Ceramics specific heat values

The specific heat of Si3N4 ceramics is in the temperature range 293 up to 1200 K [Cp (293 K) = 0.67 KJ (K kg)-1] nearly independent of the composition of the additives. The isobaric specific heat values agree well with the isochoric specific heat calculated by Debye s theory. Also the Dulong Petit s rule can applied as an approximation of the Cv values [25 J(K mol)-1] at temperatures >1100 K [371]. From the Cp values at around 100 K the amount of the amorphous grain boundary phase can be calculated [371]. 

Discussion This example demonstrates how steady one-dimensional heat conduction problems in composite media can be solved. We could also solve this problem by determining the heat flux at the interface by dividing the total heat generated in the wire by the surface area of the wire, and then using this value as the specifed heat flux boundary condition for both the wire and the ceramic tayer. This way the two problems are decoupled and can be solved separately. 

In these expressions, p denotes the density of cordicnte ceramic (41.15 g/in. ), P is the fractional porosity of the cell wall, and Cp is the specific heat of the cell wall (0 25 cal/ g°C). TIF is a measure of the temperature gradient the substrate can withstand prior to fracture MIF is a measure of the crush strength of the substrate in the diagonal direction Rf IS a measure of back pressure, H, is a measure of steady-state heat transfer, and LOF IS a measure of light-off performance An ideal substrate must offer high GSA, OFA, TIF, MIF, H and LOF values and low D, p, and Rf values. A close examination of the expressions indicates that certain compromises are necessary in arriving at the optimum substrate, as discussed in the next section. 

The above consideration of nanoparticles has been carried out in a supposition that they have more or less the same size. To be more precise, we assumed that the width of the nanoparticles sizes distribution function is smaller then its mean value. The mean value R is usually extracted from, e.g., X-Ray diffraction measurements [91] and it is supposed, that the size of all the particles corresponds to R. In this part we will show, that the neglection of sizes distribution can lead to incorrect results, when measurements are performed on the samples with essential scattering of sizes. Besides that, actually the size distribution defines the spectral lines inhomogeneous broadening. Moreover, it essentially influences the observed anomalies of many physical properties (like specific heat and dielectric or magnetic permittivity) of nanomaterials. Note that in real nanomaterials, like nanoparticles powders and/or nanogranular ceramics there is unavoidable size distribution which in general case should be taken into account. However, we will show below, that in perfect samples, where the width of size distribution is small, it is possible to suppose safely that all particles have the same size. In this part we primarily follow the approaches from the paper [92]. 

The results of specific heat measurements were reported earlier in the Sect. 2.2.1.4 (Chap. 2) for nanogranular BaTiOj ceramics. As in this case the ferroelectric phase transition is of the first kind, the Td R) in Eq. (3.85) is a boundary of paraelectric phase stability, while the real transition temperature is shifted from it by some R-independent value [93]. With respect to this statement it is possible to write specific heat Cp on the base of Eq. (3.85) with the only /(-dependent free energy coefficient Ar T). Since Cp = -7 (d /dr )(4> is a free energy) one can find, that the difference between specific heat in ferroelectric and paraelectric phases reads ... 

But as we have seen, masonry materials can have a mixed behavior vitreous and crystalline, the determination of the conductivity and specific heat curves is inclined to the crystalline nature of the materials. According to Eurocode 1996-1-2 2005 values of thermal expansion ( ), specific heat (c), and thermal conductivity (A) of ceramic materials subjected to high temperatures should be taken by testing in a database data (test) or the National Annex of each country. 

Experimentally, it is known that the heat capacity of ceramic systems increases from a low value to a value close to 25 J/mol K when the temperature is about 1000 °C. From this temperature, the heat capacity remains roughly constant. Data that are available show that the specific heat is substantially independent of the density of the brick [7, 30]. The experimental calculation of the heat capacity of a ceramic can vary greatly depending on the porosity thereof. This is because a porous ceramic containing air inside, so that the energy needed to increase the porous ceramic is less than that required to raise the temperature of a non-porous ceramic same composition (different densities). 

Values of specific heat capacity of some pol5miers are given in Table 3 for comparison, values of several ceramics and metals are included. Polymers have relatively large values, t3q)ically on the order of 750-2500 J/(kg-K), which at first glance might seem confusing. However, heat capacity is expressed on a per unit... 

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