RU2716472C1 - Method of measuring specific heat capacity of materials - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measurement equipment of thermophysical properties of substances, is intended for measurement of specific heat capacity of materials and can be used in metrology, in industry, in scientific research and for development of new materials with preset properties. Disclosed is a method of measuring specific heat capacity of materials, according to which container, reference measure and analyzed sample are made with given accuracy of identical weight. Note here that container and reference gauge are made from the same material with specific heat capacity known at preset accuracy; heating element and primary temperature transducer are built into container. Total heat capacities of the heating element and the primary temperature transducer are considered to be known with given accuracy. Container is placed in an adiabatic calorimeter; a standard measure is placed in the container; initial temperature of the container and measures are set. Due the heating element of the container, a specified amount of heat is introduced into the container with a measure the specified number of times; at that, the total introduced amount of heat should be such that the maximum heating of the container does not exceed the specified value. After each introduction of heat, the temperature of the container established after introduction of specified heat is recorded and temperature increase is calculated relative to its initial value. Dependence of the amount of total heat input on the total temperature increase for the reference measure is approximated and a derivative of the obtained relationship is found. Measured sample is replaced with operations identical to those of the reference measure. Dependence of the amount of total heat input on the total temperature increase for the analyzed sample is approximated, the derivative of the obtained relationship is found and the unknown specific heat capacity of the analyzed sample is calculated.

EFFECT: high accuracy of measurements with simultaneous expansion of the dynamic range and nomenclature of analyzed materials.

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Description

The invention relates to a measuring technique for the thermophysical properties of substances, is intended to measure the specific heat capacity of materials and can be used in metrology, in industry, in scientific research and for the development of new materials with predetermined properties.

A known method for determining the heat capacity of a material at the same time as determining the coefficient of its thermal expansion (RF patent, No. 2439511, IPC G01K 17/00, publ. 10.01.2012), according to which the desired heat capacity is obtained based on the results of several experiments conducted in an adiabatic container.

The disadvantage of this method is the low accuracy associated with the need for a calibration experiment to determine the heat capacity of a hollow container.

There is also a method for determining the heat capacity of materials, according to which the corundum sample, with a thermometer pre-installed in it, is placed in an adiabatic container with a known mass, made of pure silver and equipped with a heater, a measuring pulse of electric current is supplied to the heater due to heat release Q providing a given rise in the temperature of the sample ΔT, and taking into account additional experience in determining the heat capacity of a hollow container, determine the desired heat capacity C _arr according to the ratio C _arr = (Q / ΔT-C _p ), where C _p = Q _p / ΔT _p is the heat capacity of the hollow container, determined during the calibration experiment by passing a measuring pulse through the heater, due to the release of heat Q _p , which provides a temperature rise ΔT _p (Frenkel I.M., Sergeev O.A. State primary standard of unit specific heat of solids in the temperature range from 273.15 to 700 K // Measuring technique, 1975, No. 4. - P. 45-49).

The main disadvantage of this method is the insufficiently wide dynamic range and the need for a calibration experiment; as a result, the relatively high error of the measurement results.

Closest to the proposed one is a method for determining the heat capacity of materials (prototype), which consists in the fact that the test sample with a thermometer pre-installed in it is placed in an adiabatic container with a heater of known heat capacity, a measuring pulse of electric current is passed through the heater due to the release of heat providing a specified temperature rise of the sample, the test sample is replaced with a reference sample with the same geometric dimensions, with obviously no less heat capacity Stu and provided with an additional heater. In this case, the reference sample and the container with known masses are made of the same dielectric. Then the measuring impulse is repeated and an additional impulse is synchronously passed through an additional heater, reaching a predetermined temperature rise. After the experiment is completed, the desired heat capacity is determined by subtracting the ratio of the amount of heat released due to the additional pulse to the given temperature difference from the product of the ratio of the mass of the reference sample to the total mass of the reference sample and the container by the difference in the quotient of the total amount of heat released by repeated and an additional impulse, for a given rise in temperature and heat capacity of the heater (RF patent No. 2690717, IPC G01N 25/20, publ. 06/05/2019; Sokolov N.A., Sokolov A.N. high measurement class: multi-valued measures of heat capacity of solids // Devices. 2018. No. 8. P. 39-43).

The disadvantages of the method are as follows.

The measurement accuracy claimed in the method does not take into account the uncertainty of knowing the specific heat of a measure (reference sample), which replaces the test sample. To date, the best relative uncertainty in the value of the specific heat measure is 5410 ^-4 (Frenkel I.M., Sergeev O.A. State primary standard for the unit specific heat capacity of solids in the temperature range from 273.15 to 700 K // Measurement technique , 1975, No. 4. - S. 45-49). Therefore, the error of the method is higher than stated in the description of the invention. The flawed error is the additive that the method brings to the total error.

In addition, the proposed method is limited by the dynamic range and nomenclature of the investigated materials. This is due to the fact that in the theoretical derivation of the method measurement equation the equality of the specific heat capacities of the system of bodies of the container-test sample and the container-reference measure is accepted. This equality is fulfilled only in one case - when the sample and the reference measure are made of identical material. Therefore, the method provides a given accuracy and is applicable only for materials whose specific heat is equal to the specific heat of the measure. For cases when the measure and the sample are made of different materials, the method is inoperative and does not provide the stated specified accuracy (Zarichnyak Yu.P., Kompan T.A., Khodunkov V.P., Kulagin V.I. On the possibility of implementing multi-valued measures in calorimetry // Instruments. 2019.№5. S. 22-26).

The technical result from the application of the proposed method is to increase the accuracy of measurements while expanding the dynamic range and nomenclature of the investigated materials.

This technical result is achieved by the fact that in the proposed method for measuring the specific heat of materials, the container, the reference measure and the test sample are made with a given accuracy with the same mass, while the container and the reference measure are made of the same material with a specific heat, known with a given accuracy, embedded in container heating element and primary temperature transducer, while the full heat capacity of the heating element and primary transducer the temperatures are considered known with a given accuracy, the container is placed in an adiabatic calorimeter, the reference measure is placed in the container, the initial temperature of the container and measures are set, with the help of the heating element of the container, a predetermined amount of heat is introduced into the container with a measure, the total amount of heat entered must be such that the maximum heating of the container does not exceed a predetermined value, after each heat input, the steady state after the introduction of a predetermined heat is recorded heat the temperature of the container and calculate the temperature increase relative to its initial value, approximate the dependence of the amount of heat introduced on the total temperature increase for the reference measure and find the derivative of the obtained dependence, replace the measure with the test sample and perform operations identical to the operations with the reference measure for it, approximate the quantity dependence the total heat input from the total temperature increase for the test sample and find the derivative obtained Depending constant and calculate the desired value of the specific heat of the test sample, wherein the calculation performed by the relation:

Where

with _O - specific heat of the test sample,

with _M - specific heat of the reference measure,

- отношение производных,

- the ratio of derivatives,

- производная, полученная для исследуемого образца,

- derivative obtained for the test sample,

- производная, полученная для эталонной меры,

- the derivative obtained for the reference measure,

m _M is the mass of the measure (sample),

With _N is the total heat capacity of the heating element,

With _D is the total heat capacity of the primary temperature transducer.

The essence of the method is illustrated by figures. In FIG. 1 shows a general view of a measuring cell for two cases when a measure and a test sample are placed in the cell; in FIG. 2 is a graphical illustration of the temperature course of the process when heat is introduced into a container with a measure or sample; in FIG. 3 shows graphical dependences of the amount of heat supplied on the value of temperature heating for the test sample and for the reference measure; in FIG. Figure 4 shows the dependences of the estimated error introduced by the method into the total error for two cases when sapphire (line 1 on the graph) and silver (line 2 on the graph) are used as a measure.

The measuring cell is a container 1, made, for example, in the form of a hollow cylinder with a removable cover 2 and a stationary bottom. A heating element 3 and a low-inertia primary temperature converter 4, for example, a platinum resistance thermometer or a thermocouple, are mounted inside the container. When taking measurements, a reference measure of specific heat 5 and the test sample 6 are inserted into the container alternately. Using the heating element 3, a predetermined amount of heat is supplied to the sample and measure. Using the primary temperature transducer 4 measure the temperature of the measuring cell.

The reference measure of specific heat 5 is either a powdery filling of granules or a monolithic body, for example, a solid cylinder of a given diameter and length.

The studied sample 6 is either a powdery filling, or a liquid, or a set of bodies of various shapes and sizes (granules, balls, cylinders), or a monolithic body, for example, a cylinder.

The reference measure and the container are made of the same material and have the same mass, therefore their specific and total heat capacities are also the same. The test sample is made (formed) so that its mass is also equal to the mass of the container and the mass of the reference measure.

The measuring cell is in adiabatic heat transfer conditions, heat exchange with the environment is completely absent. The adiabatic conditions for the measuring cell are realized by placing it in an adiabatic calorimeter.

The theoretical basis of the method.

For the case when there is a reference measure 5 inside the container, when a predetermined amount of heat Q _1i is supplied to the measuring cell, this heat is spent on changing the heat content of the container, the reference measure, the heating element and the primary transducer. In this case, a part of the heat equal to Q _1i ^* is removed through the connecting wires of the heater and the primary converter to the shells and the casing of the adiabatic calorimeter. In addition, some (small) part of the heat equal to Q _1i ^** , due to the imperfect calorimeter temperature control system, is diverted to the internal adiabatic shell surrounding the container. The sum of the heats Q _1i ^* + Q _1i ^** is the heat loss of the calorimeter, which, as a rule, is no more than 1% of the summed heat amount Q _1i , i.e. Q _1i ^* + Q _1i ^** = nQ _1i , where n <0.01. For small changes in temperature (ΔT = 5-10K), the value of the coefficient n can be taken with high accuracy to be constant, i.e. n = const.

Based on the foregoing, for the steady-state stationary thermal regime of the measuring cell, the following heat balance equation is valid:

Where

with _K , m _K - specific heat and mass of the container, respectively;

with _M , m _M - specific heat and mass of the reference measure, respectively;

With _N is the total heat capacity of the heating element;

C _D is the total heat capacity of the primary temperature transducer;

- значение стационарного температурного нагрева эталонной меры;

- конечное значение температуры эталонной меры;

- начальное значение температуры эталонной меры;

- the value of the stationary temperature heating of the reference measure;

- the final temperature of the reference measure;

- the initial temperature of the reference measure;

n is the coefficient of heat loss of the measuring cell.

Since the masses and specific heat of the container and the reference measure are the same, i.e. m _K = m _M ; with _M = with _K , then the ratio (1) takes the form:

For the case when the test sample 6 is located inside the container, when a specified amount of heat Q _2i is supplied to the measuring cell, this heat is spent on changing the heat content of the container, the test sample, heating element and primary transducer, as well as on heat losses equal to Q _2i ^* + Q _2i ^** = Q _2i For this case, in the steady-state stationary thermal mode of the measuring cell, the following heat balance equation is valid:

Where

with _O , m _O - specific heat and mass of the sample, respectively;

- значение стационарного температурного нагрева исследуемого образца;

- конечное значение температуры исследуемого образца;

- начальное значение температуры исследуемого образца.

- the value of the stationary temperature heating of the test sample;

- the final temperature value of the test sample;

- the initial temperature value of the test sample.

Since the mass of the container, the measures and the test sample are the same, i.e. m _K = m _O = m _M , and the specific heat of the measure is equal to the specific heat of the container, i.e. with _M = with _K , then the ratio (3) takes the form:

From equations (2), (4) we find the derivatives of the amount of heat with respect to temperature increase, i.e. derivatives of Q with respect to ΔT, we obtain:

Transforming (5), (6) we get:

Divide (7) by (8), we obtain:

From relation (9) the following equality follows:

Solving equality (10) with respect to the specific heat of the test sample, we obtain:

Denote the derivatives as follows:

The coefficients k ₁ and k ₂ in relations (12) are nothing but the angular coefficients of the linear dependences of the amount of heat supplied on the temperature difference, i.e. dependencies of the form: Q _i = k _i ΔT (Fig. 3). Taking into account relations (12), the measurement equation for the proposed method takes the form:

Denote the ratio of the angular coefficients k ₂ / k ₁ = γ, then the measurement equation (13) takes the form:

Where

- расчетная поправка, учитывающая полные теплоемкости нагревательного элемента и первичного преобразователя температуры.

- calculation amendment taking into account the total heat capacity of the heating element and the primary temperature transducer.

Given that the derivatives k ₂ and k ₁ can be both greater and less relative to each other, therefore, to exclude negative values of specific heat, relations (14) and (15) should be presented in a modular form:

In the proposed method, equation (16, 17) is the basic measurement equation. The conditions for applying this measurement equation:

1. Equal masses of the container, reference measure and sample.

2. Equality of specific heat capacities of the reference measure and the container.

According to (16, 17), in order to find the desired value of the specific heat of the sample, it is necessary for the sample and measure to perform several measurements of the temperature increments ΔT _i corresponding to different quantities of introduced heat Q _i , and then perform mathematical approximation of the obtained dependences Q _i (ΔT _i ), find their angular coefficients (derivatives) and from their ratio calculate the desired specific heat of the sample. In this case, the angular coefficient of dependence Q ₁ = ƒ (ΔT) for the reference measure is measured once and is considered constant for all subsequent measurements of the specific heat capacity of the studied samples. Thus, the measurement process reduces to measuring the angular coefficient k _{2 of the} dependence Q ₂ = ƒ (ΔT) for the test sample with the known (pre-measured) angular coefficient k _{1 of the} dependence Q ₁ = ƒ (ΔT) for the reference measure. This significantly reduces the complexity of the measurement procedure.

Thus, according to the measurement equation (16, or 17), for measuring the specific heat capacity of the test sample experimentally obtained separately for the test sample and for the reference measure, the dependence of the amount of heat supplied on the value of temperature overheating Q ₁ = ƒ (ΔT) (Fig. 3), find the ratio of the derivatives of the obtained dependencies (angular coefficients). The found value is substituted into the measurement equation (16, or 17) and the desired specific heat is calculated. In this case, depending on the required accuracy, either the correction δс is taken into account in the measurement equation and then it is calculated, or the correction δс is not taken into account. Since the heat capacity of the heating element and the primary temperature transducer can technically be made much smaller than the total heat capacity of the sample and measure, they can, in most cases, be ignored. In this case, the equation of measurements is simplified and takes the form:

An example implementation of the method.

To implement the method, the necessary dimensions of the container, the reference measure and the test sample are initially determined. Suppose, for example, a container and a reference measure are made of silver. The specific heat capacity of silver at a temperature T = 300 K is c _Ag = 235.4 J / (kg⋅K), the specific density ρ _k = 10493 kg / m ³ .

The container is made in the form of a hollow cylinder with a bottom and a removable lid with the following specified overall dimensions: the outer diameter of the container D _{k, nar} = 50 mm, the inner diameter D _{k, vn} = 47 mm (wall thickness 1.5 mm), the height of the cylinder N _k = 85 mm, the outer diameters of the bottom and the lid are the same and equal to D _drug = D _{to, drug} = 50 mm, their thickness h = 1.5 mm. The volume of cylinder material with a bottom and a cover is:

The mass of the container is equal to m _to = ρ _to V _to = 0.2656 kg. Based on the mass of the container, the volume of the reference measure is calculated.

Let the reference measure be a monolithic cylinder. Like the container, it is made of silver, therefore its volume is V _m = m _k / ρ _k = 2.532⋅10 ^-5 m ³ , i.e. equal to the volume of the container material V _to . We set the height of the reference measure equal to, for example, N _m = 25 mm, then its outer diameter is:

When choosing the test sample, we take the extreme case - take the material with the maximum specific heat and low specific gravity, and check if the container capacity is sufficient to accommodate this sample. As such material we take, for example, beryllium. The specific heat of beryllium at a temperature of T = 300 K is equal to _Be = 2398 J / (kg⋅K), the specific density ρ _Be = 1848 kg / m ³ . To achieve mass equality, it is necessary that beryllium occupies a volume equal to: V _Be = m _k / ρ _Be = 0.2656 / 1848 = 1.4372⋅10 ^-4 m ³ . We set the height of the test sample (beryllium) equal to H _Be = 84 mm, then the calculated value of the outer diameter of the test sample is:

The resulting value is less than the inner diameter of the container, therefore, the capacity of the container allows you to place the sample in it. Thus, this container design provides the ability to analyze the specific heat of materials, the specific gravity of which is not lower than 1848 kg / m ³ . In the case when it is required to analyze materials with a lower density, it is necessary to choose another container material that also has a lower density, for example, beryllium (ρ = 1848 kg / m ³ ), zirconium (ρ = 6450 kg / m ³ ), tin (ρ = 7300 kg / m ³ ), antimony (ρ = 6691 kg / m ³ ), beryllium ceramic (ρ = 3005 kg / m ³ ), aluminitride ceramic (ρ = 3260 kg / m ³ ), etc. In this case, preference should be given to the most thermally conductive materials, such as beryllium or aluminitride ceramics, since they provide the most uniform temperature field inside the container.

After determining the required overall dimensions, a container, a reference measure, a test sample are made and the measurements are started.

First, measure 5 is placed in the container 1. The specified amount of heat Q _{1.1 is} introduced into the measuring cell and, after establishing the stationary thermal regime, the achieved stationary heating ΔT _{1.1 is} recorded (Fig. 2). A predetermined amount of heat Q _1.1 is associated with the achieved stationary heating ΔT _1.1 . Then, a predetermined amount of heat is introduced into the measuring cell, and after the establishment of the stationary thermal regime, the stationary heating ΔT _1.2 achieved relative to the zero (initial) value is recorded. The total heat input equal to Q _1.1-2 = Q _1.1 + Q _1.2 is associated with the achieved stationary heating ΔT _1.2 . A predetermined amount of heat Q _{1, i is} introduced into the measuring cell and, after establishing the stationary thermal regime, the stationary heating ΔT _{1, i} achieved relative to the zero (initial) value is recorded. The total amount of heat introduced, equal to Q _1,1-2 = Q _1,1 + Q _1,2 + ... + Q _{1, i} is associated with the achieved stationary heating ΔT _{1, i} . The number of operations to enter a given amount of heat into a measuring cell is usually N = 5-10 times, while the maximum amount of heat introduced Q _{1, i = N is} selected so that the maximum heating of the measuring cell does not exceed a predetermined value, for example, ΔT _max = 10 K Based on the value of Q _{1, i = N} set the value of Q _{1, i} . Then, using the linear dependence Q _{1, i} (ΔT) obtained for the reference measure, the value of its angular coefficient k _{1 is} calculated.

The measure is removed from the container and the test sample 6 is placed in it. After this, the operations are identical to those performed with the measure. From the linear dependence Q _{2, i} (ΔT) obtained for the test sample, the value of its angular coefficient k _{2 is} calculated by calculation. Then, the desired specific heat capacity of the test sample is calculated, and either (16) or (17) is applied and the previously calculated correction value δс is used, or the calculated ratio (18) is applied and the δc correction is not taken into account.

As a result of performing these operations with high accuracy, the desired value of specific heat of the test sample is obtained. In comparison with the known methods, this method minimizes the error due to the systematic error of temperature measurement by the primary temperature transducer, which vanishes during the differentiation operation.

Estimation of the error of the method. According to the measurement equation (16), the calculated ratio for the absolute uncertainty of measuring the specific heat of the sample has the form:

where the symbol δ means the absolute measurement uncertainty of the corresponding physical quantity.

The uncertainty of measuring the ratio of derivatives γ is calculated taking into account relation (12) according to the following relation:

Evaluation of the non-excluded systematic error (NPS) of the measurement of the amount of heat, as in the prototype, is taken equal to δ (dQ _1i ) / dQ _1i = δ (dQ _2i ) / dQ _2i = 0,004%.

The calculation of the error (NSP) of the method, taking into account the uncertainty of the measure, is performed for two measures (silver and sapphire) and the following parameter values:

C _H = 0.13 J / K; C _D = 0.05 J / K; c _M1 = 788.8 J / K (sapphire), with _M2 = 235.4 J / K (silver) at room temperature; m _M = 0.1 kg; δС _M = 0.39 J / K; δC _H = 0.00013 J / K; δС _d = 0.00005 J / K; δm _M = 10 ^-7 kg; δγ = 5.7⋅10 ^-5 (calculated by the relation (20)).

The uncertainty introduced by the claimed method to the uncertainty of the measure is calculated by the formula:

Where

δс _m / s _m = 5⋅10 ⁴ - relative uncertainty of the specific heat of the measure;

δc _o / c _o - the relative uncertainty of the measurement of the specific heat of the sample, calculated by the relation (19).

In FIG. 4 presents the results of the calculation of the uncertainty according to (21), introduced by the claimed method into the general uncertainty, where line 1 corresponds to the uncertainty when using a sapphire measure, line 2 to silver. As follows from the presented dependencies, in the dynamic range of specific heat for known materials, the method provides an uncertainty much less than in the prototype. For the case when the specific heat of the measure and the test sample are equal, as in the prototype method, regardless of the measure used, the relative uncertainty is δс _о ^* / с _о = 0.015%. Thus, the advantages of the method are obvious.

Claims (11)

A method for measuring the specific heat capacity of materials, which consists in the fact that the container, the reference measure and the test sample are made with a given accuracy with the same mass, while the container and the reference measure are made of the same material with a specific heat, known with a given accuracy, a heating element is built into the container and a primary temperature transducer, while the total heat capacity of the heating element and the primary temperature transducer is considered known with a given accuracy, place the container in an adiabatic calorimeter, place the reference measure in the container, set the initial temperature of the container and measure, use the heating element of the container to enter the specified amount of heat a certain number of times into the container with the measure, while the total amount of heat entered should be such that the maximum heating of the container did not exceed the set value, after each heat input, the temperature of the container, established after the set heat was introduced, was recorded and calculated the temperature increase relative to its initial value, approximate the dependence of the amount of total heat input on the total temperature increase for the reference measure and find the derivative of the obtained dependence, replace the measure with the test sample and perform operations identical to the operations with the reference measure for it, approximate the dependence of the total heat input on the total temperature increase for the test sample and find the derivative of the obtained dependence and calculate the desired The values of specific heat of the test sample, wherein the calculation performed by the relation

Where c _O - specific heat of the test sample, c _M is the specific heat of the reference measure,

- the ratio of derivatives,

- derivative obtained for the test sample,

- the derivative obtained for the reference measure, m _M is the mass of the measure (sample), C _H is the total heat capacity of the heating element, With _D is the total heat capacity of the primary temperature transducer.

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