Diatomic gas

The rigid rotor is the simplest model of a diatomic molecule with fixed inter-nuclear distance Requii between two atoms that have masses m and m2. The 

Quantum mechanics indicates that the square of orbital angular momentum is quantized, with = j j + )h /An. The z component of orbital angular momentum is also quantized, with Mj = m hjln and —j m j. Hence, there are 27 +1 quantum states of with the same energy E and squared orbital angular momentum unless a magnetic field is present. In other words, E and are functions of j but not of in the 

Before evaluating 2rotation, it is instructive to calculate B as well as the ratio TjB at normal operating temperatures. The generalized constants of interest are  

Contribution of Rotational Motion to the Internal Energy and Heat Capacity. 

As illustrated by equation (28-62), rotational motion of diatomic and polyatomic nonlinear ideal gases contributes to the internal energy as follows  

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Figure A2.2.2. The rotational-vibrational specific heat, C, of the diatomic gases HD, HT and DT as a fiinction of temperature. From Statistical Mechanics by Raj Pathria. Reprinted by pennission of Butterwortii Heinemann.

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

The simplification of equation 33 to equation 34 is possible only if r = 1 that is, foi simple monoatomic and diatomic gases. Foi other systems the design equation can be obtained by a direct rearrangement of equation 33. 

TABLE 10-13 Values of X for Normal Air and Perfect Diatomic Gases... 

K = Cp/Cv the ratio of specific heats at constant pressure to constant volume. This ratio is 1.4 for most diatomic gases, g = 32.2ft/sec"... 

Typical values of y range from 1.1 to 1.67, wliich give rcm values of 1.71 to 2.05. Thus, for releases of most diatomic gases (y = 1.4) to tlie atmosphere, upstream pressures over 1.9 bar absolute will result in sonic flow. Note tliat tlie inverse of rent is occasionally used by industry. 

HF is a colourless volatile liquid and an oligomeric H-bonded gas (HF), whereas the heavier HX are colourless diatomic gases at room temperature. Some molecular and bulk physical properties are summarized in Table 17.10. The influence of H bonding on the (low) vapour pressure, (long) liquid range and (high) dielectric constant of HF have already been discussed... 

Although real gases deviate from ideal gas behavior and therefore require different equations of state, the deviations are relatively small under certain conditions. An error of 1% or less should result if the ideal gas law were used for diatomic gases whenV> 5 f/ gm-mole (80 ftyib-mole) and for other gases and light hydrocarbon vapors when V > 20 f/gm-mole (320 ftyib-mole) [61, p. 67]. 

The highest value of c, 1 667, which is that predicted by the kinetic theory of gases, is observed only with monatomic gases (argon, mercury). Diatomic gases have the value 1 4, triatomic 1 3, and k decreases with increasing molecular complexity (cf. Chap. XVIII.). 

Exit temperature should not exceed 350-400°F for diatomic gases (Cp/Cv = 1.4) this corresponds to a compression ratio of about 4. 

C06-0138. According to Table 6H, molar heat capacities of monatomic gases (He, Ar) are significantly smaller than those of diatomic gases (N2, O2, H2). Explain in molecular terms why more heat must be supplied to raise the temperature of I mol of diatomic gas by I K than to raise the temperature of I mol of monatomic gas by 1 K. 

Table 3.2. Summary of the most important results of statistical mechanics for diatomic gases.

While first-order kinetics are observed with most diatomic gases that adsorb in molecular form, dissociative adsorption of gases such as H2 and N2 follows second order kinetics. In the limit of the empty surface the rate of adsorption is... 

The specific heat ratio k is approximately 1.4 for diatomic gases (02, N2, etc.) and 1.3 for triatomic and higher gases (NH3, H20, C02, etc.). The corresponding expression for isothermal conditions follows from Eq. (8-17) ... 

First, however, the choked pressure across the pipe must be determined to ensure critical flow. For diatomic gases the choked pressure is given as (see chapter 4)... 

Imes, E. S. Measurements on the near infrared absorption of some diatomic gases. Astrophys. J. 50, 251-276 (1919). 

For the reversible adiabatic expansion, a definite expression can be derived to relate the initial and final temperatures to the respective volumes or pressures if we assume that the heat capacity is independent of temperature. This assumption is exact at all temperatures for monatomic gases and above room temperature for diatomic gases. Again we start with Equation (5.39). Recognizing the restriction of reversibility, we obtain... 

R.G. Rehm, "Population Distributions During Vibrational Relaxation of Diatomic Gases , Ibid (1967), pp 37-48 12) R.L. 

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