The method for determining the coefficient of thermal expansion of solids


(57) Abstract:

(57) the Invention relates to the field of thermophysical measurements and is intended to define thermal expansion coefficient of solid phone Task: getting the true crown-rump length of material at a given temperature and shorter duration tests. The inventive sample continuous section of material with a known density and specific heat capacity at a given initial temperature is subjected to adiabatic compression (tension) is known voltage, measure the resulting temperature change of the sample and calculate thermal expansion coefficient according to the formula. Technical result: improving the performance of the tests when determining KTR solids, the ability to create dilatometric without a measure of the elongation of the sample. table 1.

The invention relates to the field of thermophysical measurements and can be used in experimental determination of the coefficient of thermal expansion of a solid phone

Known methods of determining the coefficient of thermal expansion (CTE) [1] is that the sample is heated (cooled) by a given value of temperature/Voand KTR is calculated by the formula:

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This method is adopted for the prototype.

It should be noted that all the variety of existing methods for determining the CTE is the difference or the method of measuring the elongation of a test specimen, either way its heat.

For example, there is an absolute way to determine KTR [2] in which to measure the elongation of the sample is used in the interferometer. The main disadvantage of this method should be considered a necessary step of heating the sample in increments of not less than 5oC K, i.e., at such a significant amount that when calculating the CTD occurs the problem of allocating the found values to a certain temperature. It should be noted and low performance measurements in this method, associated with the necessity of long-keeping model if any change of its temperature in order to achieve its homogeneity volume of the sample. These shortcomings anlauttabelle fatal, because the attempt to reduce the step size of the temperature changes in the experiments leads to a significant drop in accuracy (see Mazurin, O. V. and other Thermal expansion of the glass. L. Nauka, 1969, S. 7).

There are Springe differential expansion of the standard and sample at the same temperature. (see Amatuni, A. N. Methods and devices for determining the temperature coefficients of linear expansion of the materials. M. Of standards, 1972). The measurement of the difference of the progress of the sample and the reference is a photovoltaic device. Knowing thermal expansion of the Etalon, calculate the CTE of the sample.

Some constructive improvements of this method, however, does not allow to get rid of the above shortcomings, are fully characterized and differential methods of determining CTD.

The task, which is aimed by the invention, obtaining the true value of the CTE of the material at a given temperature and a significant reduction in time to conduct the related tests.

The solution to this problem is possible when using effect related thermoelastic solid phone Its essence lies in the fact that during the adiabatic change of the internal energy of a rigid body, by performing external work, the temperature is changing (see Goldenblatt I. I. Nonlinear problems of elasticity theory. M. Nauka, 1969, S. 169-173.

In the particular case, when the body is subjected to uniaxial compression or tension, change>Thethe coefficient of linear thermal expansion, K-1;

Tothe initial sample temperature, K;

the density of the sample, kg/m3;

Cspecific heat, j/kgK;

s1voltage, H/m2;

=T-Tothe adiabatic temperature increment, K.

The above formula allows us to Express the coefficient of thermal expansion through measurable in the experience of the parameters as

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The invention consists in the fact that the sample constant cross-section (prism, cylinder, etc.,) with known density and specific heat capacity at a given initial temperature is affected by adiabatic compression (tension) is known voltage, measure the resulting impact of the temperature change of the sample and calculate thermal expansion coefficient in the above formula.

In the study of materials related to the declared object not found objects with attributes identical to the characteristics of the proposed technical solution, based on which a conclusion is made about its compliance with the criterion of "inventive step". As well as not found solutions that would contain the full set of features offer the population KTR solids has the following advantages over the prototype. Because the definition of the coefficient of thermal expansion of the proposed method was accompanied by a very small deviation from the initial temperature (at least in the 50oC100 times less than in protivopostavljaemyh ways), the calculated value of KTR is really true, attributed to the initial temperature of the experience. Due ecogarantie method can be effectively used when the radiation KTR In his area of significant changes, for example, in the area of phase transitions.

In addition, if contrasted how the duration of a single experience is on the order of hours, which is associated with the requirement of homogeneity of the sample temperature, to experiment the proposed method is not more than 2 to 3 seconds, i.e. about 1000 times less.

To check the possibility of determining the coefficient of thermal expansion of solids of the proposed method and compare the obtained results with the available reference data were tested samples of aluminum and organic glass (copolymer of PMMA brand 2-55). Samples of aluminum with dimensions h,5x1,8 mm, and samples of organic glass with dimensions HH,1 mm was subjected to tensile PR heat transfer of the sample with the surrounding air is negligible, that allows us to consider the conditions of the experiment are very close to adiabatic. As temperature sensors were used film Nickel resistance thermometers included in the pavement measuring circuit so that its output has formed an electrical signal proportional to the temperature difference between the sample and the environment.

The following table presents the results of these experiments, from which it follows that the values of the coefficient of thermal expansion are in satisfactory agreement with the reference data (see Tables of physical quantities. Under. Ed. by Acad. And. Of K. Kikoin. M Atomizdat, 1976. - 1008 S. Gudimov M. M. Petrov B. C. Organic glass. M. Chemistry, 1981. - 216 C.)

These examples suggest the feasibility of the method of determining the CTE of solids, in which this option could actually be considered a true value relating to virtually point temperature and not the temperature interval.

In addition, the proposed method of determining KTR very productive, since the time of the experiment is determined solely by the mechanical speed of the loading system and the inertia of t is camping in that affect the pattern of constant cross-section with known density and specific heat capacity at a given initial temperature, measure the temperature change before and after exposure to determine the coefficient of thermal expansion, wherein the effect on the sample is carried out by adiabatic compression (tension) is known voltage, and thermal expansion coefficient is determined by the formula

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where the density is kg/m3;

Cspecific heat, DN/kg;

T initial sample temperature, K;

s axial stress in the sample, n/m2;

q adiabatic temperature increment sample K.


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