True specific heat

The variation of specific heat with temperature was discovered by Dulong and Petit in 1819. It explains why so many different heat units exist (cf. 5), and requires the definition of specific heat to be so framed as to allow for this variation. For this purpose we replace the finite changes by infinitesimal ones. If SQ units of heat are absorbed when unit mass of a substance is raised in temperature from 6— SO) to 0- - SO) underspecified conditions, the true specific heat at the temperature 0 is ... 

Corollaries.—(1) To find the true specific heat when the mean specific heat is given, multiply the latter by 6 and differentiate with respect to 6. 

The method just described leads to the mean specific heats over a fairly large range. Nernst, Koref, and Lindemann (1910) have recently described a method of measuring the true specific heat at a given low temperature. The substance is contained in a block of copper cooled to the requisite temperature in liquid carbon dioxide, liquid air, etc., and energy is supplied by a heating spiral of platinum wire carrying an electric current, the measurement of the resistance of which serves at the same time to determine the temperature. 

Measurements of the true specific heats at low temperatures have been carried out by Eucken, who worked in such a way that to a weighed quantity of the substance in the form of a block, or in a proper isolated vessel, a known quantity of heat was added by means of an electrically heated platinum spiral, the resistance of wThich at the same time served to measure the temperature. The quotient of the electrical energy spent by the rise of temperature gives the specific heat. The correction for cooling (in vacuum of 5 Jo mm.) amounted to 20 per cent., and for heat capacity of the apparatus 5 per cent., yet the results are stated to be accurate to 1 per cent. 

If the true specific heat of an ideal gas is a function of temperature of the form ... 

The calculation may be extended to specific heats which are quadratic functions of temperature, etc., and we may also replace the integral of the true specific heat by a mean specific heat multiplied by the difference of temperatures ( 6) ... 

Its true specific heat between 0° and 300° C. is given by the expression 3 ... 

Conduction and radiation of heat mean and true specific heat. 

These facts make it necessary to define the conception Specific Heat more closely, and we are led to consider two new conceptions, viz. True Specific Heat and Mean Specific Heat. ... 

Considering unit mass of the substances, the above equation tells us that the specific heat c is given by the ratio of the quantity of heat Q necessary to produce the rise in temperature 2 - to this same difference in temperature - h- In future this quantity will be called the Mean Specific Heat between the temperature and and will be written If we find that has different values for different intervals of temperature 2 - hi we must look upon as the mean value of all the values which the specific heat has assumed in the interval of temperature <2 - For a temperature t the specific heat must, therefore, have a definite numerical value, which we shall call the true specific heat c, . 

In order to determine directly the true specific heat at the temperature t, it would be necessary to make a determination of the mean specific heat for a very narrow range of temperature in which t were included. The smaller we take this range of temperature, the more nearly would the measurement of the mean specific heat give us the value of the true specific heat c ,. Identity of the two could only be attained by taking the interval h h infinitely small. For <2 i we may then write... 

CONDUCTION AND RADIATION OF HEAT 23 The true specific heat for any temperature t between 0 and... 

Calculating from this table, we find the true specific heat of silver at 100° to be 0 0566. The mean specific heat between... 

Specific heat and chemical character. In 1819 Dulong and Petit discovered the following law The product of the atomic weight and the specific heat is a constant, namely 6 4, for all elements in the solid state. The atoms of the elements have all, therefore, the same specific heat (atomic heat). The following table shows that this law only holds approximately, and that several of the elements are exceptions to it, if we take the specific heat at the ordinary temperature as the basis of our calculations. The values of c are taken from the third edition of Landolt and Bornstein. The values of the true specific heat at room temperature were taken wherever possible. When Wied. Ann. 66, 235 (1898). 

The method of determining the specific heat which was used by Nemst and his collaborators was devised by Eucken. The substance was immersed in a suitable bath, such as liquid hydrogen, or Hquid air, in a vacuum vessel, and was then heated by a known electric current. The heating wire also served as a resistance thermometer. As the rise in temperature was always very small, the true specific heat was obtained directly. The following table shows the more or less rapid decrease of the specific heat with the temperature for a number of substances f... 

According to this table, the mean specific heat has a minimum at 37-5, and the true specific heat has a minimum at 25°. The specific heat of mercury decreases steadily, as the temperature rises, according to the linear equation ... 

The calculation of the equilibrium constant by equation (9) is usually a lengthy proceeding. For this purpose it is necessary to know the true specific heats, or the variation of the specific heats with the temperature. For the dissociation of water vapour, Nernst calculates from the mean specific heats of HgO, Hg, and Og an equation which, after the necessary transformation 2 X10 "... 

The temperature dependences of both mean and true specific heat are plotted for quartz glass in Fig. 51. The diagram demonstrates the characteristic behaviour of this quantity a relatively steep increase at low temperature and a gradual approach to a certain limit value. 

Thanks to the work of Behn, Tilden, Dewar, and others, something was already known of the behaviour of specific heats at low temperatures but there was no method which would give, not merely the mean energy content over a considerable temperature interval, but the true specific heat down to the lowest possible temperatures. 

To this end I searched for methods which should be very different, and therefore mutually confirmatory I think I have found them in the above described copper calorimeter and vacuum calorimeter. The latter apparatus is, of course, much more suited to our problem, since it gives the true specific heats (or, rather, the mean specific heats for a very small interval of temperature) but the copper calorimeter has also rendered us valuable service in completing, and above all in controlling, the results. For wherever a mutual control was possible—and the number of such examples is very large—an extremely satisfactory concordance has been shown between the values obtained this, of course, says much for the reliability of both methods. 

True specific heats of gases and vapors at 1 atm pressure,... 

DETERMINATION OF THE TRUE SPECIFIC HEAT OF SOLID AND LIQUID SUBSTANCES BY THE MICROCALORIMETER OF E. 

The true specific heat capacity of a material is defined as the quantity of heat required to raise the temperature of a specified mass by a specified temperature. For composites, it can be estimated based on the rale of mixture. Considering again that the material is composed of two phases - undecomposed and decomposed materials - the total heat, H, required to raise the temperature by AT of the material with the mass M should be equal to the sum of the heat required to raise the temperature of all its phases to the same level, as shown in Eq. (4.30) [12] ... 

The true specific heat capacity of a composite material was obtained by the mle of mixture and the mass fraction of each phase was determined by the decomposition and mass transfer model. The true specific heat capacity of resin or fiber was derived based on the Einstein or Debye model. The effective specific heat capacity was obtained by assembhng the trae specific heat capacity with the decomposition heat that was also described by the decomposition model. The modeling approach for effective specific heat capacity is useful in capturing the endothermic decomposition of resin and was further verified by a comparison to DSC curves. 

For sufficiently small samples, RJ 1, this expression simplifies to the true specific heat... 

Fig. 2. True specific heats o liquids. ChUton, Colburn and Fernon, ho6ed mainly on data from ""International Critical Tables " McOraw-HUl Book Company Inc., New York, 1928- 1930.)...

Eh = t/ib m + t/2b [17]. The value of t]2h < 0 for an fee structure means that the energy required for breaking all the bonds of an atom in molten state is included in terms of t/iblin, and therefore, the t]2b deviates from the true specific heat per CN. The t/2b for the fee structure should be linear dependence on... 

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