Statistical thermodynamics monatomic gases

The entries for Ar(s) and Ar( were calculated from data in Refs. 1 and 2 the entries for Ar( are statistical thermodynamic values for a monatomic ideal gas. 

The thermodynamic functions are calculated here via Boltzmann statistics assuming the electron gas to be an ideal monatomic gas with two equivalent spin states. The relative ionic mass is the electron rest mass as reported in the 1973 CODATA fundamental... 

Chapter 17 introduced some of the basic concepts that led to the development of a statistical approach to energy and entropy. This is statistical thermodynamics. By the end of the chapter, equations were applied to monatomic gases, and thermodynamic state functions—mostly entropy—were calculated whose values were very close to experimental values. Also, in some of the exercises you were asked to derive some simple expressions that were also derived from phenomenological thermodynamics. For example, we know from early chapters in this book that the equation AS = i In (V2/V1) is applicable for an isothermal change in volume of an ideal gas. We can also get this expression using the Sackur-Tetrode statistical thermodynamic expression for S. These correspondences are just two examples where phenomenological and statistical thermodynamics are consistent with each other. That is, they ultimately make the same predictions about the state functions of a system, and how they change with a process. 

Further, we approximated q = ijtrans were able to determine an expression for q in terms of various quantities, including the masses of the atoms and several universal constants. From that q, we were able to derive expressions for E, S, and related state functions and show that the statistical thermodynamic values for these state functions were very close to experiment (for S) or agreed with the values predicted by other theories (like = ffcT for a monatomic gas as predicted by kinetic theory, which we will consider in a later chapter). 

The zeroth moment of a distribution is 1, the first moment is < i>, the second moment is < P>, etc. The higher moments of a distribution hence compute successively higher averages of the distributions of the independent variable for example, in classical statistical thermodynamics the mean square velocity is the second moment of the Maxwell-Boltzmann speed distribution for an ideal gas, and is directly related to average kinetic energy < KE > = m < v >/2, and hence to temperature [= 3k TI2 for a monatomic gas]. 

The treatments in the preceding sections have been pretty abstract, and it may be hard to understand statements like Thus, if G can be determined as a function of T, P, and ,, all of the thermodynamic properties of the system can be calculated (which appeared after equation 2.5-9). However, there is one case where this can be demonstrated in detail, and that is for a monatomic ideal gas (Greiner, Neise, and Stocker, 1995). Statistical mechanics shows that the Gibbs energy of a monatomic ideal gas without electronic excitation (Silbey and Alberty,... 

This identification now makes for a completely consistent relation between the statistical properties of the gas and the thermodynamic varia-ables. The total energy of the gas, which is simply its kinetic energy for ideal monatomic gases, becomes [Eq. (VI.2.2)] for 1 mole... 

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