Heat capacity of liquids: An approach from the solid phase

We calculate the energy and heat capacity of a liquid on the basis of its elastic properties and vibrational states. The experimental decrease of liquid heat capacity with temperature is attributed to the increasing loss of two transverse modes with frequency $\omega <1/\tau$, where $\tau$ is liquid relaxation time. In a simple model, liquid heat capacity is related to viscosity and is compared with the experimental data of mercury. We also calculate the vibrational energy of a quantum liquid, and show that transverse phonons cannot be excited in the low-temperature limit. Finally, we discuss the implications of the proposed approach to liquids for the problem of glass transition.

Figure 1

(a) Circles are experimental data of viscosity of mercury, line is the fit and extrapolation using the Vogel-Fulcher-Tammann formula; (b) solid line is the experimental $c_v$ for mercury. Dashed lines are calculated values, using ${\tau }_{mt}{G}_{\infty }$ of $0.55\times {10}^{-3}\text{Pa}\text{s}$ (top) and $0.57\times {10}^{-3}\text{Pa}\text{s}$ (bottom).