Thermodynamics monatomic gases

Similar types of relationships can be found between the other thermodynamic variables. In general, specifying two variables fixes the state of the third.y Thus specifying Vm and T fixes the value of Sm, specifying Hm and Gm fixes Um, and so on. As another example, Figure 1.4 shows the (Sm, p, T) surface for an ideal monatomic gas.z The entropy, Sm is restricted to values of p and T on the surface. 

In the calculation of the thermodynamic properties of the ideal gas, the approximation is made that the energies can be separated into independent contributions from the various degrees of freedom. Translational and electronic energy levels are present in the ideal monatomic gas.ww For the molecular gas, rotational and vibrational energy levels are added. For some molecules, internal rotational energy levels are also present. The equations that relate these energy levels to the mass, moments of inertia, and vibrational frequencies are summarized in Appendix 6. 

Note that U corresponds with the translational kinetic energy in three directions. Thus all the thermodynamic properties of an ideal monatomic gas can be calculated from G(T, P,ri). 

These are the properties of the monatomic gas at a pressure of 1 bar. It should be pointed out that this standard molar Gibbs energy is not the AfG° of thermodynamic tables because there the convention in thermodynamics is that the standard formation properties of elements in their reference states are set equal to zero at each temperature. However, the standard molar entropies of monatomic gases without electronic excitation calculated using equation 2.8-11 are given in thermodynamic tables. 

Thus we have demonstrated the remarkable fact that equation 2.8-1 makes it possible to calculate all the thermodynamic properties for a monotomic ideal gas without electronic excitation. Here we have considered an ideal monatomic gas. but this illustrates the general conclusion that if any thermodynamic potential of a one-component system can be determined as a function of its natural variables, all of the thermodynamic properties of the system can be calculated. 

The thermodynamic functions of the proton gas are calculated using the recent CODAT fundamental constants (2) and assuming that the proton is an ideal monatomic gas. Since there is no electron associated with this species, there is only a translational contribution to the thermochemical function. 

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... 

Thermodynamic functions of the ideal monatomic gas were calculated using spectroscopic da a from Bacher and Goudsmit 19). Vapor pressures have been measured by... 

Thermodynamic properties of the ideal monatomic gas have been calculated from the spectroscopic information reported by Moore 341) Vapor pressure measurements have been made by Douglas (55), Hartmann and Schneider 14 )f Pilling 361), Priselkov and... 

Thermodynamic functions for the ideal monatomic gas have been calculated from spectroscopic data given by Moore (241). Older vapor pressure measurements of Harteck (145) and of Marshall, Dornte, and Norton (223) agree with the more recent measurements of Hersh (151) and of Edwards, Johnston, and Ditmars (99). From these data we find the heat of sublimation at 298 K. to be 81,100 cal./gram atom, a normal boiling point of 2855 K., and a heat of vaporization at 2iS55 K. of 72,800 cal./gram atom. 

Skochdopole, Griff el, and Spedding 310) have compared measured entropies for the rare earths with theoretically predicted values. Although they do not predict a value for europium, they believe it is somewhat higher than its immediate periodic table neighbors. On this basis, we adopt a value of 17 e. u. for the entropy of europium at 298 K. Spedding and Daane 314) remark that europium is the most volatile of the rare earths. Landolt-Bornstein 208) report available spectroscopic terms from which we have calculated the thermodynamic properties of the ideal monatomic gas. The remaining data listed for this element are estimated and are consistent with the above known facts. These data are intended for use only until measured values become available. 

The solid is not stable at one atmosphere, and can only be obtained at elevated pressures. In the range from 0° to 1° K., the required pressure is reported by Simon and Swenson (304) as 25 atmospheres. At a pressure of 103 atmospheres, Keesom (174) reports the melting point to be 3.5 K., with an associated heat of 5 cal./gram atom. Keesom also reports the second order transition (lambda point) at 2.186 K., and the normal boiling point at 4.216 K. with the associated heat of vaporization of 20 cal./gram atom. Thermodynamic prop>erties for the ideal monatomic gas have been calculated at the National Bureau of Standards (395). Kobe and Lynn (193) report the critical temperature as 5.3 K. and the critical pressure as 2.26 atmospheres. 

White, Friedman, and Johnston (343) have measured the critical constants for normal hydrogen and have found 33.244 K. and 12.797 atmospheres. Woolley, Scott, and Brickwedde have presented data on the dissociation energy and the thermodynamic properties for the ideal diatomic gas, including contributions from nuclear spin. We have omitted the spin entropy in compiling our tables. Thermodynamic properties for the ideal monatomic gas have been computed at the National Bureau of Standards (395). Note that the reference state represents 2 gram atomic weights for this element. 

Thermodynamic functions for the ideal monatomic gas have been calculated from spectroscopic data reported by Moore (2 1). The vapor pressure of iron has been measured by Jones, Langmuir, and Mackay (170) Marshall, Dornte, and Norton (22S) and... 

Clusius 60) reports 24.55 K. as the melting point, with 80.1 cal./gram atom as the heat of melting. Henning and Otto 149) have measured the vapor pressure and find the normal boiling point at 27.07 K. From the heat of sublimation calculated by Clusius 69)t we calculate the heat of vaporization at the normal boiling point to be 422 cal./gram atom. Thermodynamic functions for the ideal monatomic gas have been calculated at the National Bureau of Standards 296), Kobe and Lynn 193) report 45.5 K. for the critical temperature and 26.9 atmospheres for the critical pressure. 

---