JP4418343B2 - A method for obtaining a calibration straight line for obtaining specific heat at a desired temperature, and a specific heat measuring apparatus. - Google Patents

Description

  The present invention relates to a method for obtaining a calibration straight line for obtaining specific heat at a desired temperature, and a specific heat measuring apparatus, and more particularly, the density of a sample measured at the desired temperature and the temporal change in temperature until the desired temperature of the sample is reached. The present invention relates to a method for obtaining a calibration line for obtaining the specific heat of a sample at the desired temperature based on a thermal time constant obtained from the thermal time constant, and a specific heat measuring apparatus employing this method.

  Measuring the specific heat of a substance is very useful for grasping the thermal characteristics of the substance.

  As is known, specific heat is defined as the amount of heat required to raise the temperature of a unit mass of material by a unit temperature. However, since precise temperature control is required to accurately measure the amount of heat applied to a substance, it takes a lot of time to measure and the apparatus for measuring specific heat is very large and expensive. It has become.

  Accordingly, the applicant of the present application has proposed a specific heat measurement method and a specific heat measurement apparatus capable of measuring specific heat with a very simple configuration and high accuracy in Japanese Patent Application No. 2004-151978 filed earlier. . The measurement principle will be briefly described below with reference to FIGS.

First, as shown in FIG. 6, by introducing the sample S of a first predetermined volume of temperature t _1, the measuring cell 1 arranged in the measuring chamber 10 which has been controlled to a temperature t ₀ which is different from the temperature t _1, the The temperature change is measured by the temperature measuring means 2.

Here, assuming that the temperature of the measurement chamber 10 is maintained at the temperature t ₀ by the temperature control means 4, the temperature of the sample changes (increases) depending on a predetermined time constant with the temperature t ₀ as the end point temperature. (Or descend). The time constant at this time (hereinafter referred to as the thermal time constant) can be obtained by the computing means 3 based on the temperature change amount and the elapsed time obtained from the temperature measuring means 2, and the value depends on the material of the sample. It depends on the value.

  The thermal time constant is closely related to density and specific heat. For substances (gas and liquid) whose density and specific heat are known, the horizontal axis is density x specific heat (product of density and specific heat), and the vertical axis is When graphed as a thermal time constant at the time of temperature rise (fall), linearity is shown as shown in FIG.

That is, if the straight line shown in FIG. 7 (hereinafter referred to as a calibration straight line) is known, the specific heat can be calculated by obtaining the thermal time constant and density values of the sample. The density of the sample can be easily obtained by using, for example, a vibration density meter proposed by the applicant of the present invention in Patent Document 1 described later. Further, the thermal time constant of the sample can be determined based on, for example, a change in the vibration period when the sample at the temperature t ₁ is introduced into the environment at the temperature t _{0 in} the vibration densitometer.
Japanese Patent Publication No. 07-104249

  As described above, at a specific temperature, density × specific heat and thermal time constant are located on the same calibration line regardless of the type of substance. Conversely, the calibration straight line can be obtained by measuring the density and thermal time constant of at least two samples (hereinafter referred to as reference samples) with known specific heat and different values of density × specific heat. .

  Further, since the density and specific heat change depending on the temperature, the calibration straight line has temperature dependency. Therefore, in order to obtain the specific heat by the above-described method, it is necessary to obtain in advance a calibration straight line corresponding to the temperature at which the measurement is performed. That is, in order to measure the specific heat of a sample at a desired temperature, at least two reference samples whose specific heat at the desired temperature is known are required.

  However, as described above, the substances (especially liquids and gases) whose specific heat is known are limited, and it is difficult to prepare a plurality of reference samples whose specific heat is known at a desired temperature. The specific heat cannot be measured by the above-described method.

  The present invention has been proposed in view of the above-described conventional circumstances, and can reduce the number of reference samples required for specific heat measurement and obtain accurate specific heat at an arbitrary temperature. An object of the present invention is to provide a method for obtaining a calibration straight line for possible specific heat measurement.

  The present invention employs the following means in order to achieve the above object. That is, according to the present invention, the specific heat of the sample at the desired temperature is obtained based on the density of the sample measured at the desired temperature and the thermal time constant obtained from the temporal change of the temperature up to the desired temperature of the sample. First, the thermal time constant and density of the first sample whose specific heat at the first temperature different from the desired temperature is known, and the specific heat at the first temperature are obtained. The known thermal time constant and density of the second sample are determined. Then, from these values, a first calibration line indicating the relationship between the density at the first temperature × specific heat (the product of density and specific heat) and the thermal time constant is obtained, and in the first calibration line, A first intercept value indicating a value of density × specific heat when the time constant is zero is calculated.

  Next, based on the thermal time constant and density of the third sample whose specific heat at the desired temperature is known, and the first intercept value, the relationship between the density at the desired temperature × specific heat and the thermal time constant is shown. A calibration straight line at the desired temperature is acquired.

  In the above procedure, instead of the first intercept value, using the correction value of the first intercept value corresponding to the desired temperature obtained by performing predetermined temperature compensation on the first intercept value, A calibration straight line at the desired temperature may be obtained.

  In this way, the specific heat of the sample can be measured in a state where the influence of the temperature dependency of the heat capacity of the measurement cell filled with the sample (due to the material and structure of the measurement cell) is removed.

  The predetermined temperature compensation may be performed based on, for example, the temperature dependence of the material of the measurement cell filled with the sample when acquiring the thermal time constant of the sample. The predetermined temperature compensation can also be performed based on the first intercept value and a second intercept value mentioned below. As for the second intercept value, the thermal time constant and density of the fourth sample whose specific heat at a second temperature different from the first temperature is known, and the specific heat at the second temperature are known. Density x specific heat value when the thermal time constant is zero in the second calibration line showing the relationship between density x specific heat and thermal time constant determined based on the thermal time constant and density of the fifth sample. .

  As described above, by acquiring the first calibration line for the measurement cell (measurement system) in advance, if one reference sample with a known specific heat at the desired temperature can be prepared, the calibration line at the desired temperature can be obtained. The specific heat can be measured.

  In another aspect, the present invention can provide a specific heat measurement apparatus that employs the above-described calibration straight line acquisition method.

  That is, the specific heat measurement apparatus according to the present invention includes a measurement cell filled with a sample, a measurement chamber in which the measurement cell is disposed inside, the inside of which can be controlled to a predetermined temperature, and a time of the temperature of the sample. Temperature measuring means for measuring a change in temperature, and a thermal time constant calculating means for calculating a thermal time constant of the sample based on a temporal change in temperature until the sample reaches a desired temperature.

  In addition, the thermal time constant at the first temperature obtained by the thermal time constant calculating means for the first sample and the second sample whose specific heat is known at the first temperature, respectively, The thermal time constant calculating means for the first storage means for storing the density and specific heat at the first temperature and the third sample whose specific heat is known at a desired temperature different from the first temperature. And a second storage means for storing the obtained thermal time constant at the desired temperature and the density and specific heat of the third sample at the desired temperature.

  Further, in the first calibration straight line showing the relationship between the density at the first temperature × specific heat (product of density and specific heat) and the thermal time constant, which is determined by the information stored in the first storage means, While calculating the 1st intercept value which shows the value of density x specific heat when making a constant zero, based on the 1st intercept value and the information memorized by the 2nd storage means, the desired temperature A calibration straight line calculating means for calculating a calibration straight line at a desired temperature indicating the relationship between the density x specific heat and the thermal time constant is provided.

  Then, based on the calibration straight line of the desired temperature, the specific heat calculation means calculates the specific heat of the sample at the desired temperature.

  The calibration straight line calculating means includes temperature compensating means for obtaining a correction value of the first intercept value corresponding to the desired temperature by performing predetermined temperature compensation on the first intercept value, Instead of the intercept value, the calibration line for the desired temperature may be obtained based on the correction value.

  Further, in the above configuration, the measurement cell can be composed of a thin tube of a vibration type density meter filled with a sample of a predetermined volume, and the period detecting means of the vibration type density meter for detecting the vibration cycle of the thin tube. The temperature measuring means can be used.

  In this case, the density is calculated by the density calculating means of the vibration-type density meter based on the vibration period, and the thermal time constant calculating means is configured to calculate the thermal time constant based on a temporal change of the vibration period. Is calculated.

  According to the present invention, a calibration straight line used for specific heat measurement at a desired temperature can be accurately obtained in a short time by using one reference sample whose specific heat at the desired temperature is known.

  That is, the number of reference samples required for specific heat measurement can be reduced, and accurate specific heat at an arbitrary temperature can be obtained.

  Hereinafter, a calibration straight line acquisition method according to the present invention will be described in detail with reference to the drawings. FIG. 1 is an explanatory diagram for explaining a method for obtaining a calibration line according to the present invention.

As described above, under the condition where the temperature is the same, the value of the density × specific heat of the substance and the thermal time constant when the temperature rises (or falls) show linearity (FIG. 7). That is, if the specific heat at the temperature (first temperature) is known and the density of at least two reference samples (first and second samples) having different values of density × specific heat and the thermal time constant are measured. A point P ₁ and a point P ₂ shown in FIG. Thereby, the equation of the calibration straight line L ₁ at the first temperature can be obtained.

Here, when the thermal time constant is τ, the density is d, and the specific heat is C _P , the calibration straight line L ₁ is expressed by Equation 1. In Equation 1, A and B are constants.

For example, when the first temperature is 300 K, the specific heat C _p , density d, and thermal time constant τ of water and toluene are as shown in Table 1. When the values of A and B in the above equation 1 are calculated based on these values, the equation of the above equation 1 becomes the equation shown in the equation 2.

In the calibration line acquisition method according to the present invention, the point P ₀ at which the thermal time constant τ is zero is used in the calibration line L ₁ thus obtained. That is, as shown in FIG. 1A, a reference sample (third sample) having a known specific heat at the point P ₀ and a temperature at which the specific heat of the sample is desired (hereinafter referred to as a desired temperature) is known. The calibration straight line L ₂ at the desired temperature is obtained based on the point P ₃ determined by measuring the density and the thermal time constant.

Here, the point P ₀ where the thermal time constant τ becomes zero on the calibration line L ₁ will be described.

As shown in FIG. 1A, the point P ₀ belongs to a region where the value of density × specific heat is negative. Density × specific heat is a product of the density of the sample and the specific heat of the sample, and is a physical quantity indicating the heat capacity C ₁ per unit volume of the sample. That is, if this value is negative, it is presumed that it indicates the heat capacity at which the sample does not participate, that is, the heat capacity C ₂ of the measurement system other than the sample. This estimation can be judged to be appropriate from the physical meaning that the thermal time constant τ is zero, that is, “follow the temperature change without delay”. Note that the measurement system other than the sample is a measurement cell or the like that is filled with the sample when measuring the thermal time constant τ, and the part involved in heat conduction when the temperature of the sample rises (or falls). Point to. Therefore, it can be said that the point P ₀ is unique to the measurement system. Of course, as long as the measurement system is made of a substance, it has temperature dependence, so the position of the point P ₀ changes depending on the temperature.

Therefore, in the method for obtaining a calibration straight line according to the present invention, the calibration straight line L ₂ at a desired temperature is obtained by the following procedure. That is, as shown in FIG. 1A, the density x specific heat value (first intercept value) at the point P ₀ at which the thermal time constant τ becomes zero is obtained on the calibration line L ₁ . Then, a predetermined temperature compensation (described later) is performed on the first intercept value as necessary to determine the value of the density × specific heat at the point P ₀ ′ corresponding to the desired temperature, and the point P ₀ ′. And a calibration straight line L ₂ at a predetermined temperature determined by the point P ₃ described above. When the temperature dependency of the heat capacity C ₂ is small, the point P ₀ and the point P ₀ ′ can be regarded as the same point as shown in FIG.

FIG. 2 shows the intercept value obtained from the equation shown in Equation 2, −1.41, the specific heat of water at each temperature of 280K, 290K, 310K, and 320K shown in Table 2, and the density measured at each temperature. using the point P ₃ defined by d and the thermal time constant τ is a diagram illustrating a result of obtaining the calibration straight line L ₂ at each temperature. In this example, temperature compensation for the point P ₀ is not performed.

  2 plots the specific heat of toluene at each temperature shown in Table 3 (reference value), and points based on the density d and thermal time constant τ obtained by the measurement, and Table 3 shows the measured values. 3 shows the specific heat obtained from the calibration straight line at each temperature shown in FIG. 2 based on the density d and the thermal time constant τ obtained by the above.

From FIG. 2 and Table 3, it can be confirmed that the specific heat obtained from the calibration straight line L ₂ obtained by the present invention and the specific heat in the literature agree well.

By the way, the predetermined temperature compensation for the point P ₀ can be performed, for example, based on the temperature dependence of the material of the measurement cell filled with the sample when measuring the thermal time constant τ of the sample. For example, the position of the point P ₀ ′ can be obtained by interpolation based on the temperature dependence of the density of the substance used as the material of the measurement cell × specific heat (document value) as shown in FIG. In addition, the borosilicate glass in Table 4 is the material of the measurement cell used in the example of FIG.

In addition, as another temperature compensation for the point P _0, for example, at a temperature (second temperature) different from the first intercept value, two reference samples (fourth and fourth samples) whose specific heat at the temperature is known. In the calibration straight line (second calibration straight line) obtained using the sample No. 5), a second intercept value indicating a value of density × specific heat when the thermal time constant is zero is obtained, and the second intercept value is obtained. Based on the first intercept value, the correction value of the intercept value at a desired temperature may be obtained by interpolation.

  Note that temperature compensation is not necessarily performed, and may be appropriately performed according to the configuration of the measurement system and the required measurement accuracy of specific heat.

As described above, the point P ₀ is unique to the measurement system, and therefore only needs to be obtained once. Therefore, according to the present invention, when the specific heat is measured at the desired temperature, it is only necessary to measure the density d and the thermal time constant τ of one reference sample whose specific heat is known at the desired temperature. it is possible to obtain a calibration straight line L _2. That is, the number of reference samples required for specific heat measurement can be reduced, and accurate specific heat at an arbitrary temperature can be obtained.

  The method for obtaining the density d and the thermal time constant τ is not particularly limited, and may be obtained by any known method. However, it is necessary to use the same measurement cell for obtaining the thermal time constant τ in all measurements.

  A vibration density meter suitable for measuring these values will be briefly described below. FIG. 3 and FIG. 4 are diagrams showing a vibration type density meter, and each of the above measured values is also acquired by this apparatus.

  As shown in FIG. 3, the vibration type density meter has a U-shaped tubule 1 constituting a measurement cell arranged in a measurement chamber 10, and a liquid or gas sample is placed in a predetermined volume on the U-shaped tubule 1. It can be introduced.

As shown in FIG. 4, when a pulsed drive current S ₂ flows from the pulse generation circuit 13 to the drive coil 31, an external force is applied to the narrow tube 1 via the magnetic body 5 attached to the tip of the thin tube 1. The narrow tube 1 starts to vibrate. The sine wave S ₂ generated in the detection coil 21 in response to this vibration is processed by the period detecting means 15 to obtain the vibration period of the narrow tube 1, and the density calculating means 16 obtains the density of the sample based on this result. It has become. The drive current S ₁ is given at predetermined time intervals while synchronizing with the detected sine wave S ₂ .

For the density d, the driving force described above is applied to the capillary tube 1 (of course, the sample temperature is also maintained at the temperature t ₀ ) while the measuring chamber 10 is maintained at the predetermined temperature t _0. ) And can be obtained from the natural vibration period T _{x at} that time by the equation shown in Equation 3.

Here, the sample is maintained at a temperature t ₁ necessary for storage of the sample, and before being introduced into the narrow tube 1, the temperature t ₁ is different from the temperature t _{0 of the} measurement chamber. It is normal. Therefore, when the sample at the temperature t ₁ is introduced into the measurement chamber 10 maintained at another temperature t ₀ , the temperature changes from the temperature t ₁ to the temperature t ₀ according to the thermal time constant τ. At this time, the vibration cycle also changes with a change in temperature, but the change in the vibration cycle naturally depends on the predetermined thermal time constant τ.

Therefore, the thermal time constant τ defining the temperature change from the temperature t ₁ to the temperature t ₀ can be obtained by measuring the change in the vibration period of the thin tube 1. The thermal time constant τ is defined by the equation shown in Equation 4, and the vibration period of the thin tube 1 varies according to Equation 4.

Also, the oscillation period of the temperature t ₀ is not intended to found only at a temperature t _0, when measured change in the vibration cycle from the sample temperature t ₁ is introduced into the capillary 1 (temperature change), final temperature even without a t ₀ can be obtained by calculation. This calculation method is described in detail in Patent Document 1 described above.

  By the way, by using the vibration type density meter described above, it is possible to configure a specific heat measuring apparatus that employs the above-described method for obtaining a calibration straight line.

  That is, as shown in FIG. 5, this specific heat measurement apparatus uses the thin tube 1 as a measurement cell and, based on the temporal change of the vibration period detected by the period detection means 15, the thermal time constant according to Equation 4. Thermal time constant calculating means 17 for calculating τ is provided. Further, the density calculation means 16 provided in the present apparatus calculates the density of the sample filled in the thin tube 1 according to the equation shown in Equation 3 based on the vibration period detected by the period detection means 15.

  Further, the apparatus is provided with a storage means 18 (first storage means and second storage means), and two specific heats measured at the first temperature and previously measured by the apparatus are known. The thermal time constant and density of the reference sample (first and second samples) are stored together with the specific heat of each sample.

  When measuring the specific heat of a sample at a desired temperature in this apparatus, first, prior to measuring the sample, measure one reference sample (third sample) whose specific heat at the desired temperature is known, The thermal time constant, density, and specific heat of the reference sample are stored in the storage means 18.

Next, the calibration straight line calculation means 19 uses the first time of the first calibration straight line L ₁ based on the thermal time constant, density and specific heat of each reference sample at the first temperature stored in the storage means 18. Calculate the intercept value. The calibration straight line calculating means 19 calculates a calibration straight line L ₂ of the desired temperature based on the first intercept value and the thermal time constant, density and specific heat of the reference sample at the desired temperature stored in the storage means 18. To do.

When the thermal time constant and density of the sample are measured at the desired temperature, the specific heat calculating means 20 calculates the specific heat of the sample based on these measured values and the calibration straight line L ₂ of the desired temperature.

  According to this configuration, as described above, the number of reference samples necessary for specific heat measurement can be reduced, and accurate specific heat at an arbitrary temperature can be obtained.

In the specific heat measurement apparatus, when the above-described temperature correction is performed, the calibration straight line calculating means 19 obtains a correction value for the first intercept value by performing predetermined temperature compensation on the first intercept value. The temperature compensation means 191 may be provided, and the calibration line calculation means 19 may obtain the desired temperature calibration line L ₂ based on the correction value of the first intercept value obtained by the temperature compensation means 191.

  Further, as shown in FIG. 3, the narrow tube 1 (measurement cell) is arranged inside a measurement chamber 10 in which the inside can be controlled to a predetermined temperature, and the data of each temperature described above is stored in the measurement chamber 10. Needless to say, it can be obtained from the temperature control means 4 for controlling the temperature of the liquid crystal. In addition, the density calculating means 16, the thermal time constant calculating means 17, and the calibration straight line calculating means 19 described above can be configured by hardware such as a microprocessor, a program executed on the hardware, or the like. is there.

  The present invention has an effect of reducing the number of reference samples required for specific heat measurement and obtaining an accurate specific heat at an arbitrary temperature, and is useful for specific heat measurement. It is.

Explanatory drawing explaining the principle of this invention. The figure which shows the calibration straight line acquired by this invention. The conceptual diagram of a vibration type density meter. The block diagram which shows the circuit part of a vibration type density meter. The block diagram which shows the circuit part of a specific heat measuring apparatus. Explanatory drawing explaining a thermal time constant. The figure which shows the relationship between a density x specific heat and a thermal time constant.

Explanation of symbols

1 Measurement cell (narrow tube)
2 Temperature measurement means 3 Calculation means 15 Vibration period detection means (temperature measurement means)
16 Density calculation means 17 Thermal time constant calculation means 18 Storage means (first and second storage means)
19 Calibration straight line calculation means 20 Specific heat calculation means L ₁ Calibration straight line at the first temperature L ₂ Calibration straight line at the desired temperature P ₀ First intercept

Claims (7)

Calibration straight line used to determine the specific heat of the sample at the desired temperature based on the density of the sample measured at the desired temperature and the thermal time constant obtained from the temporal change in temperature up to the desired temperature of the sample The acquisition method of
Based on the thermal time constant and density of a first sample whose specific heat at a first temperature different from the desired temperature is known, and the thermal time constant and density of a second sample whose specific heat at a first temperature is known Obtaining a first calibration line indicating the relationship between density x specific heat at the first temperature (product of density and specific heat) and a thermal time constant;
Calculating a first intercept value indicating a value of density × specific heat when the thermal time constant is set to zero in the first calibration line;
The desired temperature indicating the relationship between density at the desired temperature × specific heat and the thermal time constant based on the thermal time constant and density of the third sample whose specific heat at the desired temperature is known and the first intercept value. Obtaining a calibration straight line for
A method for obtaining a calibration straight line for obtaining specific heat at a desired temperature.   Instead of the first intercept value, using the correction value of the first intercept value corresponding to the desired temperature obtained by performing predetermined temperature compensation on the first intercept value, the desired temperature The method for obtaining a calibration line for obtaining specific heat at a desired temperature according to claim 1, wherein the calibration line is obtained.   3. The specific heat at a desired temperature according to claim 2, wherein the predetermined temperature compensation is performed based on the temperature dependence of the material of the measurement cell filled with the sample when acquiring the thermal time constant of the sample. To obtain a calibration straight line for   The predetermined temperature compensation is such that the thermal time constant and density of the fourth sample whose specific heat at the second temperature is known, and the thermal time constant and density of the fifth sample whose specific heat at the second temperature are known. In the second calibration line showing the relationship between density × specific heat and thermal time constant determined based on the above, the second intercept value showing the value of density × specific heat when the thermal time constant is zero, and the first The method for obtaining a calibration straight line for obtaining specific heat at a desired temperature according to claim 2, which is performed on the basis of the intercept value. A measurement cell filled with a sample;
The measurement cell is arranged inside, and a measurement chamber capable of controlling the inside to a predetermined temperature;
Temperature measuring means for measuring a temporal change in the temperature of the sample;
A thermal time constant calculating means for calculating a thermal time constant of the sample based on a temporal change in temperature until the sample reaches a desired temperature;
The thermal time constant at the first temperature obtained by the thermal time constant calculating means for the first sample and the second sample whose specific heats are respectively known at the first temperature, and the first time of each sample. First storage means for storing density and specific heat at a temperature of 1,
The thermal time constant at the desired temperature obtained by the thermal time constant calculating means for the third sample whose specific heat is known at a desired temperature different from the first temperature, and the third sample Second storage means for storing density and specific heat at a desired temperature;
The thermal time constant is determined on the first calibration line indicating the relationship between the density at the first temperature x specific heat (product of density and specific heat) and the thermal time constant, which is determined by the information stored in the first storage means. A first intercept value indicating a value of density x specific heat when zero is calculated, and at the desired temperature based on the first intercept value and information stored in the second storage means A calibration straight line calculation means for calculating a calibration straight line at a desired temperature indicating the relationship between density × specific heat and thermal time constant;
Specific heat calculation means for calculating the specific heat of the sample at the desired temperature based on the calibration line of the desired temperature;
A specific heat measuring apparatus comprising:   The calibration straight line calculation means includes temperature compensation means for obtaining a correction value of the first intercept value corresponding to the desired temperature by performing predetermined temperature compensation on the first intercept value, and the first intercept value 6. The specific heat measuring apparatus according to claim 5, wherein a calibration straight line of the desired temperature is obtained based on the correction value instead of the intercept value. The measuring cell is a capillary tube of a vibrating densimeter filled with a predetermined volume of sample,
The temperature measuring means detects the vibration period of the capillary tube;
The density is calculated by the density calculating means of the vibratory densimeter based on the vibration period, and the thermal time constant calculating means calculates the thermal time constant based on a temporal change of the vibration period. The specific heat measuring device according to claim 5 or 6.

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