γ for an ideal diatomic gas is to be calculated. Concept introduction: Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C . Mathematically, the heat capacity of the system between two temperature T 1 and T 2 can be expressed as C ( T 2 , T 1 ) = q / ( T 2 – T 1 ) Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as C v = ( δ U / δ T ) v The molar heat capacity of gaseous system at constant pressure can be expressed as C p = ( δ H / δ T ) p

Question

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Answer 1

Question

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

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Answer 2

Question

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

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Answer 3

Question

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

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Answer 4

Question

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

Answer 6

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R

We know that, Cp – Cv = R

Cp = Cv + R

= 5/2 R + R

∴Cp = 7/2 R

The ratio of heat capacity at constant pressure and constant volume is called as heat capacity ratio or Poisson constant.

γ = Cp / Cv

= (7/2 R) / (5/2 R)

= 7/5

∴γ = 1.4

Thus, heat capacity ratio for a diatomic gas is 1.4

Conclusion

Thus, γ for an ideal diatomic gas is calculated.

Answer 7

Chapter 2, Problem 2.61E

Interpretation Introduction

Interpretation:

γ for an ideal diatomic gas is to be calculated.

Concept introduction:

Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T₁ and T₂ can be expressed as

C (T2, T1) = q / (T2 – T1)

Intriguingly, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

The molar heat capacity of gaseous system at constant pressure can be expressed as

Cp = (δH/ δT)p

Answer 8

Expert Solution & Answer

Answer to Problem 2.61E

The ratio of heat capacities (γ) for an ideal diatomic gas calculated as follows;

Cv = 5/2 R

We know that Cp – Cv = R

Cp = 7/2 R, therefore,

γ = 7/5 = 1.4

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Generally, the molar heat capacity of gaseous system is determined at constant volume and can be expressed as

Cv = (δU/ δT)v

This equation relates the change in internal energy with the change in temperature at constant volume. Similarly, the molar heat capacity of gaseous system at constant pressure can be expressed as;

Cp = (δH/ δT)p

This equation relates the change in enthalpy of a system with the change in temperature at constant pressure.

For a diatomic gas Cv = 5/2 R