Monatomic gases, specific heat

The molecular weight (mean relative molecular mass) was obtained by determination of density but, in order to determine that the gas was monatomic and its atomic and molecular weights identical, it was necessary to measure the velocity of sound in the gas and to derive from this the ratio of its specific heats kinetic theory predicts that Cp/C = 1.67 for a monatomic and 1.40 for a diatomic gas. 

The trends of the results in Fig. 4.23 can be readily explained. Argon and nitrogen have thermal diffusivities that are approximately equal. However, Ar is a monatomic gas whose specific heat is lower than that of N2. Since the... 

Formerly these metallic properties were attributed to the presence of free electrons. The classical theory of this electron gas (Lorentz) leads, however, to absurdities for instance, a specific heat of 3/2 R had to be expected for this monatomic gas, contrary to the experience that Dulong and Petit s rule (atomic specific heat 6/2 R) holds for both conductors and non-conductors. The calculated ratio of heat conductivity to electrical conductivity (Wiedemann-Franz constant) also did not agree with observation. 

For crystals containing relatively massive ions (SFj", UF ", GeF6 , etc.), the zero-point energy (t/ ) is small (6.2-0.4 kcal mol" ). For crystals containing lighter ions, this term is more important and may be estimated from Waddington s correlation of 5 29 with V. The specific heat (Cp) of the crystal is taken to be 3J /ion Cp is taken to be /iR for monatomic, /iR for diatomic, and 4R for nonlinear polyatomic ions in the gas phase. 

The specific heat (referred to 1 mole) of a substance is given by the energy which must be supplied to the substance to raise its temperature by 1°. For a monatomic gas, it follows immediately from this definition that the specific heat at constant volume is... 

On closer examination, however, several doubtful points arise in particular, the older theory has difficulty in explaining the gradual rise of specific heat at higher temperatures, which is always observed in practice. I was able to show (51) in 1911 that application of the quantum theory not only overcomes these difficulties, but may lead to totally new points of view. I pointed out also at the Solvay Congress (1911) that even the conceptions with which the kinetic theory supplies us for a monatomic gas cannot be completely satisfactory, and that quite a different state of affairs must exist, particularly at very low temperatures (cf. also Nemst, 47 and 66). 

Argon is a monatomic gas, with a specific-heat ratio, Y = 1.67. The throat pressure ratio at choking is given by equation (9.4) as ... 

Given the specific-heat ratio, y, th pipe-flow function, fpipf, may be calculated for flow through pipes with a wide range of total frictional losses, Kt, and over the full range of pressure ratios. Tables A2.1 to A2.4 give the results of calculations for a monatomic gas, a diatomic gas, superheated steam/polyatomic gas... 

Atomic weights found by Cannizzaro s principle might still be multiples of the true value, but the value for mercury, 200, was confirmed by a measurement of the velocity of sound in mercury vapour by Kundt and Warburg, giving a value for the ratio of specific heats, cjc = r666, characteristic of a monatomic gas. 

The new gas was found to be almost twenty times more dense than hydrogen. Ramsay found that the ratio of its specific heat capacities was 1.66, indicating that the gas was monatomic, and it therefore followed that its atomic weight was nearly 40. All attempts to induce the new gas to combine chemically met with failure. 

To a first (rather crude) approximation these contributions are independent - the translational contribution is like that of a monatomic gas, and the other contributions correspond to the transport of molecular internal energy by a diffusion mechanism. Approximations of this sort actually predate the more elaborate kinetic-theory treatments based on an extended Boltzmann-like equation, and are often accurate to about a 10% level, with the notable exception of strongly polar gases, which have anomalously low thermal conductivities. In this approximation X can be calculated from t, D and the specific heat of the gas. 

Consider the partial 1894 periodic table below, with atomic weights beneath. Ramsay resorted to specific heat measurements to determine the atomicity of the gas since this would give the atomic weight needed to place the gas in the periodic table. It appeared to be monatomic, with an atomic weight of about 40. 

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