Serway & Jewett — The Kinetic Theory of Gases: Problem 40.

A triatomic molecule can have a linear configuration, as does \(CO_2\) (Fig. P20.40a), or it can be nonlinear, like \(H_2O\) (Fig. P20.40b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant, (a) if the molecules are linear and (b) if the molecules are nonlinear? At high temperatures, a triatomic molecule has two modes of vibration, and each contributes \(\frac{1}{2}R\) to the molar specific heat for its kinetic energy and another \(\frac{1}{2}R\) for its potential energy. Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of (c) linear molecules and (d) nonlinear molecules. (e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear. Are the data in Table 20.2 sufficient to make this determination?