CN109425630A - A kind of method of quick searching quaternary molten salt system minimum fusing point - Google Patents
A kind of method of quick searching quaternary molten salt system minimum fusing point Download PDFInfo
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- CN109425630A CN109425630A CN201710717942.5A CN201710717942A CN109425630A CN 109425630 A CN109425630 A CN 109425630A CN 201710717942 A CN201710717942 A CN 201710717942A CN 109425630 A CN109425630 A CN 109425630A
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Abstract
The invention discloses a kind of methods for finding quaternary molten salt system minimum fusing point, comprising: 1) draws the constitutional diagram of quaternary molten salt system;2) face for representing ternary molten salt system I is selected, the fusing point on 3 vertex of measuring surface I, each edge inside and face I at least 1 point at least 1 point;3) using above-mentioned fusing point as data point, Software on Drawing isothermal curve is utilized;4) it in low-melting component region, tests in the same way, estimation range is reduced, until finding minimum fusing point a;5) continue to obtain triangle II on positive tetrahedron, repeat aforesaid operations and obtain the minimum fusing point b of triangle II;6) at least 1 step 5) is repeated, then obtains at least one minimum fusing point;7) using above-mentioned minimum fusing point as data point, using Software on Drawing isothermal curve, the fusing point of quaternary molten salt system is prejudged with the changing rule of component, obtains the minimum fusing point of quaternary molten salt system.Method of the invention can be quickly found out the minimum fusing point of quaternary fused salt.
Description
Technical field
The invention belongs to quaternary molten salt system fusing point field of measuring technique, are related to a kind of searching quaternary molten salt system most eutectic
The method of point, especially a kind of method for quickly finding quaternary molten salt system minimum fusing point.
Background technique
Currently, in industrial accumulation of energy and solar energy high temperature heat utilization field, for the heat storage medium that conducts heat with nitric acid molten salt body
Based on system, Molten Binary Salts KNO3-NaNO3System although fusing point with higher, but the blocking of pipeline is easily caused, influence system
Safety, therefore exploitation low melting point fused salt becomes very urgent.Quaternary molten salt system is because have low melting point and good high temperature steady
It is qualitative, it is receive more and more attention.
Currently, unique reliable mode for finding system minimum fusing point is to draw molten salt system phasor.Molten Salt Phase Diagrams are shown
Phase relation of the molten salt system in equilibrium state is macroscopic properties or even the fused salts such as research fused salt transformation temperature, solubility, thermal capacitance
The important foundation of structure, in practical applications and pass accumulation of heat fused salt selection basic foundation.Quaternary Molten Salt Phase Diagrams are drawn at present
During be primarily present following problems:
1. quaternary molten salt system is more complicated with respect to binary system and ternary system, the process for finding minimum fusing point is more multiple
It is miscellaneous.
2. finding the fusing point of polynary molten salt system, need to test a large amount of fused salt formulas, process is slow, not earlier work
Formula corresponding to corresponding minimum fusing point is prejudged, fused salt recipe determination is very blindly.
3. the method for obtaining fusing point by calculating Molten Salt Phase Diagrams, and it is unreliable, it is still necessary to it relies on experimental data and is subject to meter
The verifying of calculation method.
Summary of the invention
For the above-mentioned problems in the prior art, the purpose of the present invention is to provide a kind of searching quaternary molten salt systems
The method of minimum fusing point, especially a kind of method for quickly finding quaternary molten salt system minimum fusing point.Method of the invention passes through
The selection of rational deployment experimental point, and software program models is combined to draw isothermal curve, invalid experimental work amount can be reduced,
It is quickly found out the minimum fusing point of quaternary fused salt;Moreover, can also be searching eutectic for there are the quaternary molten salt systems of eutectic point
Point reduces the scope, i.e., quickly narrows down to eutectic point within the scope of minimum fusing point, and then be conducive to quickly find eutectic point.
In order to achieve the above object, the invention adopts the following technical scheme:
A method of quaternary molten salt system minimum fusing point being found, especially a kind of quickly searching quaternary molten salt system is minimum
The method of fusing point, comprising the following steps:
(1) constitutional diagram of quaternary molten salt system is drawn, the constitutional diagram is denoted as positive tetrahedron ABCD, and (specific name does not limit
It is fixed), then 4 vertex respectively represent 4 kinds of pure materials, and the face of 4 triangles respectively represents 4 kinds of ternary molten salts, inside positive tetrahedron
Point represent quaternary fused salt mixt;
(2) an optional face I from the face of 4 triangles for representing ternary molten salt system measures 3 tops in the face I
Fusing point at point, the fusing point inside the fusing point and face I in each edge at least 1 point at least 1 point;
(3) obtained melting temperature is measured as data point, using Software on Drawing isothermal curve, thus in advance using step (2)
The fusing point of the ternary molten salt system of the representative of face I is sentenced with the changing rule of component;
(4) in low-melting component region, with same procedure described in step (2) and (3), measurement data, with further
Estimation range is reduced, the minimum fusing point a of the ternary molten salt system of the representative of face I is eventually found;
(5) continuation connects on positive tetrahedron at 3 points and obtains triangle II, and the operation for repeating step (2)-(4) obtains triangle
The minimum fusing point b for the ternary molten salt system that shape II represents;
(6) at least 1 step (5) is repeated, at least one triangle and at least one minimum fusing point are obtained;
(7) using the temperature of the obtained at least one minimum fusing point of minimum fusing point a, minimum fusing point b and step (6) as number
Strong point to prejudge the fusing point of quaternary molten salt system with the changing rule of component, and then is obtained using Software on Drawing isothermal curve
The minimum fusing point of quaternary molten salt system.
Below as the optimal technical scheme of the method for the invention, but not as a limitation of the invention, use with
Lower optimal technical scheme can preferably reach the beneficial effect that the present invention claims.
Preferably, quaternary molten salt system includes NaNO3-KNO3-LiNO3-Ca(NO3)2Nitric acid molten salt system, NaNO3-
KNO3-NaNO2-Ca(NO3)2Nitric acid molten salt system or NaNO3-KNO3-Mg(NO3)2-Ca(NO3)2Nitric acid molten salt system, NaCl-
KCl-CaCl2-MgCl2Chlorides molten salts or Na2SO4-K2SO4-Al2(SO4)3-MgSO4It is any in sulfuric acid molten salt system
It is a kind of.But it is not limited to the above-mentioned quaternary molten salt system enumerated, other quaternary molten salt systems commonly used in the art can also be used for this
Invention.
Preferably, the fusing point in step (2) measurement each edge at least 2 points, and this at least 2 points are impartial by the side where it
It is divided into 3 parts.
In all the points measured as the optimal technical scheme of the method for the invention, step (2), the interval of consecutive points is equal
It is equal.In order to reach this effect, following proposal can be used: 3 sides being divided into identical number respectively, cross Along ent
Make the parallel lines on 3 sides and intersection, the intersection point on 3 obtained vertex, Along ent and triangle interior on 3 sides meets
" interval of consecutive points is equal ".
Preferably, the fusing point in step (2) measurement each edge at least four point, and this at least four point is by the side where it
It is divided into 5 parts.
Preferably, the fusing point at least 6 points inside step (2) measuring surface I.
Preferably, step (2) measures the fusing point of 3 apexes;Fusing point in each edge at 4 points, in each edge 4 points by its
The side at place is divided into 5 parts;And the fusing point at 6 point of triangle interior is measured, described 6 points were to make face I at 4 points in each edge
The intersection point being located inside face I that the parallel lines on Atria side obtain.
In the present invention, step (3) and step (7) method using Software on Drawing isothermal curve are not construed as limiting, example
Such as, it can be but not limited to draw isothermal curve using Matlab interpolation method.
Preferably, step (4) the low-melting component region is found by the following method: comparison step (2) measurement obtains
Melting temperature height, the region that three minimum points of melting temperature are formed by connecting be low-melting component region.
As the optimal technical scheme of the method for the invention, step (5) triangle II and step (2) described face I
In parallel.
Preferably, step (6) is repeated 3 times step (5), obtains 3 minimum fusing points, is denoted as minimum fusing point c, minimum fusing point d
With minimum fusing point e;
Preferably, the step (7) are as follows: with minimum fusing point a, minimum fusing point b, minimum fusing point c, minimum fusing point d and minimum
The temperature of fusing point e is as data point, using Software on Drawing isothermal curve, to prejudge the fusing point of quaternary molten salt system with component
Changing rule, and then obtain the minimum fusing point of quaternary molten salt system.
As the optimal technical scheme of the method for the invention, step (5) triangle II is parallel with face I, is repeated 4 times
Step (5) obtains triangle III, triangle IV, triangle V and triangle VI;Moreover, triangle II, triangle III, triangle
IV, triangle V and triangle VI are by the equal equal part of the vertical line in positive tetrahedron vertex to face I.For example, positive tetrahedron represents A-
B-C-D quaternary molten salt system, triangle ABC represent A-B-C ternary molten salt system, then the content of component D is 0 in triangle ABC,
Make the triangle II parallel with triangle ABC, triangle III, triangle IV, triangle V, due to parallel relation, above-mentioned this is several
The content of D is all constant in a triangle.Under preferable case, triangle II, triangle III, triangle IV, triangle can be made
The content sequence equal difference of shape V changes, for example the content of D is made to be respectively 20%, 40%, 60% and 80%.But it does not limit necessary
Equal difference variation, such as can also be respectively 10%, 20%, 30% and 50% etc..
It should be pointed out that other A, B and component C are most when the content of D in the face parallel with face ABC is definite value x%
Big content is (1-x) %.
As the optimal technical scheme of the method for the invention, the method also includes measuring low-melting component areas adjacent
The temperature of unmeasured point, to verify the accuracy for inferring temperature value, if inferring, temperature value is different with the actual value that measurement obtains,
It is corrected as actual value.
Preferably, the method also includes the temperature of unmeasured point near the low temperature line in measurement isothermal curve, with verifying
Infer the accuracy of temperature value, temperature value is different with the actual value that measurement obtains if inferring, is corrected as actual value.
As the further preferred technical solution of the method for the invention, the described method comprises the following steps:
(1) constitutional diagram of quaternary molten salt system is drawn, the constitutional diagram is denoted as positive tetrahedron ABCD, and 4 of positive tetrahedron
Vertex respectively represents 4 kinds of pure materials, and the face of 4 triangles respectively represents 4 kinds of ternary molten salt systems, the point generation inside positive tetrahedron
Table quaternary fused salt mixt;
(2) fusing point of 3 apexes of the face ABC is measured;Fusing point in each edge at 4 points, in each edge 4 points by its
The side at place is divided into 5 parts;And the fusing point inside measuring surface ABC at 6 points, described 6 points were to make face ABC at 4 points in each edge
Three sides parallel lines obtain be located at face ABC inside intersection point;
(3) obtained melting temperature is measured as data point, using Software on Drawing isothermal curve, thus in advance using step (2)
The fusing point of the ternary molten salt system of face ABC representative is sentenced with the changing rule of component;
(4) in low-melting component region, with same procedure described in step (2) and (3), measurement data, with further
Estimation range is reduced, the minimum fusing point a of the ternary molten salt system of face ABC representative is eventually found;
(5) continuation connects on positive tetrahedron at 3 points and obtains the face A ' B ' C ' parallel with face ABC, repeats step (2)-(4)
Operation obtains the minimum fusing point b of the ternary molten salt system of triangle A ' B ' C ' representative;
(6) step (5) are repeated 4 times, 4 faces parallel with face ABC are obtained, and 4 be located in 4 faces are minimum
Fusing point (minimum fusing point c, minimum fusing point d, minimum fusing point e, minimum fusing point f);
The content that 4 faces that face A ' B ' C ' and step (6) obtain respectively correspond D is 20%, 40%, 50%, 60% and
80%;
(7) with the temperature of minimum fusing point a, minimum fusing point b, minimum fusing point c, minimum fusing point d, minimum fusing point e, minimum fusing point f
Degree is used as data point, using Software on Drawing isothermal curve, thus prejudge the fusing point of quaternary molten salt system with the changing rule of component,
And then obtain the minimum fusing point of quaternary molten salt system.
Method of the invention based on theoretical basis be: be not in molten in adjacent area for quaternary molten salt system
Point rise sharply or rapid drawdown.
Compared with the prior art, the invention has the following beneficial effects:
(1) present invention determines low-melting component region, and combine software program models by reasonably selecting experimental formula point
Isothermal curve is drawn, invalid experimental work amount is can be reduced, can quickly find quaternary molten salt system minimum fusing point.
(2) in practical applications, the problems such as not necessarily selecting the fused salt of minimum fusing point to use, further account for cost, selection
Optimal use component ratio is of great significance.Quaternary Molten Salt Phase Diagrams can be made by means of the present invention, it may also be used for commented
The variation of cost and fusing point caused by constituent content changes is estimated, to be conducive to select optimal practical component ratio.
(3) in phasor of the invention, the fusing point of some points is it is known that the fusing point and datum obtained by means of the present invention
According to substantially coincident, this also illustrates the reliabilities of the method for the present invention.
(4) present invention Binding experiment while reasonable prediction is verified, and improves the reliability of experiment.
(5) method of the invention can not only prejudge the minimum fusing point of composite fused salt system, quickly search out quaternary fused salt
The minimum fusing point of system, moreover, can also reduce the scope for there are the quaternary molten salt systems of eutectic point to find eutectic point,
Quickly eutectic point is narrowed down within the scope of minimum fusing point, and then is conducive to quickly find eutectic point.
Detailed description of the invention
Fig. 1 is the constitutional diagram of the quaternary molten salt system of embodiment 1;
Fig. 2 is the constitutional diagram for the ternary molten salt system that the face ABC of embodiment 1 is represented, wherein the point marked is matching for experiment
Fang Dian, that is, the point tested;
Fig. 3 is the constitutional diagram for the system that the face A ' B ' C ' of embodiment 1 is represented, wherein the point marked is the formula point of experiment,
The point tested.
Specific embodiment
To further illustrate the technical scheme of the present invention below with reference to the accompanying drawings and specific embodiments.
Embodiment 1
The present embodiment provides a kind of methods for quickly finding quaternary molten salt system minimum fusing point, comprising the following steps:
(1) constitutional diagram (referring to Fig. 1) of drafting quaternary molten salt system (component A- component B- component C- component D), described group
Component is denoted as positive tetrahedron ABCD, 4 vertex of positive tetrahedron respectively represent 4 kinds of pure materials (i.e. A substance, B substance, C substance and
D substance), the face of 4 triangles respectively represents 4 kinds of ternary molten salt systems (i.e. A-B-D ternary molten salt system, A-C-D ternary molten salt
System, B-C-D ternary molten salt system, A-B-C ternary molten salt system);
(2) fusing point of 3 apexes of measuring surface ABC (constitutional diagram of its ternary molten salt system represented is referring to fig. 2), often
At upper 4 point fusing point (this 4 points by locating for it while be divided into 5 parts) and 6 points of face ABC internal-internal at it is molten
Point (this 6 points were that the parallel lines on three sides that the point in the ABC each edge of face makees face ABC intersect);
(3) obtained melting temperature is measured as data point, using Software on Drawing isothermal curve, thus in advance using step (2)
The fusing point of the ternary molten salt system of face ABC representative is sentenced with the changing rule of component;
(4) in low-melting component region, with same procedure described in step (2) and (3), measurement data, with further
Estimation range is reduced, the minimum fusing point a of the ternary molten salt system of face ABC representative is eventually found;
(5) continuation connects on positive tetrahedron ABCD at 3 points and obtains the face A ' B ' C ' parallel with face ABC, repeats step (2)-
(4) operation obtains the minimum fusing point b of the ternary molten salt system of triangle A ' B ' C ' representative;
(6) step (5) are repeated 4 times, 4 faces parallel with face ABC are obtained, and 4 be located in 4 faces are minimum
Fusing point (minimum fusing point c, minimum fusing point d, minimum fusing point e, minimum fusing point f);
The content that 4 faces that face A ' B ' C ' and step (6) obtain respectively correspond D is 20%, 40%, 50%, 60% and
80%;
(7) with the temperature of minimum fusing point a, minimum fusing point b, minimum fusing point c, minimum fusing point d, minimum fusing point e, minimum fusing point f
Degree is used as data point, using Software on Drawing isothermal curve, thus prejudge the fusing point of quaternary molten salt system with the changing rule of component,
And then obtain the minimum fusing point of quaternary molten salt system.
Embodiment 2
(1) constitutional diagram of quaternary molten salt system (component A- component B- component C- component D) is drawn, the constitutional diagram is denoted as just
Tetrahedron ABCD, 4 vertex of positive tetrahedron respectively represent 4 kinds of pure materials (i.e. A substance, B substance, C substance and D substance), and 4
The face of triangle respectively represents 4 kinds of ternary molten salt systems (i.e. A-B-D ternary molten salt system, A-C-D ternary molten salt system, B-C-D
Ternary molten salt system, A-B-C ternary molten salt system);
(2) fusing point of 3 apexes of measuring surface BCD, (this 4 points are by the side locating for it for the fusing point in each edge at 4 points
Be divided into 5 parts) and face BCD inside fusing point at 6 points (this 6 points were that the point in the BCD each edge of face makees the three of face BCD
What the parallel lines on side intersected);
(3) obtained melting temperature is measured as data point, using Software on Drawing isothermal curve, thus in advance using step (2)
The fusing point of ternary molten salt system is sentenced with the changing rule of component, and is further drawn and obtained the ternary molten salt phasor of face BCD representative;
(4) height of melting temperature obtained by comparing step (2) measurement, the minimum three points connection of melting temperature and
At region be determined as low-melting component region, in the low-melting component region with step (2) and the identical method of step (3),
Test data, the minimum fusing point a to further reduce estimation range, until eventually finding ternary molten salt system;
(5) continuation connects on positive tetrahedron ABCD at 3 points and obtains the face B ' C ' D ' parallel with face BCD, repeats step (2)-
(4) operation obtains the minimum fusing point b of the ternary molten salt system of triangle B ' C ' D ' representative;
(6) step (5) are repeated 3 times, 3 faces parallel with face BCD are obtained, and 3 be located in 3 faces are minimum
Fusing point (minimum fusing point c, minimum fusing point d, minimum fusing point e);
The content that 4 faces that face A ' B ' C ' and step (6) obtain respectively correspond D is 20%, 40%, 60% and 80%;
(7) using minimum fusing point a, minimum fusing point b, minimum fusing point c, minimum fusing point d, minimum fusing point e temperature as data
Point to prejudge the fusing point of quaternary molten salt system with the changing rule of component, and then obtains four using Software on Drawing isothermal curve
The minimum fusing point of first molten salt system.
Embodiment 3
Except the content that 4 faces that face A ' B ' C ' and step (6) obtain respectively correspond D is 10%, 20%, 30%, 50%
Outside 70%, other test methods and condition are same as Example 1.
In the embodiment of the present invention, except in the other positions point at mark point, having can partially look into from Hitec system fused salt
The data of readding obtains, and the melting temperature consulted and the result detected using method of the invention are almost the same, demonstrates this
The reliability of inventive method.
Comparative example 1
Quaternary fused salt (Ca (NO is drawn using conventional method3)2-NaNO3-NaNO2-KNO3) phasor, using conventional method benefit
When being tested with conventional phasor, the selection of formula is more blindly, excessively intensive in the experimental point of some interval selections, results in
Unnecessary test, and some section blank are resulted in, without experimental point, cause the unreliability of experiment.
Embodiment 1-3 and comparative example 1 are compared, it is known that using the method for this patent, it is invalid effectively to reduce
Experimental work amount, the selection of rational deployment experimental point determines low-melting component region, and software program models is combined to draw etc.
Warm curve can be quickly found out the minimum fusing point of quaternary fused salt.
The Applicant declares that the present invention is explained by the above embodiments method detailed of the invention, but the present invention not office
Be limited to above-mentioned method detailed, that is, do not mean that the invention must rely on the above detailed methods to implement.Technical field
Technical staff it will be clearly understood that any improvement in the present invention, equivalence replacement and auxiliary element to each raw material of product of the present invention
Addition, selection of concrete mode etc., all of which fall within the scope of protection and disclosure of the present invention.
Claims (10)
1. a kind of method for finding quaternary molten salt system minimum fusing point, which is characterized in that the described method comprises the following steps:
(1) constitutional diagram of quaternary molten salt system is drawn, the constitutional diagram is denoted as positive tetrahedron ABCD, 4 vertex of positive tetrahedron
4 kinds of pure materials are respectively represented, the face of 4 triangles respectively represents 4 kinds of ternary molten salt systems, and the point inside positive tetrahedron represents four
First fused salt mixt;
(2) an optional face I from the face of 4 triangles for representing ternary molten salt system, measures 3 apexes in the face I
Fusing point, the fusing point inside the fusing point and face I in each edge at least 1 point at least 1 point;
(3) obtained melting temperature is measured as data point, using Software on Drawing isothermal curve, to prejudge face I using step (2)
The fusing point of the ternary molten salt system of representative with component changing rule;
(4) in low-melting component region, with same procedure described in step (2) and (3), measurement data, to further reduce
Estimation range, the minimum fusing point a of the ternary molten salt system until eventually finding the representative of face I;
(5) continuation connects on positive tetrahedron at 3 points and obtains triangle II, and the operation for repeating step (2)-(4) obtains triangle II
The minimum fusing point b of the ternary molten salt system of representative;
(6) at least 1 step (5) is repeated, at least one triangle and at least one minimum fusing point are obtained;
(7) using the temperature of the obtained at least one minimum fusing point of minimum fusing point a, minimum fusing point b and step (6) as data point,
Using Software on Drawing isothermal curve, to prejudge the fusing point of quaternary molten salt system with the changing rule of component, and then quaternary is obtained
The minimum fusing point of molten salt system.
2. the method according to claim 1, wherein the quaternary molten salt system includes NaNO3-KNO3-LiNO3-
Ca(NO3)2Nitric acid molten salt system, NaNO3-KNO3-NaNO2-Ca(NO3)2Nitric acid molten salt system or NaNO3-KNO3-Mg(NO3)2-
Ca(NO3)2Nitric acid molten salt system, NaCl-KCl-CaCl2-MgCl2Chlorides molten salts or Na2SO4-K2SO4-Al2(SO4)3-
MgSO4Any one in sulfuric acid molten salt system.
3. method according to claim 1 or 2, which is characterized in that step (2) measures molten at least 2 points in each edge
Point, and this at least the side where it is divided into 3 parts by 2 points;
Preferably, in all the points of step (2) measurement, the interval of consecutive points is equal;
Preferably, which is characterized in that step (2) measures the fusing point in each edge at least four point, and this at least four point by its
The side at place is divided into 5 parts;
Preferably, the fusing point at least 6 points inside step (2) measuring surface I.
4. method according to claim 1-3, which is characterized in that step (2) measures the fusing point of 3 apexes;
Side where it is divided into 5 parts at 4 points in each edge by the fusing point in each edge at 4 points;And the fusing point at internal 6 points is measured,
Described 6 points be 4 points of Atria sides for making face I in each edge parallel lines obtain be located at face I inside intersection point.
5. method according to claim 1-4, which is characterized in that step (3) and step (7) it is described utilize software
The method for drawing isothermal curve includes: to draw isothermal curve using Matlab interpolation method.
6. method according to claim 1-5, which is characterized in that step (4) the low-melting component region is logical
Following method is crossed to find: the height of melting temperature that comparison step (2) measurement obtains, the minimum three points connection of melting temperature and
At region be low-melting component region.
7. method according to claim 1-6, which is characterized in that step (5) triangle II and step (2)
The face I is parallel.
8. method according to claim 1-7, which is characterized in that step (6) is repeated 3 times step (5), obtains 3
A minimum fusing point is denoted as minimum fusing point c, minimum fusing point d and minimum fusing point e;
Preferably, the step (7) are as follows: with minimum fusing point a, minimum fusing point b, minimum fusing point c, minimum fusing point d and minimum fusing point e
Temperature as data point, using Software on Drawing isothermal curve, to prejudge the fusing point of quaternary molten salt system with the variation of component
Rule, and then obtain the minimum fusing point of quaternary molten salt system.
9. method according to claim 1-8, which is characterized in that step (5) triangle II and face I are flat
Row, is repeated 4 times step (5) and obtains triangle III, triangle IV, triangle V and triangle VI;
Moreover, triangle II, triangle III, triangle IV, triangle V and triangle VI hanging down positive tetrahedron vertex to face I
The equal equal part of line.
10. method according to claim 8 or claim 9, which is characterized in that the method also includes measuring low-melting component region
The temperature of neighbouring unmeasured point, to verify the accuracy for inferring temperature value, if the actual value that deduction temperature value and measurement obtain is not
Together, then it is corrected as actual value;
Preferably, the method also includes the temperature of unmeasured point near the low temperature line in measurement isothermal curve, inferred with verifying
The accuracy of temperature value, if inferring, temperature value is different with the actual value that measurement obtains, and is corrected as actual value.
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