In-situ measurement method and system for density Virie coefficient and characteristic thermodynamic temperature thereof

Abstract

The invention relates to the field of thermophysical property measurement, and provides an in-situ measurement method and system for a density Virie coefficient and a characteristic thermodynamic temperature thereof, and the measurement method comprises the steps: S1, carrying out the in-situ measurement of the density Virie coefficient and the thermodynamic temperature: S10, carrying out the vacuum pumping of the measurement system, measuring the resonant frequency of a resonator in a vacuum state at a preset temperature, introducing a gas to be measured, and measuring the resonant frequency of the resonator under a preset pressure and a preset temperature; s11, according to the resonant frequency measurement result, calculating the experimental refractive index of the gas, and calculating the theoretical refractive index of the gas through a Virie state equation and a dielectric Virie theory; s12, iteratively solving to obtain experimental values Bexp of the thermodynamic temperature T and the density Virie coefficient; and S2, carrying out in-situ fitting or in-situ iteration on the characteristic temperature. Aiming at the problems of complex flow, poor measurement accuracy and the like of an existing measurement method, high-precision in-situ measurement of the gas density Virie coefficient and the characteristic temperature of the gas density Virie coefficient is realized.

Description

Technical Field

[0001] This invention relates to the field of thermophysical property measurement technology, and in particular to an in-situ measurement method and system for the density virial coefficient and its characteristic thermodynamic temperature. Background Technology

[0002] The density virial coefficient is a key thermophysical parameter describing the deviation of real gas properties from ideal gas behavior, and plays a vital role in establishing high-precision gas equations of state and developing theories of intermolecular interactions.

[0003] The virial equation of state is usually expressed as:

[0004] In formula (1), Z It is the compression factor. P It's pressure. T It is thermodynamic temperature. ρ It is the density of the medium. R It is the universal gas constant, coefficient B ( T ), C ( T The coefficients are the second and third density virial coefficients, which are functions of temperature and characterize the interactions between bimolecules and tripolecules, respectively.

[0005] On the curve of density virial coefficient versus thermodynamic temperature, there exist some thermodynamic temperatures with special physical significance, which this invention defines as "characteristic thermodynamic temperatures" or simply "characteristic temperatures." The first type of density virial coefficient characteristic temperature refers to the temperature corresponding to a density virial coefficient of zero. The second type of density virial coefficient... B ( T Taking (e.g., its first type of characteristic temperature) B ( T )=0 is the famous Boyle temperature (denoted as ) T B At this temperature, the attraction and repulsion effects between molecules reach macroscopic equilibrium, and the gas exhibits near-ideal gas behavior under low pressure. The characteristic temperature of the second-type density virial coefficient, also known as the reversal temperature (denoted as ), is... T R The virial coefficient (d) refers to the temperature at which the first derivative of the virial coefficient with respect to temperature is zero. B ( T ) / d T =0, which corresponds to the temperature point where intermolecular interactions are strongest or weakest. These characteristic temperatures are intrinsic properties of gases and can serve as potential temperature standard fixed points for calibrating and verifying the accuracy of temperature measurements, or for assessing the reliability of ab initio virial coefficients in quantum mechanics.

[0006] However, there are currently many challenges in accurately measuring these density virial coefficients and characteristic temperatures. Traditional methods such as PVT Measurement methods, such as gas phase sound velocity measurement, have problems such as complex measurement procedures and low accuracy. Furthermore, it is difficult to achieve simultaneous in-situ measurement of thermodynamic temperature and density virial coefficient. Most characteristic temperature values ​​rely on theoretical calculations or extrapolation based on non-in-situ measurement data ("non-in-situ" refers to temperatures calibrated by other devices on the International Temperature Scale or thermodynamic temperature), making it difficult to guarantee their accuracy and reliability.

[0007] Therefore, there is an urgent need to develop an experimental method and apparatus that can accurately and in situ measure the density virial coefficient and its first and second type characteristic temperatures. Summary of the Invention

[0008] This invention provides an in-situ measurement method and system for the density virial coefficient and its characteristic thermodynamic temperature, aiming to achieve high-precision in-situ experimental measurement of the density virial coefficient of a gas and its first and second type characteristic temperatures.

[0009] This invention provides an in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature, comprising the following steps: S1. In-situ measurement of density virial coefficient and thermodynamic temperature: S10. Evacuate the measurement system and measure the resonant frequency of the resonator under vacuum at a preset temperature. Then introduce the gas to be measured and measure the resonant frequency of the resonator at a preset pressure and preset temperature. S11. Based on the resonant frequency measurement results, calculate the experimental refractive index of the gas, and calculate the theoretical refractive index of the gas using the virial equation of state and dielectric virial theory. S12. The thermodynamic temperature is obtained by iterative solution. T Experimental values ​​of density virial coefficient B exp ; S2. Perform in-situ fitting or in-situ iteration of the characteristic temperature.

[0010] According to the in-situ measurement method of density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, step S2, when performing in-situ fitting of the characteristic temperature, includes the following steps: S20. Repeat step S1 at multiple different temperature points to obtain a series of data points. T , B exp The functional relationship is obtained by fitting. B exp =f ( T ); S21, Solve f (T )=0 yields the experimental value of the first type of characteristic temperature, and / or, solves d f ( T ) / d T =0 yields the experimental value of the second type of characteristic temperature.

[0011] According to the in-situ measurement method of density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, when the density virial coefficient and thermodynamic temperature are measured by the multi-isotherm method, the gas refractive index measurement data under multiple isotherms are simultaneously fitted, and the density virial coefficient at different temperatures is fitted as a function of temperature, wherein the coefficient to be fitted in the function is not greater than the number of measurement temperature points.

[0012] According to the in-situ measurement method of density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, step S2, when performing in-situ iteration of the characteristic temperature, includes the following steps: The temperature change step size is calculated using Newton's iterative formula. After adjusting the temperature control, the measurement and iteration are repeated until the absolute deviation between two adjacent characteristic temperatures meets the convergence condition.

[0013] According to the in-situ measurement method of density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, the gas to be measured is one or more of helium, nitrogen, argon, hydrogen, and methane, or a mixture of helium-3 and helium-4.

[0014] According to the in-situ measurement method of density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, the operating temperature of the measurement system includes room temperature, low temperature zone and extremely low temperature zone, and the operating pressure of the measurement system includes low pressure zone, medium pressure zone and high pressure zone.

[0015] The present invention also provides an in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature, which can be applied to the in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature as described above. The measurement system includes: The measuring unit has a sealed working chamber, in which a resonator and a standard reference thermometer are installed; A cryogenic control unit, including a refrigerator, is used to provide a cryogenic environment for the measurement system; A vacuum unit is used to provide a vacuum environment for the resonator; A gas supply unit is used to provide the gas to be measured to the resonator and control the gas pressure. The data processing and control unit is used to perform corresponding calculations based on the measurement data.

[0016] According to the in-situ measurement system for density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, the measurement unit further includes a primary radiation shield and a secondary radiation shield disposed inside the primary radiation shield, the resonator being disposed inside the secondary radiation shield and fixed by a mounting bracket.

[0017] According to the in-situ measurement system for density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, the resonator is a microwave resonator, and the resonator is provided with a microwave antenna to be connected to a microwave cable through the microwave antenna. The microwave cable passes through a feedthrough component and exits each level of radiation shielding screen.

[0018] According to the in-situ measurement system for density virial coefficient and its characteristic thermodynamic temperature provided by the present invention, the gas supply unit includes a gas cylinder and a gas supply pipe. One end of the gas supply pipe is connected to the gas cylinder, and the other end extends into the working chamber and is connected to the cavity of the resonator. The gas supply pipe located in the measurement unit extends in a zigzag or spiral shape.

[0019] The in-situ measurement method and system for density virial coefficient and its characteristic thermodynamic temperature provided by this invention utilizes the principle of gas refractive index thermometry to transform the measurement of thermodynamic quantities into a high-precision measurement of resonant frequencies. Combined with the single isotherm method or multiple isotherm method proposed in this invention, the accuracy and reliability of the in-situ measurement results of thermodynamic temperature and density virial coefficient are ensured.

[0020] This invention achieves simultaneous in-situ measurement of thermodynamic temperature and density virial coefficient, avoiding systematic errors introduced by non-in-situ measurements. Through measurement, calculation, and verification, it ensures that the final characteristic temperature value is a true physical quantity directly verified by in-situ experiments, rather than an extrapolated or estimated value. The entire measurement process is highly automated, faster than traditional methods, effectively shortening the experimental cycle and enabling iterative verification. It is adaptable to different temperature zones, pressure ranges, and various gases (pure gas, mixed gas), making it suitable for a wide range of applications. The measured characteristic temperature can serve as a new thermodynamic temperature fixed point, which can be used for comparison and verification of gas reference temperature measurement methods, calibration of high-precision temperature sensors, and reliability assessment of quantum mechanical ab initio virial coefficient calculations. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1This is a schematic flowchart of the in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature provided by the present invention.

[0023] Figure 2 This is a schematic diagram of the in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature provided by the present invention.

[0024] Figure 3 This is a schematic diagram of fitting the first type of characteristic temperature provided by the present invention.

[0025] Figure 4 This is a schematic diagram of the in-situ iteration of the first type of characteristic temperature provided by the present invention.

[0026] Figure 5 This is a schematic diagram of simultaneous in-situ measurement of density virial coefficient and thermodynamic temperature provided by the present invention.

[0027] Figure 6 This is a schematic diagram comparing the experimental and theoretical values ​​of the characteristic thermodynamic temperature of Helium-4 provided by the present invention.

[0028] Figure 7 This is a schematic diagram comparing the experimental and theoretical values ​​of the second density virial coefficient of helium-4 provided by the present invention.

[0029] Figure label: 100. Resonator; 101. Standard reference thermometer; 102. Refrigeration unit; 103. Primary radiation shield; 104. Secondary radiation shield; 105. Working chamber; 106. Mounting bracket; 107. Upper antenna; 108. Lower antenna; 109. Microwave cable; 110. Feedthrough component; 111. Vector network analyzer; 112. Computer; 113. Time standard; 114. Gas cylinder; 115. Gas supply pipe; 116. Regulating valve; 117. Vacuum pump; 118. Pressure controller; 119. Pressure gauge. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0031] In the description of this invention, it should be understood that the terms "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0032] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0033] In this invention, unless otherwise expressly specified and limited, the first feature "on" or "below" the second feature may be in direct contact with the first and second features, or indirect contact through an intermediate medium. In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0034] like Figure 1 As shown, the present invention provides an in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature, comprising the following steps: S1. In-situ measurement of density virial coefficient and thermodynamic temperature: S10. Evacuate the measurement system and measure the resonant frequency of the resonator under vacuum at a preset temperature. Then introduce the gas to be measured and measure the resonant frequency of the resonator at a preset pressure and preset temperature. S11. Based on the resonant frequency measurement results, calculate the experimental refractive index of the gas, and calculate the theoretical refractive index of the gas using the virial equation of state and dielectric virial theory. S12. The thermodynamic temperature is obtained by iterative solution. T Experimental values ​​of density virial coefficient B exp ; S2. Perform in-situ fitting or in-situ iteration of the characteristic temperature.

[0035] More specifically, in some embodiments, when step S2 performs in-situ fitting of the characteristic temperature, it includes the following steps: S20. Repeat step S1 at multiple different temperature points to obtain a series of data points. T , B exp The functional relationship is obtained by fitting. B exp =f ( T ); S21, Solve f ( T )=0 yields the experimental value of the first type of characteristic temperature, and / or, solves d f ( T ) / d T =0 yields the experimental value of the second type of characteristic temperature.

[0036] In other embodiments, when step S2 performs in-situ iteration of the characteristic temperature, the temperature change step size is calculated using Newton's iteration formula. The temperature control temperature is adjusted, and the measurement iteration is repeated until the absolute deviation between two adjacent characteristic temperatures meets the convergence condition. Based on the obtained experimental value of the characteristic temperature, the measurement system temperature is controlled to the experimental value of the characteristic temperature, and step S1 is repeated for in-situ verification. If the measured... B exp If its derivative is not zero, the new measurement data is incorporated into the fit and iteratively corrected until the zero value matches the experimental result within the uncertainty range.

[0037] To better understand the measurement method of the present invention, a detailed description is provided below in conjunction with the measurement system.

[0038] like Figure 2 As shown, the in-situ measurement system for density virial coefficient and its characteristic thermodynamic temperature includes: a measurement unit having a sealed working chamber 105, wherein a resonator 100 and a standard reference thermometer 101 are provided in the working chamber 105; A low-temperature control unit, including a refrigerator 102, is used to provide a low-temperature environment for the measurement system; A vacuum unit is used to provide a vacuum environment for the resonator 100; A gas supply unit is used to provide the gas to be measured to the resonator 100 and control the gas pressure; The data processing and control unit is used to perform corresponding calculations based on the measurement data.

[0039] Specifically, in some embodiments, a secondary radiation shield 104 and a primary radiation shield 103 are sequentially provided on the outside of the working cavity 105. The resonator 100 is disposed inside the secondary radiation shield 104. The primary radiation shield 103 provides a high-vacuum thermal insulation environment, significantly reducing the interference of external ambient temperature on the internal measurement area through heat conduction and convection, creating a constant temperature foundation for the resonator 100, and avoiding temperature fluctuations from affecting the accuracy of microwave resonant frequency measurement. The secondary radiation shield 104 further blocks external radiant heat input, reducing the temperature non-uniformity of the measurement area caused by radiant heat leakage, making the temperature field around the resonator 100 more uniform and stable, and ensuring that the gas refractive index measurement is not affected by local temperature deviations. Figure 2 As shown, a mounting bracket 106 is provided inside the working cavity 105 to fix the resonator 100, achieving a stable positioning of the resonator 100. This also reduces heat conduction between the resonator 100 and surrounding components, ensuring that the resonator 100 remains in a stable physical state and temperature environment. This provides a reliable hardware foundation for frequency measurement, refractive index calculation, and subsequent iterative solutions. To ensure temperature measurement accuracy, a standard reference thermometer 101 can be attached to the outer wall of the resonator 100 or inserted into the resonator 100, ensuring that the measured temperature is synchronized with the gas temperature inside the resonator 100, thus guaranteeing measurement accuracy.

[0040] The refrigeration unit 102 is located outside the primary radiation shield 103. The cold head of the refrigeration unit 102 can be located between the primary radiation shield 103 and the secondary radiation shield 104, and between the secondary radiation shield 104 and the working chamber 105, so as to provide the working chamber 105 with the required temperature.

[0041] Furthermore, the resonator 100 is, for example, a microwave resonator, and the resonator 100 is equipped with a microwave antenna, which includes, for example, an upper antenna 107 and a lower antenna 108, respectively connected to the upper and lower ends of the resonator 100. The microwave antenna is connected to a microwave cable 109, and the microwave cable 109 passes through a feedthrough 110 and exits the secondary radiation shield 104 and the primary radiation shield 103. Figure 2 As shown, the microwave cable 109 extending externally is connected to the vector network analyzer 111, which is also connected to the computer 112 and the time standard 113, which is also connected to the computer 112. The vector network analyzer 111, the time standard 113, and the computer 112 provide relevant measurements, calculations, and control.

[0042] Furthermore, such as Figure 2As shown, the gas supply unit includes a gas cylinder 114 and a gas supply pipe 115. One end of the gas supply pipe 115 is connected to the gas cylinder 114, and the other end extends into the working chamber and connects to the cavity of the resonator 100. The external gas supply pipe 115 is also equipped with a regulating valve 116, a vacuum pump 117, a pressure controller 118, and a pressure gauge 119 to achieve vacuuming, introduce the gas to be measured into the resonator 100, and control the gas pressure.

[0043] Optionally, the gas supply pipe 115 extending into the primary radiation shield 103 and the secondary radiation shield 104 can be zigzag or spiral, or a combination of both. The zigzag or spiral structure extends the heat exchange path of the gas supply pipe 115 within the measurement unit, allowing the introduced gas to fully exchange heat with the working chamber, quickly reaching the same temperature as the resonator 100. This avoids localized temperature fluctuations caused by low-temperature / high-temperature gases directly entering the resonator 100, ensuring temperature consistency in gas refractive index measurement. The zigzag or spiral structure allows for a reasonable layout within a limited space, reducing pipe space occupation, lowering gas flow velocity, and minimizing the impact of airflow disturbances on the gas density uniformity within the resonator 100, providing a stable gas state basis for density virial coefficient calculation.

[0044] refer to Figure 2 , Figure 3 and Figure 5 In a specific embodiment, the in-situ measurement method of the density virial coefficient and its characteristic thermodynamic temperature is implemented as follows: Step S1: In-situ measurement of density virial coefficient and thermodynamic temperature using a single isotherm method: (1) such as Figure 2 The entire gas supply pipe 115 and the inside of the resonator 100 are evacuated by vacuum pump 117, achieving a vacuum level better than 10. -5 Pa; Start the refrigerator 102 to cool the measuring unit to the starting point of the target temperature range, for example, 15 K.

[0045] (2) After the temperature stabilizes, the accurate temperature is measured by the standard reference thermometer 101. T 1. The vector network analyzer 111, controlled by computer 112, measures the resonant frequency of resonator 100 in vacuum state through microwave cable 109, feedthrough 110, and microwave antenna, under the condition that a stable time base signal is provided by time standard 113, and records it as follows: f 0,i (Where i takes the values ​​1, 2, 3, 4, ..., corresponding to the subscripts of the measured temperatures mentioned above).

[0046] (3) Turn off the vacuum pump 117, open the regulating valve 116, and introduce high-purity helium from the gas cylinder 114 into the resonator 100. Use the pressure controller 118 to precisely control and stabilize the pressure in the resonator 100 at the preset value. P j The pressure is monitored by pressure gauge 119. Wait for the temperature to stabilize again. T At time 1, the vector network analyzer 111 again measured the microwave resonant frequency of the resonator 100 in the gas and recorded it as follows: f p,i,j (The meaning of i is the same as above).

[0047] (4) The following calculations are performed automatically by the data processing program in the computer: Based on the results of vacuum and pressurized microwave resonant frequency measurements, the refractive index of the experimental gas under this state is calculated using formula (2). n exp,j :

[0048] in, k T (T i ) It is the resonator material (such as oxygen-free copper) at temperature T i The isothermal compressibility coefficient.

[0049] (5) Assume the initial thermodynamic temperature T 0 and density virial coefficient B 0 or ( B 0 ,C 0) or ( B 0 ,C 0 ,D 0), the pressure is calculated using the gas virial equation of state, i.e., formula (1). P j Corresponding gas density ρ j According to the dielectric virial theory, the theoretical value of the gas refractive index can be obtained by solving formula (3). n theo,j : (3) in, A μ is the magnetic virial coefficient of the gas; A ε , B ε (T i ) , C ε(T i ) The parameters are the dielectric virial coefficients of the gas.

[0050] (6) For a single isotherm, with the objective function or ,in w As the weighting coefficients, the LM algorithm is used to solve for the thermodynamic temperature in situ. T i and the target density virial coefficient (such as the second density virial coefficient) B ( T i Experimental values ​​of )) B exp .

[0051] Step S2: In-situ fitting measurement of the characteristic temperature of the density virial coefficient: (7) Set the system temperature to the new temperature point. T 2, T 3, ..., T i Repeat steps (1)-(6) above at each temperature point to obtain a series of data points. T i , B exp ( T i The least squares method is used to fit these data points into a polynomial or other form of functional relationship. B exp = f ( T ).

[0052] (8) Solve the equation f ( T )=0, thus obtaining the experimental value of the first type of characteristic temperature. T B,exp For helium-4 gas, this value is around 23.187 K.

[0053] (9) Based on the uncertainty of each independent variable parameter (such as frequency and pressure) during the measurement process, according to the difference principle, by repeatedly calculating steps (6)-(8), the change of dependent variable caused by the uncertainty of each independent variable parameter is obtained. Then, by adopting the error propagation principle, the measurement uncertainty of thermodynamic temperature, density virial coefficient and characteristic temperature can be determined.

[0054] The process of measuring the second type of characteristic temperature is similar, except that the equation to be solved in step (8) becomes d. f ( T ) / d T =0.

[0055] This invention relates to an in-situ gas density measurement method based on gas refractive index, which can be used for other methods that rely on... P-ρ-T Precise measurement of the fundamental physical parameters of the relationship, such as molar electric susceptibility, molar magnetic susceptibility, and universal gas constant. R wait.

[0056] It is understood that, in addition to the single isotherm measurement method described above, this invention can also apply the multi-isotherm method. When using the multi-isotherm method, gas refractive index measurement data from multiple isotherms are simultaneously fitted, and the density virial coefficient at different temperatures is fitted as a function of temperature. In this function, the coefficient to be fitted is no greater than the number of measurement temperature points. This can achieve more accurate in-situ measurement of thermodynamic temperature and density virial coefficient, as well as determination of characteristic temperatures. It can simplify the measurement process, improve efficiency, enhance measurement accuracy, and strengthen the stability of parameter solving.

[0057] In other embodiments, when performing in-situ iteration of the characteristic temperature in step S2, combined with Figure 4 Taking the Boyle temperature as an example, determine the ( ) at two adjacent temperatures. T 1, B 1) ( , ) data, of which That is Figure 4 In T 1+ h ,and T 1. A temperature difference of 1 mK is used to calculate the temperature change step size using Newton's iterative formula. Adjust and control the temperature to the new value. T 2= T 1+Δ T 1. Repeat the in-situ measurement iteration of the single isotherm method described above to obtain... T 3. T 4…. T n until the absolute deviation of two adjacent characteristic temperatures |Δ T |Satisfies the convergence condition (e.g., within the temperature control stability range, or less than 1 μK).

[0058] Furthermore, to optimize the verification, the characteristic temperature that meets the convergence condition can be used to check... B exp If the uncertainty value approaches zero within the experimental uncertainty range, and if not, continue iterating until the verification condition is met. This double verification ensures the reliability of the results.

[0059] It is understood that in the in-situ measurement method and system for the density virial coefficient and its characteristic thermodynamic temperature of this invention, the gas to be measured can be one or more of helium, nitrogen, argon, hydrogen, and methane, or a mixture of helium-3 and helium-4. To meet the measurement performance under specific conditions, the measurement system can operate in different temperature ranges such as room temperature, low temperature, and extremely low temperature, as well as different pressure ranges such as low pressure, medium pressure, and high pressure. It can be used to accurately measure fundamental physical constants such as molar polarizability and gas constant, and has broad application prospects. The resonator in the measurement unit can be of different shapes (such as cylindrical, spherical, etc.) or made of different materials, and can also be an optical resonant cavity, suitable for different microwave or optical measurement modes.

[0060] The characteristic temperature measured by this invention can be used as a new thermodynamic temperature fixed point, and can be used for comparison and verification of gas reference temperature measurement methods (e.g.) Figure 6 ), verification of high-precision temperature sensors, reliability assessment of quantum mechanical ab initio virial coefficients (such as...), Figure 7 ),in, Figure 6 This demonstrates the first-type characteristic temperatures corresponding to the second, third, fourth, and fifth density virial coefficients of Helium-4. T B , T C , T D , T E Comparison with experimental results Figure 7 The results show a comparison between in-situ experimental results of the second density virial coefficient of helium-4 and ab initio calculations using quantum mechanics to assess the reliability of the calculated values.

[0061] The in-situ measurement method and system for density virial coefficient and its characteristic thermodynamic temperature provided by this invention, by means of the gas refractive index thermometry principle, transforms the measurement of thermodynamic quantities into a high-precision measurement of resonant frequencies, and combined with the "single isotherm method" or "multiple isotherm method" proposed in this invention, ensures the accuracy and reliability of the in-situ measurement results of thermodynamic temperature and density virial coefficient.

[0062] This method achieves simultaneous in-situ measurement of thermodynamic temperature and density virial coefficient, avoiding systematic errors introduced by non-in-situ measurements. Through measurement, calculation, and verification, it ensures that the final characteristic temperature value is a true physical quantity directly verified by in-situ experiments, rather than an extrapolated or estimated value. The entire measurement process is highly automated, faster than traditional methods, and can effectively shorten the experimental cycle, enabling iterative verification. It is adaptable to different temperature zones, pressure ranges, and various gases (pure gas, mixed gas), making it suitable for a wide range of scenarios. The measured characteristic temperature can serve as a new thermodynamic temperature fixed point, which can be used for comparison and verification of gas reference temperature measurement methods, calibration of high-precision temperature sensors, and reliability assessment of quantum mechanical ab initio virial coefficient calculations.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature, characterized in that, Includes the following steps: S1. In-situ measurement of density virial coefficient and thermodynamic temperature: S10. Evacuate the measurement system and measure the resonant frequency of the resonator under vacuum at a preset temperature. Then introduce the gas to be measured and measure the resonant frequency of the resonator at a preset pressure and preset temperature. S11. Based on the resonant frequency measurement results, calculate the experimental refractive index of the gas, and calculate the theoretical refractive index of the gas using the virial equation of state and dielectric virial theory. S12. The thermodynamic temperature is obtained by iterative solution. T Experimental values ​​of density virial coefficient B exp ; S2. Perform in-situ fitting or in-situ iteration of the characteristic temperature.

2. The in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature according to claim 1, characterized in that, Step S2, which involves in-situ fitting of the characteristic temperature, includes the following steps: S20. Repeat step S1 at multiple different temperature points to obtain a series of data points. T , B exp The functional relationship is obtained by fitting. B exp =f ( T ); S21, Solve f ( T )=0 yields the experimental value of the first type of characteristic temperature, and / or, solves d f ( T ) / d T =0 yields the experimental value of the second type of characteristic temperature.

3. The in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature according to claim 1, characterized in that, When the density virial coefficient and thermodynamic temperature are measured using the multiple isotherm method, the gas refractive index measurement data under multiple isotherms are simultaneously fitted, and the density virial coefficient at different temperatures is fitted as a function of temperature, wherein the coefficient to be fitted in the function is no greater than the number of measurement temperature points.

4. The in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature according to claim 1, characterized in that, Step S2, which involves in-situ iteration of the characteristic temperature, includes the following steps: The temperature change step size is calculated using Newton's iterative formula. After adjusting the temperature control, the measurement and iteration are repeated until the absolute deviation between two adjacent characteristic temperatures meets the convergence condition.

5. The in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature according to any one of claims 1-4, characterized in that, The gas to be tested is one or more of helium, nitrogen, argon, hydrogen, and methane, or a mixture of helium-3 and helium-4.

6. The in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature according to any one of claims 1-4, characterized in that, The operating temperature of the measurement system includes room temperature, low temperature range and extremely low temperature range, and the operating pressure of the measurement system includes low pressure range, medium pressure range and high pressure range.

7. An in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature, characterized in that, An in-situ measurement method for the density virial coefficient and its characteristic thermodynamic temperature as described in any one of claims 1-6 can be applied, wherein the measurement system comprises: The measuring unit has a sealed working chamber, in which a resonator and a standard reference thermometer are installed; A cryogenic control unit, including a refrigerator, is used to provide a cryogenic environment for the measurement system; A vacuum unit is used to provide a vacuum environment for the resonator; A gas supply unit is used to provide the gas to be measured to the resonator and control the gas pressure. The data processing and control unit is used to perform corresponding calculations based on the measurement data.

8. The in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature according to claim 7, characterized in that, The measurement unit also includes a primary radiation shield and a secondary radiation shield located inside the primary radiation shield. The resonator is located inside the secondary radiation shield and is fixed by a mounting bracket.

9. The in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature according to claim 8, characterized in that, The resonator is a microwave resonator, and the resonator is equipped with a microwave antenna to be connected to a microwave cable. The microwave cable passes through a feedthrough component and exits each level of radiation shielding.

10. The in-situ measurement system for the density virial coefficient and its characteristic thermodynamic temperature according to claim 7, characterized in that, The gas supply unit includes a gas cylinder and a gas supply pipe. One end of the gas supply pipe is connected to the gas cylinder, and the other end extends into the working chamber and is connected to the cavity of the resonator. The gas supply pipe located in the measurement unit extends in a zigzag or spiral shape.

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