Specific heats of materials

Figure 13.2 Glass transition temperature. Because the DSC 7 directly measures changes in the specific heat of material, the parameters associated with the glass transition of amorphous materials are easily made. As shown in this sample of polystyrene, the temperature where these changes occur, as well as the magnitude of the specific heat changes at the glass transition, are calculated using the TAS 7 TG program.

Early attempts at applying finite element analysis to solidification problems focused only on heat conduction. The most important phenomena taken into account are the release of latent heat due to phase change. If this is incorporated in the governing equations as a variation in the specific heat of material, it is evident that there occurs a jump at the phase-change temperature in the specific heat curve. This is analogous to the peak of a Dirac delta function. In order that this peak is not missed in the analysis, an alternate averaging procedure on the smoother enthalpy-temperature curve was suggested [60]. 

The increased sensitivity has many benefits, allowing small sample masses to be used, small transitions to be easily observed, and potentially increased accuracy for measurement of specific heat of materials. The reason for the increased sensitivity is that energy flows more quickly at the higher scan rates. The amount of energy involved remains the same but the time during which it flows is reduced as the scan rate is increased, so the y-axis response of the DSC records the energy flow increases with scan rate. See Section 1.4.3 of Chapter 1 for a full explanation. 

The expansion coefficient of a solid can be estimated with the aid of an approximate thermodynamic equation of state for solids which equates the thermal expansion coefficient with the quantity where yis the Griineisen dimensionless ratio, C, is the specific heat of the solid, p is the density of the material, and B is the bulk modulus. For fee metals the average value of the Griineisen constant is near 2.3. However, there is a tendency for this constant to increase with atomic number. 

W = weight of heated portion in kgm 8 - specific heat of the material of windings, in watt-s/kgm. °C. 

The specific heat of polyethylene is higher than for most thermoplastics and is strongly dependent on temperature. Low-density materials have a value of about 2.3 J/g at room temperature and a value of 2.9 J/g at 120-140°C. A somewhat schematic representation is given in Figure 10.9. The peaks in these curves may... 

The resin is too brittle to give a tme meaning to mechanical properties. The thermal properties are interesting in that there appears to be a transition point at 46°C. Above this temperature, specific heat and temperature coefficient of expansion are much greater than below it. The specific heat of hardened shellac at 50°C is lower than that of unhardened material, this no doubt reflecting the disappearance, or at least the elevation, of the transition temperature. 

Under steady-state conditions, the temperature distribution in the wall is only spatial and not time dependent. This is the case, e.g., if the boundary conditions on both sides of the wall are kept constant over a longer time period. The time to achieve such a steady-state condition is dependent on the thickness, conductivity, and specific heat of the material. If this time is much shorter than the change in time of the boundary conditions on the wall surface, then this is termed a quasi-steady-state condition. On the contrary, if this time is longer, the temperature distribution and the heat fluxes in the wall are not constant in time, and therefore the dynamic heat transfer must be analyzed (Fig. 11.32). 

The heat capacity or specific heat of a unit mass of material is the amount of energy required to raise its temperature 1°C It can be measured either at constant pressure or constant volume. At constant pressure it can be larger than at constant volume, because additional energy is required to bring about a volume change against external pressure. 

The specific heats of the most common organic and inorganic materials can usually be found in the handbooks. 

Moreover at low temperatures, the latent heat of vaporization L (20 J/g at 1.5 K for 4He) is still very large compared to the specific heat of most materials. Hence, it is possible to cool these materials (metals) using L. 

To evaluate the specific heat of a material, the various excitations that take place in the material are to be considered. This is the reason why the specific heat gives plenty of information about the material. 

In particular, if the magnetic field is strong enough, the material does not enter the superconducting state. The latter property is shown in Fig. 3.4(a) where the specific heat of A1 was measured [17] in no-field and in a moderate field. 

There are several types of magnetic behaviour that affect the specific heat of a material paramagnetism, ferromagnetism, antiferromagnetism and ferrimagnetism. Diamagnetism, being independent of temperature, causes no specific heat contribution and is not considered. 

The magnetic specific heats of some alloys containing paramagnetic atoms together with copper for comparison are shown in Fig. 3.8. Note that below 0.1 K, magnetic materials as manganin have a specific heat 103 higher than copper. 

Figure 3.10 shows the typical dependence on temperature of the specific heat of an amorphous and a crystalline polymer. For both materials, the specific heat has a steep dependence on temperature, but the behaviour is more complex in the case of the amorphous material. 

As an example, in Fig. 3.11, a schematic two-dimension representation of the structure of cristobalite (a crystalline form of Si02) and of vitreous Si02 is shown. A, B and C represent three cases of double possible equilibrium positions for the atoms of the material in the amorphous state [41]. Atoms can tunnel from one position to another. The thermal excitation of TLS is responsible for the linear contribution to the specific heat of amorphous solids. 

The model proposed by Anderson and Phillips gives a phenomenological explanation of the properties of the amorphous materials without supplying a detailed microscopic description [42]. Low-temperature measurements of the specific heat of amorphous solids have however shown that instead of a linear contribution as expected from the TLS theory, the best representation of data is obtained with an overlinear term of the type [43,44] ... 

From Fig. 3.12, we see that at fixed (low) temperature, the specific heat of various solids range over many orders of magnitude. Low specific heat materials (high Debye temperature) are for example very important in the realization of detectors (see Chapter 15). High specific heat materials are essential as regenerators in cryocoolers (see Chapter 5 and Fig. 3.13). 

Fig. 3.13. Specific heat of some materials used in regenerators for cryocoolers [70].

If c is the specific heat of the material [J/Kcm3], k the thermal conductivity, A the cross-sectional area of the sample and L the length of the sample, a simplified calculation gives ... 

As we said, the material of the regenerator of a PTR must have a high specific heat to provide a good heat storage. Unfortunately, below 20 K, the specific heat of most regenerators rapidly decreases, whereas the heat capacity of helium increases and has a maximum at 10K (see Fig. 5.20). 

Figure 4.8 shows the comparison of three lots of loperamide hydrochloride, each obtained from a different supplier. The displayed thermograms represent normal behavior for this material, and while the figure shows the uniqueness of each source, the variations were within acceptable limits. Owing to the decomposition that followed on the end of the melting endotherm, specific heats of fusion were not calculated in this case. 

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