(a) Interpretation: The ratio of the populations of two energy states whose energies differ by 1000 J at ( a ) 200 K and the trend is to be calculated. Concept introduction: From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as, Probability = e – ( ΔE RT )

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Answer 1

Question

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

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Answer 2

Question

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

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Answer 3

Question

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

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Answer 4

Question

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

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Answer 5

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Answer 6

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Answer 7

Chapter 1, Problem 1.74E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Answer 8

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 9

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 10

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Answer 11

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 1000 J at (c) 1000 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of an ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e –(ΔERT)

Answer 12

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Answer 13

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Answer 14

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Answer 15

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Solution Summary: The author explains how Boltzmann utilized this concept to derive a relationship as the natural logarithm of the number of particles in two energy states is directly proportional to the negative of their energy separation.

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