Heat capacity surface

CP = bT1 layer lattice crystals, like graphite and boron nitride, and surface heat capacity Cp = yr + aT3 metals... 

When the excess surface heat capacity estimated by Sorai et al. between 80 and 130 K was assumed to remain constant up to 300 K values of C° ,(Ni(OH)2, cr,... 

Experimental Estimates The temperature derivative of the specific surface enthalpy is the specific surface heat capacity C)> ... 

Theoretical Estimates The use of the Debye model (Figure 3.2), which assumes that a solid behaves as a three-dimensional elastic continuum with a frequency distribution/(j ) = allows accurate prediction of the temperature dependence of the vibrational heat capacity C / of solids at low temperatures Cy oc r ), as well as at high temperatures (Cy = Wks). One may also use the same model with confidence to evaluate the temperature dependence of the surface heat capacity due to vibrations of atoms in the surface. 

We see that, at low temperatures, the surface heat capacity Cp is proportional to T, as opposed to the dependence of the bulk-heat capacity. However, the model we have considered here, consisting of a surface layer of atomic thickness, is quite unrealistic it would be difficult to measure the heat capacity of a single atomic layer. In most cases the solid samples that can be used in experiments are small particles of variable surface/volume ratio or thin films many atomic layers thick. It would therefore be important to consider the heat capacity of such a sample and to see what contribution, if any, the surface makes to the total vibrational heat capacity. 

We would like to find the contribution of the surface heat capacity to the total lattice heat capacity at a given temperature for a particle of a given size. Because the surface heat capacity is proportional to the surface area and the bulk term is proportional to the volume, the surface/volume ratio will clearly play an important role in determining the magnitude of the contribution of the surface heat capacity to the total heat capacity. The ratio of the bulk- and surface-heat-capacity tenns indicates both the temperature range and the thickness of the specimen for which the surface-heat-capacity contribution will become detectable. The ratio fora cube with sides of length L is approximately given by... 

The surface heat capacity has a different temperature dependence than the three-dimensional heat capacity. 

Estimate the surface-heat-capacity contribution to the total heat capacity of a nickel cube with a side length of 100 A. 

Chapter 3 Ratio of surface heat capacity to bulk heat capacity... 

The purpose of this chapter, in a book about transport properties, is to give advice to the reader on the best methods for converting the data, which are usually measured as a function of P and T, to a function of p and T, which is the form required for the correlating equations and, in addition, to provide sources for values of the ideal-gas isobaric heat capacities, which are also required for the transport-property calculations. Both of these purposes can be fulfilled by calculations from a single equation of state which has been fitted to the whole thermodynamic surface. Heat capacities of the real fluid are required only for the calculation of the critical enhancement of the thermal conductivity and viscosity, as described in Chapter 6 discussion of these properties in this chapter will be restricted to Section 8.4.4. 

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