parameter of the solid BCC iron is 2.92 Å.
Use the data in Table 9-1 and the specific heat data given below to calculate the undercooling required to keep the dendritic fraction at 0.5 for each metal. (Data given in the book. You can also find it out in other literature.)
Calculate the fraction of solidification that occurs dendritically when silver nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously.
Calculate the fraction of solidification that occurs dendritically when iron nucleates (a) at 10°C undercooling; (b) at 100°C undercooling; and (c) homogeneously.
8. Analysis of a nickel casting suggests that 28% of the solidification process occurred in a dendritic manner. Calculate the temperature at which nucleation occurred.
Find the mold constant B and exponent n in Chvorinov’s rule using the following data and a log–log plot: Use data given in problem 9.33
A 2 in cube solidifies in 4.6 min. Assume n = 2. Calculate (a) the mold constant in Chvorinov’s rule and (b) the solidification time for a 0.5 in. x0.5 in.x 6 in. bar cast under the same conditions.
A 5-cm-diameter sphere solidifies in 1050 s. Calculate the solidification time for a 0.3cm x 10 cm x 20 cm plate cast under the same conditions. Assume that n = 2.
1. Find the constants B and n in Chvorinov’s rule by plotting the following data on a log-log plot:
2. A 3-in.-diameter casting was produced. The times required for the solid-liquid interface to reach different distances beneath the casting surface were measured and are shown in the following table (SEE QUESTIONS IN THE EXERCISE)
An aluminum alloy plate with dimensions 20 cm x 10 cm x 2 cm needs to be cast with a secondary dendrite arm spacing of 10-2 cm (refer to Figure 9-6). What mold constant B is required (assume n = 2)?
Figure 9-5(b) shows a micrograph of an aluminum alloy. Estimate (a) the secondary dendrite arm spacing and (b) the local solidification time for that area of the casting.
Find the constants k and m relating the secondary dendrite arm spacing to the local solidification time by plotting the following data on a log-log plot: Data problem 9.42
Assume that instead of a spherical nucleus, we had a nucleus in the form of a cube of length (x). Calculate the critical dimension x* of the cube necessary for nucleation. Write down an equation similar to Equation 9-1 for a cubical nucleus, and derive an expression for x* similar to Equation 9-2.

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