(a)
The number of grains in the metal cube.
Answer to Problem 3.14P
The number of grains in the metal cube is
Explanation of Solution
Given:
The side of the copper cube is
The size of grain on each side is
The average grain boundary energy of copper is
Formula used:
The number of grain is given by,
Here,
The volume of a cube is given by,
Here,
The volume of grains is given by,
Here,
Substitute
Calculation:
The number of grains is calculated as,
Substitute
Conclusion:
Therefore, the number of grains present are
(b)
The total grain boundary area.
Answer to Problem 3.14P
The total grain boundary area is
Explanation of Solution
Given:
The side of the copper cube is
The size of grain on each side is
The average grain boundary energy of copper is
Formula used:
The total grain boundary area is given by,
Here,
Calculation:
The total grain boundary area is calculated as
Substitute
Conclusion:
Therefore, the total ground boundary area is
(c)
The total energy present in the copper cube due to grain boundaries.
Answer to Problem 3.14P
The total energy present in the copper cube due to grain boundaries is
Explanation of Solution
Given:
The side of the copper cube is
The size of grain on each side is
The average grain boundary energy of copper is
Formula used:
The total energy due to grain boundaries is given by
Here,
Calculation:
The total energy due to the grain boundary is calculated as
Substitute
Conclusion:
Therefore, the total energy present in the copper cube due to grain boundaries is
(d)
The height to which copper must be raised to increase the energy to an equal amount of energy in the grain boundaries.
Answer to Problem 3.14P
The height to which copper must be raised to increase the energy to an equal amount of energy in the grain boundaries is
Explanation of Solution
Given:
The side of the copper cube is
The size of grain on each side is
The average grain boundary energy of copper is
Formula used:
The expression for the equivalent gravitational energy is given by
Here,
Calculation:
The height to which the copper cube must be raised is calculated by
Substitute
Conclusion:
Therefore, the height to which copper must be raised to increased energy to an equal amount of energy in the grain boundaries is
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Chapter 3 Solutions
Materials Science And Engineering Properties
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- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning