Carbon specific heat capacity

Hepplestone SP, Ciavarella AM, Janke C, Srivastava GP (2006) Size and temperature dependence of the specific heat capacity of carbon nanotubes. Surface Science 600 3633-3636. 

Exactly three grams of carbon were burned to CO2 in a copper calorimeter. The mass of the calorimeter is 1 500 g, and the mass of water in the calorimeter is 2 000 g. The initial temperature was 20.0 °C and the final temperature 31.3 °C. Calculate the heat of combustion of carbon in joules per gram. Specific heat capacity of copper is 0.389 J/g - K. 

The specific heat capacity of a substance comprises an electronic contribution Ce. and a contribution Cph of the phonons. The latter is dominant in carbon nanotubes, regardless of their structure. Cph is obtained from integration over the density function of phonon states and subsequent multiplication by a factor that considers the energy and the population of individual phonon levels. 

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. 

Specific heat capacity J K kg- 1013 959 (30% glass fiber) 963 (30% carbon fiber) 1005 (graphite) ... 

Nieto de Castro CA, Murshed SMS, LourenQo MJV, Santos FJV, Lopes MLM, Franca IMP (2012) Enhanced thermal conductivity and specific heat capacity of carbon nanotubes ionanofluids. Int J Therm Sci 62 34—39... 

For specific heat capacity, mineral classes arranged in the order of decreasing mean values are silicates—> carbonates sulphates—> oxides —> sulphides and their analogies native metals. 

Another consideration is the structural complexity of the molecules themselves. Carbon dioxide, CO2, and propane, C3Hg, have molar masses of 44 g/mol, yet the specific heat capacity of C3Hg(g) is substantially larger than that of C02(g). The reason is that CgHg molecules are structurally more complex than CO2 molecules, and CgHg molecules have more ways to absorb added energy. 

With the exception of liquid alloys and fused isomorphous mixtures the heat capacity of a mixture of liquids is usually larger than the sum of those of the components, e.g. with mixtures of alcohol with water, chloroform, carbon disulphide, and benzene. The 20 per cent solution of alcohol in water has a specific heat (1 046) greater than that of any other liquid below 100°.8 The heat capacities of mixtures of benzene and chloroform are the sum of those of the components. ... 

The specific heat of mixtures of liquids can rarely be calculated additively from the specific heats of the components. There is generally a considerable deviation from the law of mixtures, and the calculated value is always larger than one would expect. Mixtures of hquids which are closely related chemically, such as ethyl and methyl alcohol, chloroform and carbon disulphide, behave normally mixtures of water with alcohol, or of alcohol with other organic hquids, show large deviations. It is noteworthy that heat is evolved on mixing these hquids, an indication that chemical combination also is taking place. This is probably the reason for the alteration in the heat capacity, since the specific heat of liquid chemical compounds cannot be calculated additively from the specific heats of the components. The regularities shown by sohd bodies do not hold even approximately for hquids. 

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