Graphite heat capacity

Figure A2.5.29. Peak positions of the liquid-vapour heat capacity as a fiinction of methane coverages on graphite. These points trace out the liquid-vapour coexistence curve. The frill curve is drawn for p = 0.127. Reproduced from [31] Kim H K and Chan M H W Phys. Rev. Lett. 53 171 (1984) figure 2. Copyright (1984) by the American Physical Society.

It was not simple (in 1992) to find out a low heat capacity (mechanically adequate) link giving such optimum G. Graphite fibres (1cm long, 8 xm in diameters) glued with Ag epoxy to the NTD Ge thermistor (see Fig. 15.11) give a G = 5 x 10-12 W/K at 0.3 K. There is, however, another contribution to G due to the nylon wires which support the absorber. The characteristics of the bolometer are summarized in Table 15.4. 

Figure 8.13 Lattice heat capacity of three different polymorphs of carbon C q [5], graphite and diamond.

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

Figure 2. The heat capacities of virgin cellulose (solid line) and cellulose chars (heavy broken lines). Graphite is also shown for reference (thin dashed line).

Graphite is used as cladding for nuclear fuel elements because of its low neutron-absorption cross section and good moderating properties, as well as its high temperature properties and high heat capacity. 

Problem The variation with temperature of the heat capacity of carbon (graphite), between 273 and 1373 K, is given by... 

Steam at a temperature of 150° C is passed over coke at 1000° C, so that the reaction C( ) + H20( ) = CO((7) + H2( ) takes place with an efficiency of 80%, i.e., 20% of the steam remains unreacted the gases emerge at 700° C. Calculate the amount of heat which must be supplied per kg. of steam passing over the coke the heat capacity of the latter may be taken as equal to that of graphite. 

It will be observed that Table XXV contains values for the free energy function of graphite this has not been obtained from equation (33.43), which is applicable to gases only. The method for the calculation of — (F — HD/T for solids is based on the use of heat capacities. For a pure solid, since So is zero, by the third law of thermodynamics, equation (23.1) becomes... 

In order to bring the sample rapidly into a hot environment, use is often made of the platform technique, as was first introduced in atomic absorption spectrometry by L vov [179]. Here the very rapid heating may enable the formation of double peaks to be avoided, which are a result of various subsequent thermochemical reactions, all of which have their own kinetics. Also the high temperature avoids the presence of any remaining molecular species, which are especially troublesome in the case of atomic absorption spectrometry. Thin platforms can be made of graphite, which have a very low heat capacity, or from refractory metals. In the latter case wire loops, on which a drop can easily be previously dried, are often used. 

Passive safety features for the MHR include ceramic, coated-particle fuel and an annular graphite core with high heat capacity and low power density. Recently, INL has used the ATHENA thermal hydraulic code to model the response of the MHR during loss-of-flow and loss-of-coolant accidents and has confirmed these passivity safety features work to maintain fuel temperatures well below failure thresholds [8]. 

The values for graphite and diamond are consistent with the principle that solids that are more ordered tend to have larger heat capacities. 

Below the Debye temperature, only the acoustic modes contribute to heat capacity. It turns out that within a plane there is a quadratic correlation to the temperature, whereas linear behavior is observed for a perpendicular orientation. These assumptions hold for graphite, which indeed exhibits two acoustic modes within its layers and one at right angles to them. In carbon nanotubes, on the other hand, there are four acoustic modes, and they consequently differ from graphite in their thermal properties. StiU at room temperature enough phonon levels are occupied for the specific heat capacity to resemble that of graphite. Only at very low temperatures the quantized phonon structure makes itself felt and a linear correlation of the specific heat capacity to the temperature is observed. This is true up to about 8 K, but above this value, the heat capacity exhibits a faster-than-Unear increase as the first quantized subbands make their contribution in addition to the acoustic modes. 

FOLLOW-UP PROBLEM 6.5 A chemist burns 0.8650 g of graphite (a form of carbon) in a new bomb calorimeter, and CO2 forms. If 393.5 kJ of heat is released per mole of graphite and T increases 2.613 K, what is the heat capacity of the bomb calorimeter ... 

Polyakov VB, Kharlashina NN (1995) The use of heat capacity data to calculate carbon dioxide fractionation between graphite, diamond, and caibon dioxide A new approach. Geochim Cosmochim Acta 59 2561-2572... 

No truly two-dimensional systems exist in a three-dimensional world. However monolayers absorbed on crystalline or fluid surfaces offer an approximation to two-dimensional behaviour. Chan and coworkers [31] have measured the coexistence curve for methane adsorbed on graphite by an ingenious method of determining the maximum in the heat capacity at various coverages. The coexistence curve (figure A2.5.29) is fitted to p = 0.127, very close to the theoretical 1/8. A 1992 review [32] summarizes the properties of rare gases on graphite. 

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