A triatomic molecule can have a linear configuration, as does Co, (Figure a), or it can be nonlinear, like H,0 (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. C H (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? EinnT = 2.5R (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? EintnT = 3R At high temperatures, a triatomic molecule has two modes of vibration, and each contributes to the molar specific heat for its kinetic energy and another R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) Eint/nT = (d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as necessary: R.) Eint/nT = (e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear.

A triatomic molecule can have a linear configuration, as does Co, (Figure a), or it can be nonlinear, like H,0 (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. C H (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? EinnT = 2.5R (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? EintnT = 3R At high temperatures, a triatomic molecule has two modes of vibration, and each contributes to the molar specific heat for its kinetic energy and another R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) Eint/nT = (d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as necessary: R.) Eint/nT = (e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear.

University Physics Volume 2

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ISBN:9781938168161

Author:OpenStax

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Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

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Question

A triatomic molecule can have a linear configuration, as does CO, (Figure a), or it can be nonlinear, like H,O (Figure b). Suppose the temperature of a gas of
triatomic molecules is sufficiently low that vibrational motion is negligible.
C
H
H
(a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear?
Eint/nT = 2.5R
(b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear?
Eint/nT = 3R
1
At high temperatures, a triatomic molecule has two modes of vibration, and each contributes R to the molar specific heat for its kinetic energy and another R
2
for its potential energy.
(c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary:
R.)
Eint/nT =
(d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as
necessary: R.)
Eint/nT =
(e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear.

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