The molar specific heat at constant volume if the molecules are linear.

Question

Consider 1.5 mol of pure nitrogen gas N2 which we will treat as a diatomic ideal gas. From 100 K to 1000 K, the gas has three translational and two rotational degrees of freedom. Above 1000 K, there are two additional vibrational degrees of freedom. The molar mass of N2 is 0.028 kg/mol. a. If the nitrogen molecules have an rms translational molecular speed of 511 m/s, what is the temperature of the gas? b. What is the internal energy U of the nitrogen gas at the temperature from part a? c. If the nitrogen gas has a pressure of 1.2 atm, what volume (in liters) does it occupy at the temperature from part a? d How much heat would be required to raise the temperature of the gas from 1500 K to 1800 K, at a constant volume? Remember that vibrational degrees of freedom are active at these temperatures.

Answer 1

Question

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

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Consider 1.5 mol of pure nitrogen gas N2 which we will treat as a diatomic ideal gas. From 100 K to 1000 K, the gas has three translational and two rotational degrees of freedom. Above 1000 K, there are two additional vibrational degrees of freedom. The molar mass of N2 is 0.028 kg/mol. a. If the nitrogen molecules have an rms translational molecular speed of 511 m/s, what is the temperature of the gas? b. What is the internal energy U of the nitrogen gas at the temperature from part a? c. If the nitrogen gas has a pressure of 1.2 atm, what volume (in liters) does it occupy at the temperature from part a? d How much heat would be required to raise the temperature of the gas from 1500 K to 1800 K, at a constant volume? Remember that vibrational degrees of freedom are active at these temperatures.

You measure the average free path λ and the average collision time τ of the molecules of a diatomic gas of molecular mass 6.00 × 10-²⁵ kg and radius r = 1.0 x 10-¹⁰ m. From these microscopic data can we obtain macroscopic properties such as temperature T and pressure P? If so, consider λ = 4.32 x 10-⁸ m and τ = 3.00 x 10-¹⁰ s and calculate T and P. indicate the correct answer: 1- Not possible2- Yes, T =150 K and P ~ 2.04 atm.3- Yes, T = 150 K and P ~ 4.08 atm.4- Yes, T = 300 K and P ~ 4.08 atm.5- Yes, T = 300 K and P ~ 5.32 atm6- Yes, T = 400 K and P ~ 4.08 atm.7- Yes, T = 400 K and P ~ 5.32 atm. obs.: If necessary, consider: R = 8.314 J/mol∙K1 cal = 4.19 Jkb =1,38 x 10⁻²³ m² kg s⁻² K⁻¹

For this question there could be one or MULTIPLE answers, Choose the best Match/Matches. For a monatomic ideal gas in thermal equilibrium near room temperature, a. U = 3/2 NkT. b. U = 5/2 NkT. c. degrees of freedom include translational and rotational motions. d. degrees of freedom include translational, rotational, and vibrational motions. e. U = 5/2 pV. f. U = 3/2 pV. Explain work please.

Answer 2

Question

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

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Answer 3

Question

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

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Answer 4

Question

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

Expert Solution & Answer

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Answer 5

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

Answer 6

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

Answer 7

Chapter 21, Problem 21.68AP

(a)

To determine

The molar specific heat at constant volume if the molecules are linear.

Answer 8

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

Answer 9

(b)

To determine

The molar specific heat at constant volume if the molecules are nonlinear.

Answer 10

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

Answer 11

(c)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

Answer 12

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

Answer 13

(d)

To determine

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

Answer 14

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

Answer 15

(e)

To determine

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

Answer 16

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Answer 17

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Ch. 21 - Two containers hold an ideal gas at the same...Ch. 21 - (i) How does the internal energy of an ideal gas...Ch. 21 - Prob. 21.3QQ Ch. 21 - Prob. 21.4QQ Ch. 21 - Cylinder A contains oxygen (O2) gas, and cylinder...Ch. 21 - An ideal gas is maintained at constant pressure....Ch. 21 - Prob. 21.3OQ Ch. 21 - A helium-filled latex balloon initially at room...Ch. 21 - Prob. 21.5OQ Ch. 21 - Prob. 21.6OQ

The molar specific heat at constant volume if the molecules are linear.

Solution Summary: The author explains the molar specific heat at constant volume if the molecules are linear and the vibrational energy is neglected.

Concept explainers

The molar specific heat at constant volume if the molecules are linear.

The molar specific heat at constant volume if the molecules are nonlinear.

The high temperature molar specific heat at constant volume for a triatomic ideal gas of linear molecules.

The high temperature molar specific heat at constant volume for a triatomic ideal gas of nonlinear molecules.

The way by which the specific heat data is used to determine whether a triatomic molecule is linear or non-linear and check whether the data in Table 20.2 is sufficient to make this determination.

Chapter 21 Solutions