(a) Interpretation: The specific value for ν sound for a monatomic ideal gas at 298 K is to be determined. Concept introduction: A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, ν sound , is given by the expression ν sound = ( γ R T M ) 1 / 2 …(2) Where, • R represents the gas constant with a value of 8.314 J / K ⋅ mol . • T represent the temperature of the gas. • M represents the molar mass of the gas. • γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

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Answer 1

Question

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

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The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.

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Answer 2

Question

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

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Answer 3

Question

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

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Answer 4

Question

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

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Answer 5

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

Answer 6

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Answer 7

Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for νsound for a monatomic ideal gas at 298 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, νsound, is given by the expression

νsound=(γRTM)1/2 …(2)

Where,

• R represents the gas constant with a value of 8.314 J/K⋅mol.

• T represent the temperature of the gas.

• M represents the molar mass of the gas.

• γ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The value of νsound for He at 273 K is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 19 - Prob. 19.1E Ch. 19 - What is the kinetic energy of a single atom of...Ch. 19 - Prob. 19.3E Ch. 19 - One mole of Ne atoms confined to a volume of 10.0L...Ch. 19 - Prob. 19.5E Ch. 19 - Prob. 19.6E Ch. 19 - Prob. 19.7E Ch. 19 - Prob. 19.8E Ch. 19 - Prob. 19.9E Ch. 19 - Prob. 19.10E

Solution Summary: The author explains how the specific value for nu_sound for a monatomic ideal gas is to be determined.

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