Zero heat capacity

Consideration should be given to whether the solid particles are small enough to be in thermal equilibrium with the liquid. If this will be the case, then an average heat capacity should be used. If the solid temperature is expected to lag behind that of the liquid, then a safe assumption is that the solid has zero heat capacity, i.e. 

Consequently, the excess of internal energy can be regarded as a universal characteristic of the interfacial layer of a liquid (see Table 1). A constant value of e is an indication of zero heat capacity excess Cs=de/dr within the interfacial layer of a single-component liquid, meaning that the interface does not provide any additional degrees of freedom associated with the motion of molecules. The finite positive q reflects the higher entropy of the... 

The non-zero heat capacity change upon protein unfolding means that all other thermodynamic functions are also temperature dependent ... 

In a basic one-dimensional heat flow model [28,25 ] for a planar sample with thermal conductivity K, the sample is assumed to be thermally coupled to the bath at Tq with a finite thermal conductance K, but the coupling medium (gas) is assumed to have zero heat capacity. The following results are obtained ... 

The formation of Be(OH)2(aq) is described by reaction (2.5), with M = Be, p=l and q = 2. Figure 7.4 shows that the data acquired for the stability constant are not a linear function of the reciprocal of absolute temperature, but a hnear function of the logarithm of temperature, indicating a fixed but non-zero heat capacity change. Thus, the relationship between the stability constant and temperature is given by the following equation ... 

The data can be described by a relationship utilising a constant but non-zero heat capacity change. This relationship provides data that are more consistent with the available data in the literature. The variation of the solubility constant as a function of temperature is shown in Figure 11.39. 

It is possible that the stability constant data could be described by an equation with a fixed but non-zero heat capacity change, but the uncertainties in two of the equation parameters were too large and these parameters were highly correlated. As such, a relationship of this form could not be justified. 

Stability constant data are also available for the two copper(I) hydrolysis species, CuOH(aq) and Cu(OH)2 . As with the solubility constant data for cuprite, these solution species data also come from the work of Palmer (2011). The stability constant data are available across a large temperature range and relate to reaction (2.5) (M = Cu, p = l, q=l or 2). The variation of the stability constants of CuOH(aq) as a function of the inverse of absolute temperature is shown in Figure 11.74. Functionality with a fixed but non-zero heat capacity change is assumed. 

The relationship between the stability constants of Cu(OH)2 and the reciprocal of absolute temperature is shown in Figure 11.75. Again, the functionality utilised is that with a fixed but non-zero heat capacity change. 

The observed behaviour of the stability constant of Cu(OH)2 is similar to that of CuOH(aq) except that the downward curvature in stability occurs at a much higher temperature (see results in Palmer (2011)). Thus, the temperature-dependent behaviour of Cu(OH)2 has been described by assuming a constant but non-zero heat capacity. This description is simpler than that used by Palmer but describes the change in the magnitude of the stability constant equally well. 

As with the other copper(II) monomeric hydrolysis species, the accepted stability constant data for Cu(OH)4 require a function where a fixed but non-zero heat capacity change is utilised. Figure 11.79 illustrates the resulting relationship which is described by using Eq. (11.47) ... 

The relationship indicates that there is a constant, but non-zero, heat capacity change since the relationship is not linear. The solubility constant calculated for 25 °C and the other thermodynamic properties are... 

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