(a) Interpretation: Whether the alloy is hypoeutectic or hypereutectic needs to be determined. Concept Introduction: The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Question

b) Another periodic waveform is defined by T c) g(t)= T with g(t+mT) = g(t) and m is an integer. (i) Sketch g(t) over two full cycles in the time domain, labelling the axes. (ii) Derive the formulae for the complex Fourier coefficients c₁ for g(t). For a periodic waveform h(t), if its complex Fourier coefficients are T T when n is odd T 2n²² T 4nn when n is even and not zero 4nn please derive the first five non-zero terms of the real Fourier series for h(t).

Answer 1

Question

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

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b) Another periodic waveform is defined by T c) g(t)= T with g(t+mT) = g(t) and m is an integer. (i) Sketch g(t) over two full cycles in the time domain, labelling the axes. (ii) Derive the formulae for the complex Fourier coefficients c₁ for g(t). For a periodic waveform h(t), if its complex Fourier coefficients are T T when n is odd T 2n²² T 4nn when n is even and not zero 4nn please derive the first five non-zero terms of the real Fourier series for h(t).

Q3)α) f(t) = (-+- 1 Isto f(t+mT) = f(t). L+- I Ost ST integer (i) sketch f(t) 2 full cycles time domain. (labelling the axis). (ii) Derive the formula for the real fourier Coefficients (i) Real Fourier series f(t), first 5 non-terms. an bn for f(t).

Q3. a) A periodic waveform is defined by T 3 0≤t< f(t) = SI

Answer 2

Question

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

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Answer 3

Question

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

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Answer 4

Question

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

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Answer 5

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 6

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Answer 7

Chapter 11, Problem 11.20P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

The composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed as a hypo-eutectic alloy. Whereas the composition of an alloy that lies to the right of the eutectic point in the alloy phase diagram is termed as a hyper-eutectic alloy. The hypereutectic alloy has a composition beyond the eutectic point.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification needs to be determined.

Concept Introduction:

Freezing is the other name for solidification. Solidification is the phase change of matter which results in the production of a solid phase. Mostly, this phase occurs when the temperature of a liquid is lowered under the freezing point. At the solidification temperature, atoms which are present in the liquid begins to bond and start the formation of crystals.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The composition and amount of each phase at 184°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 12

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 13

Interpretation Introduction

(d)

Interpretation:

The composition and amount of each phase at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 14

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 15

Interpretation Introduction

(e)

Interpretation:

The composition and amount of each microconstituent at 182°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 16

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 17

Interpretation Introduction

(f)

Interpretation:

The composition and amount of each phase at 25°C needs to be determined.

Concept Introduction:

Solidification process is also known as a Freezing process which is a phase change of matter. The phase change of matter that results in the production of the solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquids takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer 18

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Answer 29

Ch. 11 - Prob. 11.1P Ch. 11 - Prob. 11.2P Ch. 11 - Prob. 11.3P Ch. 11 - Prob. 11.4P Ch. 11 - Prob. 11.5P Ch. 11 - Prob. 11.6P Ch. 11 - Prob. 11.7P Ch. 11 - Prob. 11.8P Ch. 11 - Prob. 11.9P Ch. 11 - Prob. 11.10P

Solution Summary: The author explains that the composition of an alloy that lies to the left of the eutectic point in the alloy phase diagram is termed hypo-eutectic. The value of composition obtained during the solidification is 1

Chapter 11 Solutions