Specific heat difficulties

The measurement of the specific heat at constant volume is attended with considerable difficulty, because the thermal capacity of a vessel strong enough to contain the gas after heating has a value much greater than that of the thermal capacity of the enclosed gas. 

The model assumes a constant specific heat for water. Assuming that this varies with temperature, according to Cp = a + b T, how could this effect be implemented in the program, and what additional difficulties does it... 

The choice of a primary thermometer such as the 3He melting pressure thermometer to define the PLTS 2000 witnesses the great difficulties encountered in the measurement of very low temperatures. For example, at the beginning of 1980s, it was realized that differences up to 40% existed in the data of 3He specific heat obtained... 

As in the case of electrical resistivity, the experimental specific heat may be written as a sum of several separated contributions, leading to the same difficulties for interpreting data ... 

Specific heats and densities may be assumed to be weight averages if the solids are truly inert otherwise experimental determinations are necessary. The experimental work poses no unusual difficulties in this case. 

The thermophysical properties, such as glass transition, specific heat, melting point, and the crystallization temperature of virgin polymers are by-and-large available in the literature. However, the thermal conductivity or diffusivity, especially in the molten state, is not readily available, and values reported may differ due to experimental difficulties. The density of the polymer, or more generally, the pressure-volume-temperature (PVT) diagram, is also not readily available and the data are not easily convertible to simple analytical form. Thus, simplification or approximations have to be made to obtain a solution to the problem at hand. 

Specific heat can be predicted fairly accurately by mathematical models through statistical mechanics and quantum theory. For solids, the Debye model gives a satisfactory representation of the specific heat with temperature. Difficulties, however, are encountered when the Debye theory is applied to alloys and compounds. Plastics and glasses are other classes of solids that fail to follow this theory. In such cases, only experimental test data will provide sufficiently reliable specific heat values. 

Thus one can gee a difficulty in use of the 0°K base. Any change of the low temperature specific heat data would cause a change in HT 0 - H0° and would require recalculation of all (AHf 0 )0 data. One must remember that the (AHf )T values are obtained from the heat of reaction measured at a convenient calorimeter temperature. 

If this method is applied to thermodynamic data of polymers, the same difficulty arises as mentioned in Sect. 5.1 for the determination of the specific heat most polymer samples are partly crystalline, only. The thermodynamic quantities have values somewhere between those for purely crystalline and purely amorphous polymer. A large number of measurements are needed to derive the data for these two idealized states. Only for a limited number of polymers have data of this kind been published. 

Trinitrotoluene (also known as y-TNT) is one of the main impurities in military and commercial grades of TNT. Chick and Thorpe (1971) characterized two polymorphs. Form I (mp 376.2 K) may be obtained by recrystallization from alcohol or solidification of the melt. Form II (mp 347.2 K) is produced in small quantities with difficulty from an undercooled melt. It readily converts to Form I by mechanical perturbation or even spontaneously. Chick and Thorpe also determined latent heats of fusion, entropies of fusion, specific heats, IR spectra. Due to the conversion induced by grinding no X-ray data were presented for either form. No crystal structures have been reported. 

In Chapter IX. it was shown that the affinity of a chemical reaction can be calculated for any temperature, provided its value is known (from experiment) for any one temperature, and provided the heat of reaction and the variation of the heat of reaction with the temperature are known for the range of temperature in which we wish to calculate the affinity. The heat of reaction and its temperature coefficient, which is determined by the specific heats of the reacting substances, can both be determined calorimetrically without difficulty. On the other hand, it is not possible to calculate the affinity or the position of a chemical equilibrium by means of the two laws of thermodynamics and these thermal quantities alone. It is always necessary to know in addition the value of the affinity for some one temperature. The experimental determination of the affinity is often attended with considerable difficulty. It was thereforie eminently desirable to discover a new method which would avoid even this single determination and enable us to calculate the affinity from thermal quantities alone. The valuable researches of Nernst which resulted in the discovery of his heat theorem have placed at our disposal a means of solving this important problem. ... 

On the other hand, it gives the specific heat only as a mean value over a more or less extended interval of temperature. At very low temperatures, e.g. at the temperature of boiling hydrogen, there might be difficulties in its use this has not been tried. The apparatus next to be described is much to be preferred in these respects, and provides a solution of the problem which, from the experimental point of view, leaves nothing to be desired. 

On closer examination, however, several doubtful points arise in particular, the older theory has difficulty in explaining the gradual rise of specific heat at higher temperatures, which is always observed in practice. I was able to show (51) in 1911 that application of the quantum theory not only overcomes these difficulties, but may lead to totally new points of view. I pointed out also at the Solvay Congress (1911) that even the conceptions with which the kinetic theory supplies us for a monatomic gas cannot be completely satisfactory, and that quite a different state of affairs must exist, particularly at very low temperatures (cf. also Nemst, 47 and 66). 

Liquids, when strongly supercooled, are as a rule frozen, and so the examination of them down to very low temperatures is rendered impossible. We know, however, a large number of exceptions, in particular the glasses quartz glass may be mentioned as a striking example. Molten quartz, if cooled sufficiently rapidly, does not crystallize, but passes continuously into the condition of amorphous solid, quartz glass the specific heat of this can be measured without any special difficulty down to temperatures as low as may be desired. 

As regards the quantitative test of the Heat Theorem in the present case there must be measured, in addition to the heat of fusion, the specific heats of the crystallized substance and of the supercooled liquid down to low temperatures, if possible into the region of the T -law in both cases. The former series will not now in general offer any particular difficulty, but the examination of the liquid form is hindered by the fact that supercooling down to temperatures as low as desired is possible only in the rarest cases. 

It is known from the investigations of Tammann that benzophenone and betol are capable of extensive supercooling but difficulties, which have not yet been fully explained (Koref, 60), have been encountered in making accurate determinations, for the values obtained for the specific heats show unusually large variations. Examination of the supercooled substances was not possible in the vacuum calorimeter with the copper calorimeter the following numbers were obtained (60) —... 

The Binding of Water of Crystallization or 0 Hydration.—The affinity of this reaction can of course be calculated from the vapour pressure of the salt containing the water of crystallization and that of water at the required temperature the measurement of the specific heats of the anhydrous salt and of the salt containing water of crystallization offers no particular difficulties. The trouble that the specific heat of liquid water cannot be measured at low temperatures may be simply obviated by calculating the reaction to ice. 

We shall see, however, that this value is some 2 per cent, too low. The deviation of saturated mercury vapour from the ideal gaseous state reduces its specific heat (cf. infra), and therefore increases A, on a rough estimate, by some 80 cals. Although the error still remaining appears inconsiderable in view of the difficulty of the measurement, it is sufficient to throw out the result we arc calculating by a large amount. 

---