a H H b Figure P20.40 TABLE 20.2 Molar Specific Heats of Various Gases Molar Specific Heat (J/mol · K)* C, - C, y = C„/C, Gas C, C, Monatomic gases 8.33 8.33 1.67 1.67 Не 20.8 12.5 12.5 Ar 20.8 Ne 12.7 12.3 20.8 8.12 1.64 Kr 20.8 8.49 1.69 Diatomic gases H, N, 28.8 20.4 8.33 8.33 8.33 1.41 29.1 29.4 20.8 21.1 1.40 1.40 29.3 34.7 21.0 8.33 1.40 Cl, 25.7 8.96 1.35 Polyatomic gases CO, So, 37.0 28.5 8.50 1.30 40.4 35.4 31.4 27.0 27.1 9.00 1.29 8.37 1.30 CH, 35.5 8.41 1.31 * All values except that for water were obtained at 300 K.
A triatomic molecule can have a linear configuration, as does CO2 (as shown), or it can be nonlinear, like H2O (as shown). 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 1/2 R to the molar specific heat for its kinetic energy and another 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 as shown sufficient to make this determination?
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