Heat Capacity of Solids

Abstract

Each atom in solids oscillates about its equilibrium position over a wide range of frequencies from zero up to a maximum value, and the conduction electrons in metals are freely mobile in solids. The oscillation of atoms and movement of electrons contribute to the internal energy of solids. When we heat a sample, solids absorb heat, and some of the phonons and electrons are excited thermally, so the internal energy of solids is expected to increase. The increase in internal energy due to lattice vibration of atoms and kinetic energy of free electrons in solids can attribute to the increase in heat capacity.Heat capacity of solids is usually measured at constant pressure and defined aswhere H is the enthalpy, T is the absolute temperature, and P is the pressure. Heat capacity at constant pressure is one of the indispensable thermodynamic quantities to obtain the free energy function of solids. By using the thermodynamic quantities at the reference temperature q, the free energy function (fef) of solids at temperature T is given as follows: 2Þ where G 0 T is the standard Gibbs energy at the absolute temperature T and H 0 q is the standard enthalpy at the reference temperature q. From heat capacity data as a function of temperature in the temperature range from q to T, the free energy function of solids can be determined by using Equation 5.2.Equilibrium constants K(T) of chemical reaction at temperature T are calculated from the standard Gibbs energy change of the reaction as follows:ln KðTÞ ¼ ÀDG 0 T =ðRTÞ ¼ ÀDH 0 q =ðRTÞÀDðfef Þ TðqÞ =R;ð5:3Þ

A science‐based mixed oxide property model for developing advanced oxide nuclear fuels

“…The heat capacities at constant pressure $${C}_p$$ and volume $${C}_v$$ are assumed to be obtained using the following equations, 51 $$$$\begin{equation}\ \ {C}_p = \ {C}_l + {C}_{sch} + {C}_d + {C}_{exe}\end{equation}$$$$ $$$$\begin{equation}\ \ {C}_v = \ {C}_l + {C}_{sch} + {C}_{exe}.\end{equation}$$$$…”

Experimental Verification of the Field Theory of Specific Heat With the Scaling in Crystalline Matter

“…Therefore, as explained in [1,2], the Debye theory, and other models built upon it like the Born-von Karman theory of lattice dynamics, could not have been mathematically implemented at that time. Nevertheless, the Debye theory (or rather its elements) remains a standard model of condensed matter physics [11][12][13][14]. The Debye theory is usually presented as a model for the lattice specific heat.…”