Thermophysical property measurement method and thermophysical property measurement apparatus
10876983 ยท 2020-12-29
Assignee
Inventors
Cpc classification
International classification
G01K3/00
PHYSICS
G01K7/00
PHYSICS
Abstract
Thermophysical property measurement method and apparatus are provided that make it possible to simply and conveniently obtain a highly precise absolute thermoelectric power and thermal conductivity. Embodiments of the present invention provides a thermophysical property measurement method, including a first step of applying a DC voltage or a DC current at both ends of a metal to which a temperature gradient is applied to measure a first temperature at a center of the metal; a second step of applying DC voltages or DC currents of different polarities at both ends of the metal to measure a second temperature at the center of the metal; a third step of calculating a Thomson coefficient of the metal using the first and second temperatures measured in the first and second steps; and a fourth step of calculating at least one of absolute thermoelectric power and thermal conductivity of the metal using the Thomson coefficient calculated in the third step, the third step including: calculating an average value of a difference between the first temperature and the second temperature; calculating an average value of a sum of the first temperature and the second temperature; and dividing a product of a magnitude of a current that flows through the metal, electrical resistance of the metal, and the average value of the difference by the average value of the sum and the difference between the first temperature and the second temperature.
Claims
1. A thermophysical property measurement method, comprising: a first step of applying a DC voltage or a DC current at both ends of a metal to which a temperature gradient is applied to measure a first temperature at a center of the metal; a second step of applying DC voltages or DC currents of different polarities at both ends of the metal to measure a second temperature at the center of the metal; a third step of calculating an average value of a difference between the first temperature and the second temperature; a fourth step of calculating an average value of a sum of the first temperature and the second temperature; a fifth step of calculating a Thomson coefficient of the metal by dividing a product of a magnitude of a current that flows through the metal, electrical resistance of the metal, and the average value of the difference by the average value of the sum and the difference between temperatures at the both ends of the metal; and a sixth step of calculating at least one of absolute thermoelectric power and thermal conductivity of the metal using the Thomson coefficient calculated in the fifth step.
2. A thermophysical property measurement apparatus, comprising: a voltage application unit that applies a DC voltage at both ends of a metal to which a temperature gradient is applied; a temperature measurement unit that measures a first temperature at a center of the metal when the DC voltage is applied by the voltage application unit and measures a second temperature at the center of the metal when DC voltages of different polarities are applied by the voltage application unit; and a thermophysical property calculation unit that, calculates an average value of a difference between the first temperature and the second temperature, calculates an average value of a sum of the first temperature and the second temperature, calculates a Thomson coefficient of the metal by dividing a product of a magnitude of a current that flows through the metal, electrical resistance of the metal, and the average value of the difference by the average value of the sum and the difference between temperatures at the both ends of the metal, and calculates at least one of absolute thermoelectric power and thermal conductivity of the metal using the Thomson coefficient calculated.
3. The thermophysical property measurement apparatus as claimed in claim 2, the voltage application unit further comprising: a first DC power supply that applies the DC voltage of positive polarity to the metal; a second DC power supply that applies the DC voltage of negative polarity to the metal; and a switching unit that selectively connects one of the first DC power supply and the second DC power supply to the both ends of the metal.
4. The thermophysical property measurement apparatus as claimed in claim 2, the thermophysical property measurement apparatus further comprising: two metal blocks that are connected to the both ends of the metal; and a temperature setting unit that sets the two metal blocks to different temperatures.
5. The thermophysical property measurement apparatus as claimed in claim 4, the thermophysical property measurement apparatus further comprising: a thermocouple that measures a temperature of the metal blocks at parts of the metal blocks that are connected to the metal, wherein the temperature setting unit sets the temperature of the metal blocks in accordance with the temperature measured by the thermocouple.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1)
(2)
(3)
(4)
MODE FOR CARRYING OUT THE INVENTION
(5) Below details of embodiments of the present invention are explained with reference to the drawings. In the figures, the same letters indicate identical or corresponding parts.
(6) The absolute value of thermoelectric power of a metal material such as lead, copper, and platinum is a physical property value which is indispensable for a relative measurement method of thermoelectric power that is widely used in the field of physical property measurement. Absolute thermoelectric power uses the state in which the thermoelectric power of the metal material reaches zero and is derived by comparative measurement with a superconductor as a reference material. This method causes a measurable temperature region to be restricted to a temperature which is lower than the superconducting transition temperature, so that it is necessary to derive the absolute thermoelectric power using the Kelvin relations from the measurable Thomson conefficient to expand the measurement temperature region.
(7) Here, thermoelectric power S is generally defined as S=V/T using a voltage V which is produced when a temperature difference T is imparted to a metal or a semiconductor. A measurement value of the thermoelectric power based on this definition more accurately applies to a relative value, or, in other words, a difference in the thermoelectric power, of a metal to be measured and a wiring material (metal), so that a correction which takes into account the thermoelectric power of the wiring material is needed to determine the absolute thermoelectric power of the metal to be measured. More specifically, when the thermoelectric power of the metal to be measured is around several tens of V/K, an effect of such a correction cannot be neglected.
(8) On the other hand, the above-described Thomson coefficient is known to be shown with the following Equation (1):
(9)
(10) In the above equation, T.sub.1 and T.sub.2 are temperatures in units of K at both ends of the metal to be measured when a voltage is applied to the both ends thereof; I is a current in units of A, flowing through the metal; 1 in the denominator is a length in units of m from an end to a midpoint of the metal; is thermal conductivity in units of W/mK of the metal; a is a cross-sectional area in units of m.sup.2 of the metal; and T represents a half of a temperature change in units of K at the midpoint of the metal when a polarity-reversed DC voltage is applied to the metal to be measured. The same applies below.
(11) Then, the absolute thermoelectric power S is calculated with the Kelvin equation, or Equation (2) below:
(12)
(13) In the above Equation, T.sub.0 is the superconducting transition temperature.
(14) Here, from Equation (2), it is seen that the Thomson coefficient that is accurate is required to determine the absolute thermoelectric power S that is highly precise.
(15) Thus, hereinbelow, a thermophysical property measurement method and a thermophysical property measurement apparatus for obtaining the Thomson coefficient that is highly precise through measurement are explained in detail.
(16)
(17) Here, the user interface 51 has functions of accepting operation instructions of a user for the thermophysical property measurement device 50 and displaying generated data for the user to be able to recognize by visual inspection. Moreover, the storage device 53 stores programs to be executed by the operation device 54 and also stores data supplied via the bus 52. Moreover, the operation device 54 performs a predetermined operation on the supplied data by executing the programs stored in advance in the storage device 53 and calculates the below-described Thomson coefficient and absolute thermoelectric power and thermal conductivity. Then, the measurement device 55 measures the thermoelectric properties included in the thin metal wire (below called a metal sample), etc.
(18)
(19) Moreover, as shown in
(20) Then, the metal sample 4, for example, is installed in the measurement device 55, which has the configuration as described above, as a subject to be measured.
(21) Here, the measurement device 55 is designed such as to be able to sufficiently satisfy thermal boundary conditions in thermal analysis. More specifically, the interior of the chamber 1 is made to be a vacuum to suppress heat convection, while the metal blocks 2 and 3 of temperatures T.sub.1 and T.sub.2 are connected to the metal sample 4 to provide a temperature gradient thereto as described above at each end of the metal sample 4. These metal blocks 2 and 3 have the function of a heat bath and the temperature is monitored with the thermocouples 61 and 62 while using a Peltier element, etc., making it possible to realize a precise temperature control.
(22) It is possible to use a tubular furnace which makes ambience control possible as well as to use a stable heater as a method of providing the temperature gradient to the metal sample 4.
(23) Moreover, at the center (origin 0) of the metal sample 4, the thermocouple 5 is mounted to measure the heat absorption and the heat generation that are caused by the Thomson effect. Here, to reduce outflow of heat from the thermocouple 5, a thermocouple whose thermal conductance is sufficiently small is mounted and an output voltage from the thermocouple 5 is measured by a DC voltmeter. The temperature may possibly be measured by using a radiation thermometer in a region of high temperature.
(24) Moreover, between both ends of the metal sample 4, a DC voltage generator 100 which makes it possible to generate DC voltages of different polarities is connected.
(25) Moreover, in accordance with a control signal Ct, the switch 9 selectively connects one of the positive-polarity DC power supply 6 and the negative-polarity DC power supply 7 to both ends of the metal sample 4.
(26)
(27) First, in step S1, the metal block 2 of temperature T.sub.1 and the metal block 3 of temperature T.sub.2 are installed on the respective ends of the metal sample 4. More specifically, the metal blocks 2 and 3 are arranged on the respective ends of the metal sample 4 and, as described above, the metal blocks 2 and 3 are respectively brought to temperatures T.sub.1 and T.sub.2 using the temperature controller 65. The temperature control of the metal blocks 2 and 3 by the temperature controller 65 may be performed at any timing as long as it is before the process begins the below-described step S4.
(28) Next, in step S2, the thermocouple 5 is installed at the origin of the metal sample 4 and, in step S3, the interior of the chamber 1 is made vacuum. Next, in step S4, a DC voltage V.sub.+DC of positive polarity is applied to both ends of the metal sample 4 to measure the temperature T.sub.DC+ at the origin of the metal sample 4 with the thermocouple 5. Next, in step S5, a negative-polarity DC voltage V.sub.DC is applied to both ends of the metal sample 4 to measure the temperature T.sub.DC at the origin of the metal sample 4 with the thermocouple 5.
(29) It goes without saying that applying the DC voltages V.sub.+DC and V.sub.DC at both ends of the metal sample 4 in steps S4 and S5 represents applying a DC current at both ends of the metal sample 4.
(30) Then, in step S6, a Thomson coefficient is calculated using the temperatures T.sub.DC+ and T.sub.DC at the origin of the metal sample 4 and the calculated Thomson coefficient is used to determine an absolute thermoelectric power S of the metal sample 4 in accordance with Equation (2). Below, calculation of the Thomson coefficient in the present step is described in detail.
(31) As shown in
(32) Here, when a DC current I is passed through to the metal sample 4 that meets thermal boundary conditions, the heat transfer equation in the steady state of the metal sample 4 may be expressed as Equation (3):
(33)
(34) In Equation (3), x is a position coordinate in units of m with the midpoint in the metal sample 4 as the origin; T is the temperature in units of K at the position x; is the Thomson coefficient of the metal sample 4 in units of V/K; p is the electrical resistivity of the metal sample 4 in units of /m; p is the circumferential length of the metal sample 4 in units of m; is the Stephan-Boltzmann constant in units of W/m.sup.2K.sup.4; is the emissivity; T.sub.0 is the zero-point temperature of the thermocouple in units of K; and the same applies below.
(35) Then, in Equation (3), the first term on the left-hand side corresponds to heat conduction in the metal sample 4, the second term on the left-hand side corresponds to heat dissipation and heat absorption due to the Thomson effect, the third term on the left-hand side corresponds to the Joule heat generation, the fourth term on the left-hand side corresponds to radiant heat, and the right-hand side reaches zero since analysis in the steady state is conducted.
(36) Dividing both sides by a yields Equation (4):
(37)
(38) Heat loss caused by radiation in the fourth term on the left-hand side of Equation (4) may be neglected as it is not more than 1/100 of the Joule heat in the measurement temperature region. Here, the temperature distribution of the metal sample 4 is to be determined by heat conduction via solid, and boundary conditions do not take into account loss due to heat convection, assuming measurement in the vacuum. Moreover, the temperature distribution in the metal sample 4 is to be sufficiently small and physical property values such as the Thomson coefficient, the electrical conductivity, and the thermal conductivity are to be handled as constants. Under these assumptions, Equation (4) may be simplified as Equation (5) as follows:
(39)
(40) In Equation (5), C is a coefficient related to the Thomson term and D is a coefficient related to the Joule term, and the same applies below.
(41) Here, the coefficient C that is caused by the Thomson effect and the coefficient D that is caused by the Joule heat generation are defined as Equation (6) as follows:
(42)
(43) With reference to
(44)
(45) In Equation (8), K.sub.1 is the thermal conductance of the thermocouple 5, and the same applies below.
(46) The boundary conditions shown in Equation (8) represent the heat loss from the thermocouple 5 that is mounted at the origin of the metal sample 4. Here, when the terms of second degree or higher for the position x are neglected to expand the series, the temperature T.sub.DC in units of K at the midpoint (origin) of the metal sample 4 at the time the DC voltage is applied thereto may be obtained.
(47)
(48) Assuming that the thermal conductance of the metal sample 4 is K.sub.0 (the same applies below), N in Equation (9) becomes (1+K.sub.1/K.sub.0), representing the coefficient of the heat loss via the thermocouple 5 of the metal sample 4 (the same applies below).
(49) In Equation (9), the first term represents a temperature rise caused by the Joule heat generation and the second order Thomson effect, the second term corresponds to the initial temperature at the origin of the metal sample 4, and the third term represents a temperature change caused by the first order Thomson effect.
(50) As shown in Equation (9), heat absorption and heat generation that are caused by the first order Thomson effect depends on the polarity of the DC voltage that is applied to the metal sample 4, whereas heat generation that is caused by the Joule effect and the second order Thomson effect does not depend thereon. Then, setting the temperature distribution when the positive-polarity DC power supply 6 is connected to both ends of the metal sample 4 to pass the DC current through the metal sample 4 in the positive direction of the position coordinate as T.sub.DC+ and setting the temperature distribution when the negative-polarity DC power supply 7 is connected to both ends of the metal sample 4 to pass the DC current through the metal sample 4 in the negative direction of the position coordinate as T.sub.DC (and the same applies below), the below-described Equations (10) and (11) may be obtained from Equation (9)
(51)
(52) Here, the average difference T.sub.DC and the average value T.sub.DC+ of temperatures at the origin of the metal sample 4 are defined as the following Equations (12) and (13).
(53)
(54) Substituting Equations (10) and (11) into Equation (12), the average difference T.sub.DC is shown in the below-described Equation (14). Here, the average difference T.sub.DC may be shown as the first order Thomson effect term since the Joule heat generation term and the second order Thomson effect terms are canceled out.
(55)
(56) On the other hand, when Equations (10) and (11) are substituted into Equation (13), the average value T.sub.DC+ may be shown as the Joule heat generation term and the second order Thomson effect term since the first order Thomson effects are canceled out. Here, in the metal, the product of C and 1 takes a small value and C.sup.21.sup.2, which is the second order Thomson effect term, may be ignored, so that the average value T.sub.DC+ may be approximated as the following Equation (15).
(57)
(58) Moreover, Equation (14) may be transformed as the following Equation (16) using physical quantities such as the temperature difference between both ends of the metal sample 4, current, electrical resistance, the Thomson coefficient, and the Joule heat generation term.
(59)
(60) In Equation (16), R represents the electrical resistance in units of of the metal sample 4, and the same applies below.
(61) Then, substituting Equation (15) into Equation (16) to solve for the Thomson coefficient , the following Equation (17) is obtained.
(62)
(63) Equation (17) includes the average difference T.sub.DC and average value T.sub.DC+, while not including the thermal conductivity, the dimensions, and the heat loss coefficient of the metal sample 4 as variables. Below, calculation of the Thomson coefficient and the absolute thermoelectric power using Equation (17) will be explained in detail with reference to
(64)
(65) Then, as described above, the temperature distribution of the metal sample 4 when the positive-polarity DC voltage V.sub.+DC is applied to both ends of the metal sample 4 in step S4 is shown in a graph 30, while the temperature distribution of the metal sample 4 when the negative-polarity DC voltage V.sub.DC is applied to both ends of the metal sample 4 in step S5 is shown in a graph 20.
(66) Then, by passing the polarity-reversed current as described above, an effect of the Joule heat generated by the current is cancelled out, so that the temperature distribution of the metal sample 4 when there is no such effect as described above is shown with a graph 10, which is positioned between the graph 20 and the graph 30.
(67) Thus, when the DC voltage is applied to the metal sample 4, the temperature at the origin when the effect caused by the current is filtered out may be evaluated as (T.sub.DC++T.sub.DC)/2, or, in other words, as the above-mentioned average value T.sub.DC+. Here, the operation device 54 shown in
(68) Then, in step S6, the operation device 54 executes programs stored in advance in the storage device 53 to calculate the Thomson coefficient , by Equation (17) using the obtained temperatures T.sub.DC+ and T.sub.DC and calculate the absolute thermoelectric power S of the metal sample 4 by Equation (2) using the calculated Thomson coefficient . Here, the operation device 54 may also calculate the thermal conductivity in accordance with the following Equation (18) using the calculated Thomson coefficient .
(69)
(70) The values of the absolute thermoelectric power and the thermal conductivity that are calculated as described above are stored in the storage device 53 and the user interface 51 displays such values for the user of the thermophysical measurement device 50 to be able to recognize by visual inspection in accordance with predetermined operations instructions input by the user.
(71) As described above, a thermoelectric measurement method and a thermoelectric measurement apparatus according to embodiments of the present invention may measure the magnitude of DC current that flows through the metal sample 4 and the electrical resistance and control the polarities of the DC voltage and the DC current that are applied at both ends of the metal sample 4 to measure the temperature of the metal sample 4 to calculate the Thomson coefficient, making it possible to easily and conveniently obtain values of the absolute thermoelectric power and the thermal conductivity.
(72) Moreover, the thermophysical property measurement method and thermophysical property measurement apparatus according to the embodiment of the present invention do not require measurement of the thermal conductivity, the dimensions, and the heat loss coefficient of the metal sample 4, which highly precise measurement is generally said to be difficult in calculating the Thomson coefficient, and do not require taking into account the heat loss due to electromagnetic radiation to the measurement space in accordance with the AC frequency caused by using AC power supply, making it possible to obtain highly precise Thomson coefficient, absolute thermoelectric power and thermal conductivity.
EXPLANATIONS OF REFERENCE
(73) 2, 3 Metal blocks
(74) 4 Thin metal wire (Metal sample)
(75) 5, 61, 62 Thermocouples
(76) 6 Positive-polarity DC power supply
(77) 7 Negative-polarity DC power supply
(78) 9 Switch
(79) 50 Thermophysical property measurement device
(80) 54 Operation device
(81) 55 Measurement device
(82) 63, 64 Heaters for heating
(83) 65 Temperature controller
(84) 100 DC voltage generator