Chapter

Specific Heats

July 2009

DOI:10.1007/978-3-540-70626-7_201

In book: Compendium of Quantum Physics (pp.719-721)

Authors:

The equipartition theorem states that the average energy associated with each separable, quadratic term in the Hamiltonian results in a thermal energy of ½ RT per mole, where R is the gas constant and T the absolute temperature. This theorem, which emerged early in the history of kinetic theory in the nineteenth century, was quickly found to be in sharp disagreement with experiment, particularly for gases.

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Einstein, Specific Heats, and the Early Quantum Theory: Einstein's quantum theory of specific heat first showed the power of the new concept of energy quanta

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W Nernst
W. Nernst

Shilling: The specific heats of gases

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J. R. O'Loughlin

This investigation arose because of an interest in the magnitude of the pressure change accompanying the mixing of two gases when one is used to pressurize a container holding the other. If the two gases are separated by a flexible adiabatic membrane, the final pressure differs in general from that resulting if they are allowed to mix. A few simple cases are considered first since they are ... [Show full abstract] related to the problem of interest and serve as a basis for comparison. The ideal gas law is assumed along with constant specific heats.

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Starting from the mechanics of collision between two perfectly elastic smooth spherical molecules, the following equation for the heat transfer rate per unit volume from a gas or vapor 2 to another gas 1 in a mixture is derived based on the kinetic theory of gases: Methods of estimating molecular diameters when experimental values are not available are indicated, and values for sodium and UO2 ... [Show full abstract] vapor are estimated. For a set of typical values of the parameters, the time constant for the heat transfer is found to be of the order of 10⁻⁸ sec, which implies that for processes occurring in time periods greater than those of the order of 10⁻⁸ sec, the gases can be assumed to come to a thermal equilibrium at the instant they mix.

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Klavs Hansen

Helium is the lightest of the rare gases. As a rare gas it is chemically inactive and is only bound to other atoms, other helium atoms included, by weak and non-directional forces. The potential energy of two rare gas atoms of the same type is often described by a sum of two high powers of the reciprocal of the interatomic (internuclear, to be exact) separation.

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The general theory of van der Waals forces is used to calculate the asymptotic form of the n-particle correlation function for a simple liquid for any interparticle distance that is much greater than the interatomic separation. It is shown that when n>2 the nonadditive nature of the long-range forces leads to conditions for the weakening of the correlation which are fundamentally different from ... [Show full abstract] those obtained from theories in which a pairwise potential is assumed for intermolecular interactions. A relationship is obtained between the asymptotic forms and the n-atom potential for the case of a tenuous gas.

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Predictions are obtained for light-scattering spectra for disparate-mass gas mixtures at wave numbers such that species temperature separation produces strong deviations from hydrodynamic predictions. Recent light-scattering experiments in xenon-helium mixtures by Letamendia show good qualitative agreement with the present approximate predictions, thus providing the first experimental ... [Show full abstract] confirmation of the existence of a two-temperature regime in disparate-mass neutral gases. Physical reasons are suggested for the strong disagreement between two-temperature and hydrodynamic spectral predictions in the two-temperature regime.

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Last Updated: 30 Oct 2022