Specific heat translational contribution

Differences in specific heats can be obtained in a similar fashion. Since translational and rotational contributions to Cp at elevated temperatures are minor, the differences to be accounted for are entirely due to vibrational effects. The most effective way to accomplish this is to identify the incremental contribution of each atom or group to Cp, and add or subtract this value from... 

For a temperature of 298.15 K, a pressure of 1 bar, and 1 mole of H2S, prepare a table of (1) the entropy (J/mol K), and separately the contributions from translation, rotation, each vibrational mode, and from electronically excited levels (2) specific heat at constant volume Cv (J/mol/K), and the separate contributions from each of the types of motions listed in (1) (3) the thermal internal energy E - Eo, and the separate contributions from each type of motion as before (4) the value of the molecular partition function q, and the separate contributions from each of the types of motions listed above (5) the specific heat at constant pressure (J/mol/K) (6) the thermal contribution to the enthalpy H-Ho (J/mol). 

In the gas phase, each molecule has three degrees of translational plus two of rotational freedom so that cp iR, plus a small contribution from vibration which will increase to R at higher temperatures. At low temperatures the atoms in the adsorbed layer will be localized and vibrationally unexcited. In this temperature range the isosteric heat therefore increases as iR. As the temperature is raised, however, and surface vibrations begin to contribute, the specific heat of the adatoms will approach that of the gas and finally exceed it, causing a diminution of the heat. This trend reverses once the adsorbed layer approaches the two dimensional gas. Presumably the vibration perpendicular to the surface contributes somewhat before the vibrations in the gas phase become important. The specific heat of the adsorbed layer will therefore continue to exceed that of the gas by a quantity of the order of iR, until all vibrational degrees of freedom are excited and the gas again dominates. 

The specific heat of water (4.2 kJ-kg -K ) is typically two to three times greater than the specific heat of other common liquids such as acetonitrile (2.23 kJ-kg -K ) or ethanol (2.44 kJ kg K ), even when the water molecule is much smaller, with fewer degrees of freedom. The large value of specific heat can be attributed to the existence of the local quasi-stable low-frequency oscillatory modes. Examples include hindered translation around 50 cm , intermolecular vibration around 200 cm and librational modes around 585 cm . In addition, HB breaking and re-formation also contribute to the specific heat as all of them contribute to fluctuation in the enthalpy. Note that... 

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. 

T law the result is a straight line, but this does not, in contrast to what is expected from Debye s theory, go through the origin. Hence, in this case, a linear contribution in T is included in the specific heat. This is attributable to the translation of the electron gas in the box and can be calculated from the box energy (Eq. (2.25)) by means of Fermi-Dirac statistics. Since metals are not at the focus of our interests we will omit any further discussion here . ... 

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