Method and apparatus for measuring the heat capacity of a solid good conductor over a temperature range from low temperatures to room temperature

Abstract

This invention relates to a method and apparatus for measuring the specific heat of a solid-state good conductor at varying temperatures from low to room temperature. The apparatus includes: a solid-state good conductor sphere with a through-hole along its diameter, a heating element positioned at the center of the through-hole; a first temperature measuring element positioned at the center of the sphere to measure the temperature at the center; a second temperature measuring element positioned in the external environment to measure the ambient temperature; a temperature difference measuring element to measure the temperature difference between the environment and the surface of the sphere; a container holding a low-temperature medium; a position adjustment mechanism to adjust the height of the sphere within the container; a heating control circuit to achieve periodic heating; and a data acquisition and processing device to collect temperature, temperature difference, and heating parameters in real time. The method uses a periodic square wave heating signal to heat the sample. The temperature increment is estimated by linearly fitting the natural temperature rise process before and after heating using a temperature extrapolation method. The specific heat capacity is calculated based on the heat released by the heating element, the temperature increment of the sample, and its physical properties. This application requires no insulation or heat preservation measures, achieves continuous measurement over a wide temperature range, has high measurement accuracy, and a simple apparatus structure.

Description

Technical Field

[0001] This invention relates to the field of materials thermophysical property testing technology, and in particular to a method and apparatus for measuring the specific heat of solid conductors at varying temperatures from low temperature to room temperature. Background Technology

[0002] Specific heat capacity is an important physical quantity in thermodynamics, reflecting a material's ability to store heat. Accurately measuring the specific heat capacity of solid-state good conductors at different temperatures is crucial for understanding the macroscopic phenomena of thermal conduction in materials, studying their electronic state structure and phonon spectrum characteristics, and has wide applications in cutting-edge fields such as low-temperature physics, superconducting materials, aerospace devices, and quantum computing.

[0003] In the measurement of specific heat of solids at room temperature, commonly used methods include the electrothermal method, the mixing method, and the cooling method. The electrothermal and mixing methods require a robust insulation system to measure the temperature change of the solid under steady state, and the measurement time is typically long. The cooling method does not require an insulation system, but it has strict requirements for the consistency of the cooling environment between the reference solid and the solid being measured, making its implementation relatively demanding. None of these methods are suitable for continuous measurement of variable-temperature specific heat over a wide temperature range.

[0004] Chinese patent application publication number CN118858356A discloses a method for measuring the thermal properties of materials based on quasi-steady-state conditions. The upper surface of the sample is completely covered with a heating element, and the sides of the sample are wrapped with insulating material. A uniform heat flow is applied to the upper surface of the sample through the heating element, and the temperature rise data of the upper and lower surfaces of the sample are measured. Whether the temperature rise data shows a linear relationship determines whether the sample has entered a quasi-steady-state state. Once in a quasi-steady-state state, the thermal conductivity and specific heat capacity are calculated by linear fitting of the temperature rise data. Although this method simplifies the measurement process by utilizing quasi-steady-state theory, it still requires time to measure the temperature rise data of the upper and lower surfaces of the sample to determine whether a quasi-steady-state state has been reached. Furthermore, the device requires wrapping the sides of the sample with insulating material to construct a one-dimensional heat transfer model with no heat loss on the sides, increasing the complexity of the device.

[0005] In the measurement of low-temperature heat capacity, two main categories of methods are currently employed: adiabatic calorimetry and non-adiabatic calorimetry. Adiabatic calorimetry requires the sample to reach thermal equilibrium and is typically performed under complete or near-adiabatic conditions, resulting in complex instruments, lengthy experimental procedures, and large sample volumes. In non-adiabatic calorimetry, the sample is measured by heating, requiring insulation or the introduction of a controllable, single, and known heat leakage path. This necessitates thermal insulation or the construction of controllable heat conduction measures on the equipment, increasing the cost and complexity of the measurement device. In summary, existing technical solutions either rely on complex insulation systems or controllable heat conduction measures, leading to high costs and complex equipment; or still require partial insulation measures, increasing operational complexity; or are limited to specific small samples and have expensive systems. Therefore, developing a simple, low-cost technique suitable for measurements over a wide temperature range remains a real need. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects of the prior art by providing a method and apparatus for measuring the temperature-varying specific heat of a solid conductor from low temperature to room temperature, so as to solve the problem that conventional methods require a long time to obtain a steady state when measuring the steady-state temperature of the material before and after heat absorption to determine the temperature rise caused by heat absorption.

[0007] The objective of this invention can be achieved through the following technical solutions: One aspect of the present invention provides a method for measuring the specific heat of a solid-state good conductor at varying temperatures from low temperature to room temperature, comprising the following steps: A solid good conductor sample is immersed in a low-temperature medium to cool the sample to the temperature of the low-temperature medium and to create a temperature gradient above the low-temperature medium. The sample is raised to an environment above the low-temperature medium, and the position of the sample is adjusted so that the temperature difference between the environment and the sample surface is within a preset range. The sample is heated using a periodic heating signal, and heating parameters are collected in real time. Real-time acquisition of the sample's core temperature and ambient temperature; Real-time acquisition of the temperature difference between the environment and the sample surface; The heat released by the heating element is calculated based on the heating parameters. When the temperature difference is less than a preset threshold, heating is stopped, the position of the sample is raised to restore the temperature difference to the preset range, and heating and measurement are restarted. Linear fitting was performed on the natural temperature rise process of the sample before and after heating, and the temperature increment of the sample during heating was estimated by temperature extrapolation method. The specific heat capacity of the sample is calculated based on the heat, the temperature increment, and the physical properties of the sample.

[0008] As a preferred technical solution, the cryogenic medium is liquid nitrogen, liquid ammonia, or dry ice.

[0009] As a preferred technical solution, the low-temperature medium is left to stand for a preset time to create a temperature gradient above the low-temperature medium.

[0010] As a preferred technical solution, the preset range is 13°C to 18°C, and the preset threshold is 8°C.

[0011] As a preferred technical solution, the periodic heating signal is a square wave signal.

[0012] As a preferred technical solution, the heat released by the heating element is calculated based on the heating parameters using the following formula: in, The voltage across the sampling resistor is The voltage across the heating element. The value of the sampling resistor. The heat released by the heating element.

[0013] As a preferred technical solution, the ESP32 development board is used to collect the center temperature, ambient temperature, temperature difference and heating parameters of the sample in real time.

[0014] As a preferred technical solution, based on the heat... The temperature increment The mass of the sample m and molar mass M Through formula Calculate the specific heat capacity of the sample.

[0015] In another aspect, the present invention provides a device for measuring the variable temperature specific heat of a solid-state good conductor from low temperature to room temperature, for implementing the aforementioned method for measuring the variable temperature specific heat of a solid-state good conductor from low temperature to room temperature. The device includes a solid-state good conductor sphere, a heating element, a temperature measuring element, and a container. The solid-state good conductor sphere has a through hole along its diameter, the heating element is disposed at the center of the through hole, and the container is used to hold a low-temperature medium. The device further includes: A first temperature measuring element is disposed at the center of the solid-state good conductor sphere and is used to measure the center temperature of the solid-state good conductor sphere. The second temperature measuring element is disposed in the environment outside the solid good conductor sphere and is used to measure the ambient temperature; A temperature difference measuring element, with its measuring ends respectively disposed on the surface of the solid good conductor sphere and the outer environment, is used to measure the temperature difference between the environment and the surface of the solid good conductor sphere; A position adjustment mechanism is used to adjust the height position of the solid-state good conductor ball in the container; A heating control circuit includes a signal generator, a power amplifier, and a current sampling element. The signal generator is used to generate a periodic heating signal, the power amplifier is used to amplify the heating signal and drive the heating element, and the current sampling element is used to measure the heating current. The data acquisition and processing device is electrically connected to the first temperature measuring element, the second temperature measuring element, the temperature difference measuring element, and the heating control circuit, and is used to acquire in real time the center temperature, ambient temperature, temperature difference between the environment and the surface of the ball, and voltage parameters across the heating element and the sampling resistor of the solid good conductor ball.

[0016] As a preferred technical solution, the diameter of the through hole is 3mm, the heating element is a hollow heating wire, the heating wire is made of 0.4mm diameter nickel-chromium alloy wire tightly wound, the inner diameter is 2mm, and a four-wire connection is used. The first temperature measuring element and the second temperature measuring element are both PT100 platinum resistance thermometers with dimensions of 2mm×2mm×1mm and a four-wire connection.

[0017] As a preferred technical solution, the container is a thermos flask, and the position adjustment mechanism is a clamp.

[0018] As a preferred technical solution, the data acquisition and processing device includes an ESP32 development board, a first PT100 acquisition module, a second PT100 acquisition module, and a computer equipped with an acquisition program. The first PT100 acquisition module is connected to the first temperature measuring element, and the second PT100 acquisition module is connected to the second temperature measuring element. The first PT100 acquisition module and the second PT100 acquisition module are respectively connected to the ESP32 development board.

[0019] Compared with the prior art, the present invention has at least one of the following beneficial effects: (1) No insulation measures are required: The present invention performs measurements under the condition of free heat exchange between the solid good conductor sample and the environment. No insulation or heat insulation structure is required. It does not require complex systems such as high vacuum environment, radiation protection materials, low thermal conductivity support structure, and thermal anchor technology. This significantly reduces the complexity of the device and manufacturing cost, making it convenient to carry out low temperature specific heat measurement in conventional laboratories and experimental teaching.

[0020] (2) High measurement accuracy: By eliminating the influence of environmental heat exchange through the temperature extrapolation method, the temperature increment of the sample after absorbing heat from the heating element can be accurately obtained, and high measurement accuracy can still be achieved even without heat preservation. Taking the temperature variation specific heat measurement of industrial pure copper in the liquid nitrogen temperature range of 77K to 280K as an example, compared with the standard data of the National Institute of Standards and Technology (NIST), the relative error of specific heat at only two temperature points at the low temperature exceeds 3.0%, while the relative error of specific heat at the other temperature measurement points is within 3.0%, which has good reliability and practical value.

[0021] (3) Wide temperature range: The lower limit of measurement is determined by the selected low temperature medium. With liquid nitrogen as the low temperature medium, continuous measurement of specific heat with variable temperature can be realized in an ultra-wide temperature range of 77K to 300K, covering the main application temperature ranges in fields such as low temperature physics, superconducting materials, and aerospace devices.

[0022] (4) Easy to operate and easy to promote: The ESP32 development board is used for data acquisition and processing, which can realize the real-time display and automatic saving of measurement parameters. The operation process is simple and does not require professional personnel to be on duty. It is suitable for conventional laboratory environments and experimental teaching promotion.

[0023] (5) Low cost: The device is mainly composed of conventional components such as solid good conductor ball, heating wire, PT100 platinum resistance, T-type thermocouple, thermos bottle, clamp, ESP32 development board, etc. It does not require expensive vacuum system, heat insulation tracking device, etc. The total cost is significantly lower than that of traditional low temperature specific heat measurement equipment, making it suitable for promotion and application in experimental teaching. Attached Figure Description

[0024] Figure 1 A schematic diagram of the overall structure of a device for measuring the specific heat of a solid-state good conductor under varying temperatures; Figure 2 A schematic diagram of the process for measuring the specific heat of a solid-state good conductor under varying temperatures; Figure 3 This is a schematic diagram showing the change of the temperature difference between the surrounding environment and the surface of a sample sphere over time during the heating process. Figure 4 This is a schematic diagram showing the change in the center temperature of a sample sphere over time during a heating process. Figure 5 The voltage across the sampling resistor during a heating process U 1. Voltage across the heating wire U 2. Schematic diagram of the curve changing over time; Figure 6 To estimate the temperature increment of a sample sphere in a heating section using the temperature epitaxy method. T 增 A schematic diagram of the principle; Figure 7 This is a schematic diagram showing the change in the cumulative heat released by the heating wire over time during a heating process. Figure 8 This is a scatter plot of the specific heat values ​​of a sample at different temperatures during a heating process. Figure 9 This is a schematic diagram comparing the specific heat measurement of the sample with NIST standard data as a function of temperature. Among them, 1. heating wire, 2. solid good conductor ball, 3. PT100 platinum resistance thermometer, 4. T-type thermocouple, 5. thermos bottle, 6. low temperature medium, 7. bottle cap, 8. clip, 9. signal generator, 10. power amplifier, 11. sampling resistor, 12. ESP32 development board, 13. first PT100 acquisition module, 14. second PT100 acquisition module, 15. computer with acquisition program installed. Detailed Implementation

[0025] The technical solutions of the embodiments of the present 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 the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0026] To address the problems existing in the prior art, this embodiment provides a device for measuring the specific heat of a solid-state good conductor at varying temperatures from low to room temperature. (See [link to relevant documentation]). Figure 1 The apparatus is used to measure the variable-temperature specific heat capacity of pure copper in the range of liquid nitrogen temperature (77K) to room temperature (300K). The solid-state good conductor sphere 2 is the measurement sample, made of industrial pure copper, with a 3mm diameter perforation along its diameter. The purpose of the perforation is to accommodate the heating element and temperature measuring element. The 3mm diameter was chosen based on the following considerations: a smaller diameter would not accommodate the heating wire 1 and the PT100 platinum resistance thermometer 3; a larger diameter would remove too much sample, affecting the sample properties; and the heating wire 1 and PT100 platinum resistance thermometer 3 would not be in sufficient contact with the sphere, resulting in insufficient heat absorption and inaccurate measurement of the sphere's internal temperature. Therefore, the 3mm diameter satisfies the component installation requirements, preserves the original sample properties of the sphere, and ensures sufficient contact between the heating wire 1 and the PT100 platinum resistance thermometer 3 and the sample, facilitating heating and measurement.

[0027] A hollow heating wire 1 is placed at the center of the perforation, i.e., the center of the sphere. Heating wire 1 is made of tightly wound 0.4mm diameter nickel-chromium alloy wire with an inner diameter of 2mm, using a four-wire connection. The reasons for choosing nickel-chromium alloy wire are: nickel-chromium alloy has high resistivity and good oxidation resistance; its temperature coefficient of resistance is stable in the low-temperature to room-temperature range, providing stable and controllable heating power; the tightly wound structure allows heating wire 1 to form a uniform heat source in the center region of the sphere; the 2mm inner diameter hollow structure accommodates the temperature measuring element; and the four-wire connection eliminates the influence of wire resistance on the measurement, improving the accuracy of heating power control. The role of heating wire 1 in the overall scheme is to provide a periodic heating source, achieving the active heating stage through square wave voltage drive, so that the solid good conductor sphere 2 continuously heats up during the alternating process of natural heat absorption and active heating.

[0028] A low-temperature PT100 platinum resistance thermometer 3 (i.e., the first temperature measuring element) is placed at the center of the inner cavity of the heating wire 1, i.e., the center of the sphere, to measure the center temperature of the solid, good conductor sphere 2. The PT100 platinum resistance thermometer 3 measures 2mm × 2mm × 1mm and uses a four-wire connection, capable of measuring temperatures down to -200℃ (73K). The PT100 platinum resistance thermometer 3 was chosen because: platinum resistance thermometers offer high precision, good linearity, and stability, with a temperature measurement accuracy of ±0.15K; its small size (2mm × 2mm × 1mm) allows it to be placed at the center of the inner cavity of the heating wire 1 for accurate measurement of the sphere's center temperature; the four-wire connection eliminates the influence of wire resistance and contact resistance, improving temperature measurement accuracy; and its temperature range up to -200℃ meets the measurement requirements from liquid nitrogen temperature (77K) to room temperature (300K). The sphere's center temperature is a key parameter for calculating specific heat capacity. By linearly fitting the temperature change of the sphere's center during the natural temperature rise before and after heating, the influence of environmental heat exchange can be eliminated, accurately obtaining the temperature increment of the sample after absorbing heat from the heating element. The PT100 platinum resistance thermometer 3 is connected to the first PT100 acquisition module 13 through four wires, and transmits the temperature signal to the ESP32 development board 12 in real time for data acquisition.

[0029] Another PT100 platinum resistance thermometer 3 (i.e., the second temperature measuring element) is placed in the environment outside the solid-state good conductor sphere 2 to measure the ambient temperature. The purpose of measuring the ambient temperature is to serve as a reference for the ambient temperature at one end of the T-type thermocouple 4, thereby enabling accurate measurement of the temperature difference of the T-type thermocouple 4. The specifications of the PT100 platinum resistance thermometer 3 in the environment are exactly the same as those of the PT100 platinum resistance thermometer 3 at the center of the sphere, both being 2mm × 2mm × 1mm, using a four-wire connection, with a temperature measurement range up to -200℃, and connected to the ESP32 development board 12 through the second PT100 acquisition module 14.

[0030] One solder joint of the T-type thermocouple 4 is attached to the middle surface of the solid-state good conductor sphere 2 with copper foil, while the other solder joint is placed in the environment outside the solid-state good conductor sphere 2, at the same position as the PT100 platinum resistance thermometer 3 in the environment. The T-type thermocouple 4 has a wire diameter of 0.255 mm and two solder joints with a diameter of 0.6 mm. The reasons for choosing the T-type thermocouple 4 are as follows: the T-type thermocouple 4 is composed of copper and constantan, which has high thermoelectric potential sensitivity and fast response speed in the low temperature to room temperature range, enabling real-time and accurate measurement of temperature difference; the fine wire diameter of 0.255 mm results in a very small heat capacity of the thermocouple, and the interference to the measured temperature field is negligible; the solder joint diameter of 0.6 mm ensures good thermal contact without significantly affecting the temperature distribution on the sphere surface. The role of the T-type thermocouple 4 in the overall scheme is to monitor the temperature difference Δ between the environment and the surface of the solid-state good conductor sphere 2 in real time. TTemperature difference data serves as the basis for dynamically adjusting the sample position: when the solid good conductor sphere 2 is in the air environment above the low-temperature medium 6, there is a temperature difference between the sphere surface and the environment. The magnitude of the temperature difference reflects the heat exchange rate between the sphere and the environment. By adjusting the height of the sphere in the temperature gradient, the temperature difference can be controlled within a suitable range, ensuring that the sphere remains in a stable state of heat absorption and heating during the experiment. The T-type thermocouple 4 is connected to the ESP32 development board 12 via wires, transmitting the temperature difference signal to the data acquisition system in real time.

[0031] The thermos flask 5 is used to hold the cryogenic medium 6; in this embodiment, liquid nitrogen is selected. The thermos flask 5 was chosen because it has excellent thermal insulation properties, facilitating the formation of a stable temperature layer above the liquid nitrogen and reducing evaporation loss, thus extending the experimental time. The opening design of the thermos flask 5 also facilitates the immersion and lifting of the solid conductive sphere 2. The boiling point of the cryogenic medium 6, liquid nitrogen, is 77K (-196℃). Immersing the solid conductive sphere 2 in liquid nitrogen allows it to cool rapidly to 77K, providing a low-temperature starting point for measurements over a wide temperature range from low to room temperature. A temperature gradient naturally forms in the gas above the liquid nitrogen: the closer to the liquid nitrogen surface, the lower the temperature; the farther from the surface, the higher the temperature. This temperature gradient is formed by the heat absorption during the evaporation of liquid nitrogen, which lowers the temperature of the gas above the surface, while the gas further away from the surface is heated by the ambient room temperature, creating a continuous temperature gradient from the liquid surface to the flask opening. This temperature gradient provides the environmental conditions for subsequent adjustment of the position of the solid conductive sphere 2. The thermos flask 5 is equipped with a cap 7, and a through hole is provided on the cap 7 for the clip 8 to pass through.

[0032] Clip 8 is used to adjust the height of the solid conductive ball 2 within the thermos flask 5. One end of clip 8 holds the solid conductive ball 2, and the other end extends through the through-hole in the cap 7 to the outside of the thermos flask 5. The height of the ball can be adjusted by loosening or fixing clip 8 outside the flask. Clip 8 was chosen because it has a simple structure, is easy to operate, and allows for quick adjustment of the ball's position. The role of the position adjustment mechanism in the overall design is to adjust the position based on the temperature difference Δ monitored in real time by the temperature difference measuring element (i.e., the T-type thermocouple 4). T By dynamically adjusting the height of the solid conductive sphere 2 in the temperature gradient, the temperature difference is kept within a preset range, thereby controlling the heat exchange rate between the sphere and the environment and realizing continuous measurement over a wide temperature range from low temperature to room temperature.

[0033] The heating control circuit includes a signal generator 9, a power amplifier 10, and a sampling resistor 11, which are connected in series to form the heating circuit. The signal generator 9 provides the required waveform signal to the power amplifier 10; in this embodiment, a square wave signal is selected. The reason for choosing a square wave signal is that it has clear high and low level states. The high level phase corresponds to the active heating process, and the low level phase corresponds to the natural heat absorption process. The periodicity of the square wave allows the solid good conductor sphere 2 to continuously heat up during the alternating active heating and natural heat absorption processes, making it easy to distinguish the temperature change patterns at different stages. The power amplifier 10 amplifies the square wave signal output from the signal generator 9 to drive the heating wire 1. The sampling resistor 11, connected in series in the heating circuit, has a resistance of 0.1Ω and is used to measure the heating current. The working principle of the sampling resistor 11 is as follows: according to Ohm's law, a voltage drop is generated across the sampling resistor 11 when current flows through it. By measuring the voltage across the sampling resistor 11... U The heating current can be calculated using step 1. I = U 1 / R Therefore, based on the voltage across heating wire 1 U 2. Calculate heating power P = U 1× U 2 / R The heat released by heating wire 1 can be obtained by integrating the power over time. The reason for choosing a 0.1Ω value for sampling resistor 11 is that the heating circuit has a large current, and a 0.1Ω sampling resistor 11 generates little heat, ensuring that the sampling resistor 11 will not be damaged during the experiment.

[0034] The data acquisition and processing device includes an ESP32 development board 12, a first PT100 acquisition module 13, a second PT100 acquisition module 14, and a computer 15 equipped with the acquisition program. The first PT100 acquisition module 13 connects the PT100 platinum resistance thermometer 3 (i.e., the first temperature measuring element) at the center of the sphere to the ESP32 development board 12, and is used to acquire the temperature of the sphere's center. T 1. Signal. The second PT100 acquisition module 14 connects the ambient PT100 platinum resistance thermometer 3 (i.e., the second temperature measuring element) to the ESP32 development board 12, and is used to acquire ambient temperature. T 2. Signal. The ESP32 development board 12 also connects to a T-type thermocouple 4 for collecting temperature difference Δ. T Signal; connected to sampling resistor 11, used to acquire the voltage across sampling resistor 11. U 1. Signal; connected to heating wire 1, used to collect the voltage across heating wire 1. U2. Signal. The ESP32 development board 12 was chosen because: the ESP32 is a high-performance, low-cost microcontroller with a multi-channel analog-to-digital converter (ADC) that can simultaneously acquire multiple analog signals; it has built-in WiFi and Bluetooth modules for easy wireless communication with a computer; and it has fast processing speed, enabling real-time processing of multiple data streams. The ESP32 development board 12 connects to a computer 15 containing the acquisition program via USB or WiFi, transmitting the acquired temperature data... T 1. T 2. Temperature difference Δ T ,Voltage U 1 and U 2. Data is transmitted in real time to a computer 15 equipped with a data acquisition program. The computer program displays, stores, and processes the data in real time. The role of the data acquisition and processing device in the overall scheme is to acquire in real time the center temperature of the solid good conductor sphere 2, the ambient temperature, the temperature difference between the environment and the sphere surface, and the voltage parameters across the heating wire 1 and the sampling resistor 11. This provides the raw data basis for temperature extrapolation data processing and specific heat capacity calculation, and realizes a high degree of automation in the measurement process.

[0035] like Figure 2 As shown, the measurement process in this embodiment includes the following steps: S1. According to Figure 1 The measuring device shown is connected to a heating circuit, a temperature measuring circuit, a data acquisition system, and a computer 15 equipped with an acquisition program. The specific connection method is as follows: the output of signal generator 9 is connected to the input of power amplifier 10, the output of power amplifier 10 is connected to heating wire 1, the other end of heating wire 1 is connected to sampling resistor 11, and the other end of sampling resistor 11 is grounded, forming a series heating circuit; the spherical PT100 platinum resistance 3 (i.e., the first temperature measuring element) is connected to the first PT100 acquisition module 13 through a four-wire wire, and the ambient PT100 platinum resistance 3 (i.e., the second temperature measuring element) is connected to the second PT100 acquisition module 14 through a four-wire wire, and both the first PT100 acquisition module 13 and the second PT100 acquisition module 14 are connected to ESP32 development board 12; the two wires of T-type thermocouple 4 are connected to the analog input of ESP32 development board 12; the two ends of sampling resistor 11 are connected to the analog input of ESP32 development board 12 through wires, and the two ends of heating wire 1 are connected to the analog input of ESP32 development board 12 through wires; ESP32 development board 12 is connected to computer 15 with acquisition program installed through USB cable or WiFi. After the connection is completed, check whether each connection is firm and reliable to ensure normal signal transmission.

[0036] S2. Add cryogenic medium 6 to the thermos flask 5. The amount of liquid nitrogen added should be enough to completely submerge the solid good conductor sphere 2, typically to 1 / 3 to 1 / 2 of the thermos flask 5's volume. Immerse the solid good conductor sphere 2 in the liquid nitrogen using clamps 8, ensuring full contact between the sphere and the liquid nitrogen. After immersion in liquid nitrogen, the surface of the sphere will boil violently. This is because the initial temperature of the sphere is much higher than the boiling point of liquid nitrogen (77K), and the heat transfer from the sphere to the liquid nitrogen causes rapid vaporization. As heat exchange continues, the boiling gradually weakens until it stops, at which point the sphere's temperature has dropped to the liquid nitrogen temperature of 77K. Let it stand for 15 minutes. The purpose of this standing time is twofold: firstly, to ensure that the sphere's temperature reaches 77K completely and uniformly; and secondly, to allow a sufficiently stable temperature gradient to form in the gas layer above the liquid nitrogen. The 15-minute settling time was determined based on experimental experience: too short a settling time might result in incomplete temperature uniformity in the sphere and insufficient formation of a temperature gradient; too long a settling time would increase experimental time and liquid nitrogen consumption. The 15-minute settling time ensures both uniform temperature and the formation of a temperature gradient while maintaining experimental efficiency. During the settling process, the gas above the liquid nitrogen exhibits different temperature layers: the temperature decreases closer to the liquid nitrogen surface, approaching 77K, while the temperature gradually increases further away from the surface, approaching room temperature, forming a continuous temperature gradient from 77K to room temperature.

[0037] S3. Click the data acquisition program on computer 15 (with the acquisition program installed) to start the data acquisition function. The acquisition program begins to acquire the core temperature of the sphere transmitted by the ESP32 development board 12 in real time. T 1. Ambient temperature T 2. Temperature difference Δ T Voltage across sampling resistor 11 U Voltage across heating wire 1 U 2. Data is collected and displayed on the computer screen in real time, showing the values ​​and curves of each parameter, while the data is saved to a file for later processing.

[0038] S4. Stop the output of signal generator 9 to ensure that heating wire 1 is not working. Release clamp 8 and slowly raise the solid conductive sphere 2, allowing it to gradually detach from the liquid nitrogen surface and enter the air environment above the liquid nitrogen. During the raising process, closely observe the temperature difference Δ displayed on the computer screen. T Numerical value. For example... Figure 3 As shown, when the sphere is in liquid nitrogen, the surface temperature of the sphere and the ambient temperature are both close to 77K, and the temperature difference Δ T The initial temperature is 0℃; as the sphere begins to detach from the liquid surface and enter the air environment above, the ambient temperature rises rapidly, while the surface temperature of the sphere rises slowly as the sphere absorbs heat, resulting in a temperature difference Δ. T Start to increase, such as Figure 3 The area indicated by the red box in the middle. Continue to slowly raise the sphere; the ambient temperature continues to rise, and the temperature difference Δ... T It continues to increase. When the temperature difference Δ is observed... TWhen the temperature reaches the range of 13℃ to 18℃, the lifting is stopped, and clamp 8 is fixed to keep the sphere in a stable position. The technical basis for controlling the temperature difference within the range of 13℃ to 18℃ is as follows: if the temperature is below 13℃, it is too close to the 8℃ temperature difference during subsequent sphere lifting, resulting in fewer measurement data points for the sphere in a stable position, increasing the number of times the sphere's position needs to be adjusted; if the temperature difference is too large, such as above 18℃, the temperature difference between the sphere and the environment is too large, the heat exchange rate is too high, the sphere's natural heat absorption and heating rate is too fast, and the temperature change is too drastic, which is detrimental to the linear fitting accuracy of the temperature extrapolation method. A temperature difference range of 13℃ to 18℃ keeps the sphere in a suitable state of heat absorption and heating, ensuring a certain heat exchange rate, reducing the number of times the sphere's position needs to be adjusted, improving measurement efficiency, while avoiding excessively large temperature differences that would cause drastic temperature changes and affect measurement accuracy.

[0039] S5. Adjust the signal generator 9 to output a square wave and start the output. The square wave signal is amplified by the power amplifier 10 and drives the heating wire 1 to start heating. The computer 15 with the acquisition program collects the temperature of the ball's center in real time. T 1, such as Figure 4 As shown. When using square wave heating, the solid-state good conductor sphere 2 alternates between active heating and natural heat absorption phases: when the square wave is at a high level, the heating wire 1 is energized, and the sphere is simultaneously subjected to active heating by the heating wire 1 and natural heat absorption from the environment. Because the active heating power is greater than the natural heat absorption power, the temperature of the sphere rises rapidly, as shown. Figure 4 The steep rise segment is indicated by the red box; when the square wave is at a low level, heating wire 1 stops working, and the sphere absorbs heat naturally from the environment, causing the temperature to rise slowly, as shown in the image. Figure 4 The blue box indicates the slow temperature rise phase. Through alternating active heating and natural heat absorption, the sphere's temperature exhibits a sawtooth-like fluctuating upward trend, with the reference temperature gradually increasing in each cycle, eventually rising from 77K to room temperature. Simultaneously, the voltage across sampling resistor 11 is collected. U Voltage across heating wire 1 U 2, such as Figure 5 As shown. Figure 5 The voltage display shows a periodic pulse pattern: during the active heating phase, U 1 and U 2. Rapidly rise and maintain a stable high level during the natural heat absorption phase. U 1 and U 2 drops to zero. The voltage data is used for subsequent calculations of the heat released by heating wire 1.

[0040] S6. During the heating process, continuously monitor the temperature of the ball's center displayed on the computer screen. T 1 and temperature difference Δ T If the temperature at the center of the ball... T 1. The temperature has risen to or above room temperature, indicating that the measurement has covered the entire temperature range from 77K to room temperature, and the experiment can be stopped. If the core temperature...T 1 is still below room temperature. As the sphere continues to heat up, the surface temperature of the sphere gradually increases, while the ambient temperature remains relatively stable, resulting in a temperature difference Δ between the environment and the sphere's surface. T Continuously declining, such as Figure 3 The area shown in the blue box. When a temperature difference Δ is observed. T When the temperature drops below 8°C, the output of signal generator 9 stops, and heating wire 1 ceases operation. The clamp 8 is released, and the solid-state conductive sphere 2 is raised, allowing it to enter a higher-temperature environment, with a temperature difference Δ... T It begins to increase. When the temperature difference Δ T Once the temperature returns to the range of 13℃ to 18℃, fix clamp 8, restart the signal generator 9 output, and continue heating and measurement. Repeat steps S5 and S6, dynamically adjusting the position of the sphere in the temperature gradient to maintain the temperature difference within a suitable range, achieving continuous measurement from 77K to room temperature, until the sphere's core temperature... T 1. Raise the temperature to room temperature or above, then end the experiment. The technical basis for setting the temperature difference threshold to 8℃ is that when the temperature difference drops below 8℃, the heat exchange rate between the sphere and the environment is already low. Continuing to measure at this position will cause the sphere to heat up too slowly, reducing measurement efficiency. By increasing the height of the sphere to restore the temperature difference to 13℃ to 18℃, a suitable heat exchange rate can be maintained, ensuring measurement efficiency and data quality.

[0041] After the experiment, the computer 15 equipped with the data acquisition program saved all the acquired data, including the temperature of the sphere's core. T 1. Ambient temperature T 2. Temperature difference Δ T Voltage across sampling resistor 11 U Voltage across heating wire 1 U 2. Data on changes over time. The following section describes data processing, using the temperature extrapolation method to estimate the temperature increment of the sphere during heating, and calculating the specific heat capacity at different temperatures.

[0042] The data processing procedure includes the following steps: The first step is to select the core temperature of the ball. T 1. Analyze a complete heating segment from the change curve. A complete heating segment consists of three stages: the natural temperature rise stage before active heating, the active heating stage, and the natural temperature rise stage after active heating. For example... Figure 4 As shown, the first heating segment is selected for analysis, and the corresponding time range for this segment is approximately 85s to 190s. Figure 6 As shown, the temperature data of this heating section is extracted and plotted separately, with the horizontal axis representing time. t The vertical axis represents the temperature at the center of the sphere. T 1.

[0043] The second step involves linear fitting of the natural temperature rise process before active heating. The initial active heating phase refers to the natural heat absorption stage from the end of the previous heating cycle to the start of the current heating cycle. During this stage, the sphere absorbs heat naturally only due to environmental influences, and the temperature rises slowly, exhibiting a good linear relationship with time. Temperature data from approximately 25 seconds before the start of active heating are selected for linear fitting, and the fitting equation is: ,like Figure 6 The red fitted line is shown in the image. The slope of the fitted equation, 0.04082℃ / s, reflects the heating rate of the sphere during the natural endothermic phase.

[0044] The third step involves linear fitting of the natural temperature rise process in the latter part of the active heating phase. The latter part of the active heating phase refers to the natural heat absorption stage from the end of the current heating cycle to the start of the next heating cycle. During this stage, the sphere again absorbs heat naturally only due to environmental influences, and the temperature rises slowly. Temperature data from approximately 25 seconds before the start of the next active heating cycle are selected for linear fitting; the fitting equation is as follows: ,like Figure 6 The blue fitted line is shown in the image. The slope of the fitted equation, 0.03152℃ / s, reflects the heating rate of the sphere during the natural heat absorption phase after active heating. Comparing the slopes of the first and second segments, it can be found that the slope of the second segment is smaller than that of the first segment. This is because after active heating, the temperature of the sphere increases, the temperature difference between the sphere and the environment decreases, the heat exchange rate decreases, and the natural heating rate decreases.

[0045] The fourth step is to determine the start and end times of the active heating. Observation. Figure 5 Using the voltage data of the first heating section, identify the moments when voltage is applied to heating wire 1 and when it is removed. For example... Figure 5 The blue line indicates the time when the voltage is applied. When the voltage is removed The duration of active heating is 141.5s - 120s = 21.5s.

[0046] Fifth, calculate the intermediate time and estimate the temperature increment. Take the average of the times when the voltage is applied and removed as the intermediate time. The core idea of ​​the temperature extrapolation method is as follows: Assuming that during active heating, if there were no active heating from heating wire 1, the sphere would still heat up according to the natural heat absorption pattern, and the sphere's temperature should change along the first fitted line; however, due to the active heating from heating wire 1, the sphere absorbs additional heat, and the temperature increase is higher than the expected value of natural heat absorption. Therefore, after active heating ends, the actual temperature should change along the second fitted line; the temperature difference between the first and second fitted lines at the midpoint is the temperature increase caused by the heat generated by heating wire 1. Figure 6 middle drawing tA vertical line at 130.75s has its intersection point with the first fitted line at (130.75, -193.29684) and with the second fitted line at (130.75, -190.60111). Temperature increment. =-190.60111+193.29684=2.69573 K. The physical meaning of the temperature increment is: during active heating, after the sphere absorbs the heat released by heating wire 1, the temperature increases by 2.69573 K.

[0047] Step 6: Calculate the average temperature of the sphere. The average temperature of the sphere is the average of the temperatures at the midpoint between the first and second fitted lines. =(-190.60111-193.29684) / 2+273.15=81.20 K. The temperature value needs to be increased by 273.15 because the temperature unit in the fitted equation is Celsius, while the temperature unit in the specific heat capacity calculation is Kelvin. 81.20 K is the average temperature of the sphere corresponding to this heating section.

[0048] Step 7: Calculate the heat released by heating wire 1. Use the voltage across sampling resistor 11. U Voltage across heating wire 1 U 2. Sampling resistor 11 resistance value R =0.1Ω, according to the integral formula Calculate the cumulative heat released by heating wire 1 during active heating. The physical meaning of the integral is: the power of heating wire 1 at each moment. P = U 1× U 2 / R The cumulative heat release can be obtained by integrating the power over time. For example... Figure 7 As shown, the horizontal axis represents time. t The vertical axis represents the cumulative heat release. Q At the start of active heating At that time, the cumulative heat released At the end of active heating At that time, the cumulative heat released Therefore, the total heat released by heating wire 1 in the first heating section is .

[0049] Step 8: Calculate the mass of the copper ball. Note that after the hole is drilled in the center of the copper ball, heating wire 1 and PT100 platinum resistance thermometer 3 are placed inside. These components will also absorb heat released by heating wire 1. To simplify the calculation, assume that the mass of the copper removed by drilling the hole is equivalent to the mass of heating wire 1 and PT100 platinum resistance thermometer 3, and that the heat absorbed by them cancels each other out. Therefore, the mass of the copper ball is taken as the mass of the intact copper ball without the hole. .

[0050] Step 9: Calculate the specific heat capacity of copper at 81.20 K. According to the thermodynamic formula, the specific heat capacity of a substance is Δ... Q After the temperature rises Specific heat capacity C The calculation formula is C =Δ Q / ( × n ),in n For the amount of substance, n = / , Let be the molar mass of copper, taken as 63.546 g / mol. Substitute the data to calculate: Therefore, the specific heat capacity of copper at 81.20 K is 13.798 J·mol⁻¹. -1 ·K -1 .

[0051] Step 10: Repeat the above data processing procedure to process the data from other heating sections. For example... Figure 4 As shown, the entire measurement process includes multiple heating sections, each corresponding to a different temperature range for the sphere. By repeating steps one through nine of the data processing for each heating section, the specific heat capacity of the sphere at different temperatures can be obtained. Figure 8 As shown, the horizontal axis represents the temperature of the sphere, and the vertical axis represents the specific heat capacity. The figure illustrates a heating process, specifically, the continuous measurement of the specific heat capacity of copper at different temperatures as the sphere is heated from a certain low temperature to a higher temperature. Figure 8 It can be seen that as the temperature increases, the specific heat capacity of copper gradually increases, which is consistent with the general rule that the specific heat capacity of solids increases with increasing temperature.

[0052] Step 11 involves summarizing and processing the data from multiple heating processes. Since a single experiment requires multiple heating processes to raise the temperature from 77K to room temperature, each process corresponds to continuous measurements of the sphere at a specific height. By repeating steps 1 through 10 on the data from all heating processes, the specific heat capacity of copper across the entire temperature range, from liquid nitrogen temperature (77K) to room temperature (approximately 280K), can be obtained. Figure 9 As shown, the horizontal axis represents temperature, and the vertical axis represents specific heat capacity. The red scatter dots represent the specific heat capacity values ​​of copper measured in this invention, while the black solid line represents the standard copper specific heat capacity data provided by the National Institute of Standards and Technology (NIST). Figure 9 It can be seen that the measured values ​​of this invention are highly consistent with the trend of NIST standard data, both showing an increase in specific heat capacity with increasing temperature. The specific heat capacity is relatively small at low temperatures and tends to saturate at high temperatures, approaching the 3R value predicted by the Dulong-Petit law, where R is the gas constant, and 3R ≈ 24.9 J·mol⁻¹. -1 ·K -1 .

[0053] To quantitatively assess the measurement accuracy, the relative error between the measured values ​​and the NIST standard values ​​in this embodiment was calculated. The relative error was defined as: (Measured value - Standard value) / Standard value × 100%. Within the temperature range of 77K to 280K, the relative error of the specific heat capacity of copper was calculated at each measurement temperature point. The results showed that the relative errors were relatively large at the lowest temperature of 81.20K and the second lowest temperature of 86.13K, at 7.8% and 4.0% respectively. As the temperature increased, the relative error of the specific heat capacity remained within 3%. The reason for the larger errors at the lowest and second lowest temperatures is that the specific heat capacity of copper is the smallest at these temperatures. During the natural heat absorption process of the sphere, the temperature change is large, affecting the linear fitting accuracy of the temperature extrapolation method, resulting in the largest error in the temperature increment measurement. Despite the aforementioned errors, the relative error of this invention is higher than 3.0% only at 81.20K and 86.13K within the ultra-wide temperature range of 77K to 280K. The relative error of specific heat at other temperature measurement points does not exceed 3.0%. For a measurement method that does not require any heat preservation or insulation measures, this measurement accuracy has reached a high level and can meet the measurement needs of ordinary laboratories and the application needs of experimental teaching.

[0054] The technical effects of this embodiment can be summarized as follows: (1) A continuous measurement of specific heat capacity with variable temperature over an ultra-wide temperature range of 77K to 280K was achieved. By placing a solid good conductor sphere 2 in the air environment above the low-temperature medium 6 liquid nitrogen, and by utilizing the naturally formed temperature gradient and dynamically adjusting the position of the sphere, a full temperature range from the liquid nitrogen temperature of 77K to the room temperature of approximately 280K was achieved. The measurement temperature range spans more than 200K, far exceeding the temperature range of traditional specific heat measurement methods.

[0055] (2) No insulation or heat insulation measures are required, which significantly reduces the complexity of the device and the manufacturing cost. Traditional low-temperature specific heat measurement methods require complex insulation or heat insulation systems, such as constructing a high vacuum environment, using radiation-proof materials, adopting low thermal conductivity support structures and thermal anchoring technology, resulting in high equipment costs and complex systems. This invention allows the sample to freely exchange heat with the environment, and eliminates the influence of environmental heat exchange through the temperature extrapolation method, accurately obtaining the temperature increment of the sample after absorbing heat from the heating element. The device consists of only conventional components, and the total cost is far lower than that of traditional equipment, making it suitable for widespread application in conventional laboratory environments and experimental teaching.

[0056] (3) Simple operation and highly automated measurement process. Data acquisition and processing are performed using the ESP32 development board 12. The computer acquisition program displays and saves the measurement parameters in real time. Operators only need to adjust the position of the sphere according to the temperature difference value. No complicated operating skills are required, and no professional personnel are needed to be on duty. The operation process is simple and easy to promote and apply.

[0057] (4) The measurement accuracy is high and conforms well with international standard data. Using the NIST-published standard specific heat value of pure copper as a reference, the relative error of this invention exceeds 3.0% only at 81.20K and 86.13K within the temperature range of 77K to 280K. The relative error of the specific heat at other measurement points does not exceed 3.0%. The high level of measurement accuracy demonstrates the effectiveness of the temperature extrapolation method in eliminating the influence of environmental heat exchange under non-insulating conditions, and it possesses good reliability and practical value.

[0058] (5) High measurement efficiency. By using square wave periodic heating, the sphere continuously heats up during the alternation of active heating and natural heat absorption. Compared with the traditional static measurement method, the dynamic measurement process shortens the time of a single measurement. By dynamically adjusting the position of the sphere to maintain a suitable temperature difference range, the efficiency of continuous measurement is guaranteed. Measurements in the full temperature range from 77K to room temperature can usually be completed within 2 hours, resulting in high measurement efficiency.

[0059] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for measuring the temperature-dependent specific heat of a solid good conductor at low temperatures to room temperature, characterized in that Includes the following steps: A solid good conductor sample is immersed in a low-temperature medium to cool the sample to the temperature of the low-temperature medium and to create a temperature gradient above the low-temperature medium. The sample is raised to an environment above the low-temperature medium, and the position of the sample is adjusted so that the temperature difference between the environment and the sample surface is within a preset range. The sample is heated using a periodic heating signal, and heating parameters are collected in real time. Real-time acquisition of the sample's core temperature and ambient temperature; Real-time acquisition of the temperature difference between the environment and the sample surface; The heat released by the heating element is calculated based on the heating parameters. When the temperature difference is less than a preset threshold, heating is stopped, the position of the sample is raised to restore the temperature difference to the preset range, and heating and measurement are restarted. Linear fitting was performed on the natural temperature rise process of the sample before and after heating, and the temperature increment of the sample during heating was estimated by temperature extrapolation method. The specific heat capacity of the sample is calculated based on the heat, the temperature increment, and the physical properties of the sample.

2. The method of claim 1, wherein the solid-state good conductor is a metal. The cryogenic medium is liquid nitrogen, liquid ammonia, or dry ice.

3. The method of claim 1, wherein the solid-state good conductor low temperature to room temperature variable heat capacity measurement method is characterized by, The low-temperature medium is left to stand for a preset time to create a temperature gradient above it.

4. The method of claim 1, wherein the solid-state good conductor low temperature to room temperature variable heat capacity measurement method is characterized by, The preset range is 13°C to 18°C, and the preset threshold is 8°C.

5. The method for measuring the specific heat of a solid-state good conductor under varying temperatures from low temperature to room temperature according to claim 1, characterized in that, The periodic heating signal is a square wave signal.

6. The method for measuring the specific heat of a solid-state good conductor under varying temperatures from low temperature to room temperature according to claim 1, characterized in that, The heat released by the heating element is calculated based on the heating parameters using the following formula: in, The voltage across the sampling resistor is The voltage across the heating element. The value of the sampling resistor. The heat released by the heating element.

7. A device for measuring the specific heat of a solid-state good conductor at varying temperatures from low to room temperature, characterized in that, For implementing the method for measuring the specific heat of a solid good conductor from low temperature to room temperature as described in any one of claims 1-6, the apparatus includes a solid good conductor sphere (2), a heating element, a temperature measuring element, and a container. The solid good conductor sphere (2) has a through hole along its diameter, the heating element is disposed at the center of the through hole, and the container is used to hold a low-temperature medium. The apparatus further includes: The first temperature measuring element is located at the center of the solid good conductor ball (2) and is used to measure the center temperature of the solid good conductor ball (2); The second temperature measuring element is placed in the environment outside the solid good conductor ball (2) and is used to measure the ambient temperature; A temperature difference measuring element, with its measuring ends respectively set on the surface of the solid good conductor ball (2) and the outer environment, is used to measure the temperature difference between the environment and the surface of the solid good conductor ball; A position adjustment mechanism is used to adjust the height position of the solid good conductor ball (2) in the container; A heating control circuit includes a signal generator, a power amplifier, and a current sampling element. The signal generator is used to generate a periodic heating signal, the power amplifier is used to amplify the heating signal and drive the heating element, and the current sampling element is used to measure the heating current. The data acquisition and processing device is electrically connected to the first temperature measuring element, the second temperature measuring element, the temperature difference measuring element and the heating control circuit, and is used to collect in real time the center temperature of the solid good conductor ball (2), the ambient temperature, the temperature difference between the environment and the surface of the ball, and the voltage parameters across the heating element and the sampling resistor.

8. The device for measuring the specific heat of a solid-state good conductor from low temperature to room temperature according to claim 7, characterized in that, The diameter of the through hole is 3mm. The heating element is a hollow heating wire made of 0.4mm diameter nickel-chromium alloy wire tightly wound with an inner diameter of 2mm. It uses a four-wire connection. The first temperature measuring element and the second temperature measuring element are both PT100 platinum resistance thermometers with dimensions of 2mm×2mm×1mm and use a four-wire connection.

9. The device for measuring the specific heat of a solid-state good conductor from low temperature to room temperature according to claim 7, characterized in that, The container is a thermos (5), and the position adjustment mechanism is a clip (8).

10. The device for measuring the specific heat of a solid-state good conductor from low temperature to room temperature according to claim 7, characterized in that, The data acquisition and processing device includes an ESP32 development board (12), a first PT100 acquisition module (13), a second PT100 acquisition module (14), and a computer (15) with an acquisition program. The first PT100 acquisition module (13) is connected to the first temperature measuring element, and the second PT100 acquisition module (14) is connected to the second temperature measuring element. The first PT100 acquisition module (13) and the second PT100 acquisition module (14) are respectively connected to the ESP32 development board (12).

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