Argon, heat capacity ratio

For certain monatomic gases, such as helium, neon, argon, and mercury and sodium vapors, the ratio of the heat capacities at moderate temperatures has been found to be very close to 1.67, as required by equation (15.6). The values of the individual heat capacities at constant pressure and constant volume are 5.0 and 3.0 cal. deg. mole , respectively, in agreement with equations (15.5) and (15.4). It appears, therefore, that for a number of monatomic gases the energy of the molecules, at least that part which varies with temperature and so affects the heat capacity, is entirely, or almost entirely, translational in character (see, however, 16f). 

There is another amazing aspect in the discovery of argon beyond its total chemical inertness. Rayleigh and Ramsay reported measurements of the speed of sound in argon that indicated that the ratio of its heat capacity at constant pressure to that at constant volume (Cp/Cy) was too high for a diatomic molecule. The only other similar observation was for monatomic mercury (vapor) whose atomic weight was known since it forms compounds. At constant volume, heat added to a diatomic molecule such as N2 goes into both movement of the molecule (translation) as well as vibration of the bond. In a monatomic substance there is no bond vibration and, thus, less capacity to absorb heat. 

Since argon and neon are both monoatomic gases, they have the same heat capacity, C = fH. The thermal conductivities at 20 °C are neon, 11.07mW/mK argon, 5.236 mW/m K. (a) Calculate the ratio of the molecular diameter of argon to that of neon, (b) Calculate the molecular diameter of neon. (Use the -j factor rather than the exact one.)... 

Note that the volumetric ratio of liquid phase vs. vapor phase heat capacities is 60,000 to 1 for O2, 34,000 to 1 for N2 and 2200 to 1 for H2. Ratios of similar orders of magnitude may be shown for other media such as fluorine, argon, etc. argon, etc. 

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