Gas specific heat ratio measuring device and measuring method

Abstract

The invention discloses a gas specific heat ratio measuring device and a gas specific heat ratio measuring method, particularly relates to the technical field of gas specific heat ratio measurement, and solves the technical problems of low measuring precision, inconvenience in operation, poor safety and narrow application range of a traditional gas specific heat ratio measuring experimental device in the prior art. According to the technical scheme, an air pressure sensor measures changes of air pressure and temperature in a bottle, and data can be displayed in real time by being connected with a computer; by optimizing sensor design and a signal processing algorithm, the measuring device can respond to air temperature and pressure changes more quickly; the stepping motor is used for controlling opening and closing of the piston, and errors caused by human factors are reduced; the change of the air specific heat ratio at different temperatures can be explored by changing the temperature; according to the invention, intelligent and automatic measurement is realized, errors caused by manual operation are reduced, and data change visualization in the whole experiment process is provided, so that students can intuitively analyze the change of each physical quantity.

Description

Technical Field

[0001] This invention relates to the field of gas specific heat capacity measurement technology, specifically to a gas specific heat capacity measuring device and measurement method. Background Technology

[0002] The specific heat ratio of a gas is the ratio of its specific heat capacity at constant pressure to its specific heat capacity at constant volume. It has significant applications in fields such as thermal system optimization design, energy efficiency improvement, and gas composition detection. However, existing technologies, such as the FD-NCD-II type air specific heat ratio measuring instrument, have many shortcomings in traditional experimental devices.

[0003] First, in terms of data acquisition and processing, traditional devices suffer from lag and subjectivity. For example, they display voltage signals, which need to be manually converted into actual pressure and temperature parameters. Furthermore, the sensors have low sensitivity, resulting in data reading lag and making it difficult to capture instantaneous changes in the gas in real time. In addition, the data from traditional devices only reflects the state at a single moment, which is not conducive to real-time monitoring of the dynamic evolution of the system's state.

[0004] Secondly, the operation introduces unavoidable systematic and random errors. Traditional methods rely on the human ear to hear the sound of gas release to close the valve; however, when the pressure difference between the inside and outside is small and the sound is extremely weak, this subjective judgment is prone to error. Simultaneously, traditional manual inflation is slow, causing heat exchange between the gas inside the bottle and the outside environment during compression, significantly deviating from the ideal adiabatic conditions in physics, leading to lower measurement results. Furthermore, manual inflation cannot accurately determine the inflation volume, posing a safety hazard of container rupture.

[0005] Furthermore, existing technologies generally fail to consider environmental factors, particularly the impact of humidity on measurement results. In areas with high humidity, the difference in molar mass between water vapor and dry air alters the equivalent molar mass of the gas mixture, directly affecting the calculation results. Simultaneously, humidity also reduces the measurement accuracy of temperature and pressure sensors.

[0006] Finally, traditional devices suffer from limitations such as narrow measurement range and poor safety. They can only measure the specific heat ratio of gases at room temperature, failing to explore its relationship with temperature changes, thus limiting their application in in-depth scientific research. Furthermore, the lack of effective visual feedback makes it difficult to accurately determine whether equilibrium has been reached within the bottle, resulting in significant dispersion in the measurement results.

[0007] In summary, traditional experimental devices for measuring the specific heat ratio of gases suffer from problems such as low measurement accuracy, inconvenient operation, poor safety, and narrow applicability. Summary of the Invention

[0008] Therefore, this invention solves the technical problems of low measurement accuracy, inconvenient operation, poor safety, and narrow applicability of traditional gas specific heat ratio measurement experimental devices in the prior art. The gas specific heat ratio measurement device and method provided by this invention improves the measurement accuracy of the gas specific heat ratio by improving the experimental device and combining humidity correction and machine learning methods; it achieves intelligent and automated measurement, reduces errors caused by manual operation, and provides visualization of data changes throughout the experimental process, making it easy for students to intuitively analyze the changes in various physical quantities; it expands the measurement range by using a PID algorithm to measure the gas specific heat ratio at different temperatures; it provides error tracing guidance for physics experiments in complex environments, verifies the effectiveness of machine learning in physical parameter correction, and explores the integrated application of multi-sensor technology.

[0009] This invention provides a gas specific heat ratio measuring device, comprising: a sealed container containing a heating element and a sensor; an automated inflation device connected to the interior of the sealed container via an inflation valve; an automated deflation device connected to the sealed container via a deflation valve, the automated deflation device including a gas flow rate sensor for measuring gas flow rate and a stepper motor for controlling the automatic opening and closing of the deflation valve, the stepper motor being triggered by the gas flow rate sensor; a temperature control module including a MOS driver chip electrically connected to the heating element and an Arduino control board, the control board being configured with a PID algorithm for precisely controlling the temperature inside the sealed container; and a data processing unit connected to the sensor, temperature control module, automated inflation device, and automated deflation device via a host computer. The automated valve control uses a gas flow rate sensor to replace human auditory judgment, applying pulses to the stepper motor to automatically close the deflation valve, reducing errors caused by subjective judgment. Precise temperature control is achieved by installing a heating element inside the glass bottle and connecting it to an Arduino control board and a MOS driver chip. A PID algorithm is used to precisely control the temperature inside the bottle to a preset value, with fluctuations controlled within ±0.1℃, enabling the measurement of the specific heat ratio of gases at different temperatures. A rapid inflation device uses an electric air pump for rapid inflation, making the experimental process more similar to adiabatic compression and reducing heat exchange with the outside environment. The experimental container is replaced with a thickened high borosilicate glass bottle with a low coefficient of thermal expansion, capable of withstanding large temperature and pressure changes, to improve the safety and stability of the experiment.

[0010] Furthermore, the data processing unit is configured with a program for receiving pressure, temperature, and humidity data collected by the sensor; filtering and performing steady-state identification processing on the received data; calculating the dry air pressure under each steady state using a humidity correction formula based on the pressure, temperature, and humidity data under different steady states; and calculating the specific heat ratio of the gas using the corrected dry air pressure and temperature data.

[0011] Furthermore, the data processing unit's program is also used for real-time storage and visualization of the data collected by the sensor and the calculation results. The sealed container is a borosilicate glass bottle, and the automated inflation device is an electric inflation pump. The sensor is a BMP388 sensor. The stepper motor's electronic control drive end is connected to the motor driver's input end, and a power module is provided at the bottom of the motor driver. High-precision sensor integration incorporates the high-precision BMP388 air pressure and temperature sensor into the experiment, achieving real-time, high-precision measurement of pressure, temperature, and humidity. A Python program is designed to automate data processing, filtering, steady-state identification, real-time storage, and visualization. More importantly, the program is configured with a humidity correction formula and combines machine learning models (such as random forests) and SHAP interpretability analysis to quantify the influence of each parameter on the gas specific heat ratio, providing data support for experimental optimization. Based on the original calculation formula, by measuring the ambient humidity and using formulas such as the Antoine equation for correction, the humid air pressure is converted into dry air pressure, thereby improving the accuracy of the calculation results.

[0012] The present invention also provides a method for measuring the specific heat ratio of a gas, comprising the following steps:

[0013] S1: Use an electric air pump to quickly inflate the sealed container with air, then close the inflation valve and open the vent valve to allow the gas inside the container to communicate with the outside atmosphere. After the gas inside the container stabilizes, automatically collect the gas pressure P0, temperature T0 and humidity B0 data at this time.

[0014] S2: Close the vent valve, and use the electric air pump to quickly inflate the container again for about 3 to 4 seconds. Then close the air valve and wait for the gas state inside the container to stabilize. Automatically collect the gas pressure P1, temperature T1 and humidity B1 data inside the container. This period is marked as steady state region 1.

[0015] S3: Start the switch module, trigger the stepper motor to automatically open and close the vent valve through the gas flow rate sensor, and automatically collect the gas pressure P2, temperature T2 and humidity B2 data in the container after the gas state in the container stabilizes; this period is marked as steady state region 2;

[0016] S4: Based on the pressure, temperature, and humidity data under different steady states, calculate the dry air pressure P under each steady state using the humidity correction formula. 干0 P 干1 P 干2 ;

[0017] S5: Using the corrected dry air pressure and temperature data, calculate the specific heat ratio of the gas according to the following formula. :

[0018] ;

[0019] S6: Integrate the gas pressure, temperature, and humidity data under different steady states, along with the calculated gas specific heat ratio, into a dataset, and use a machine learning model to analyze the dataset to reveal the influence of each parameter on the specific heat ratio.

[0020] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0021] 1. The present invention provides a gas specific heat ratio measuring device and measuring method, which realizes intelligent automation, reduces errors and reduces the time consumed per measurement by electric gas filling and automatic valve control; the measurement accuracy is improved, and through humidity correction and improvements to the device and sensor, the relative error is reduced from 5.834%-7.896% to 1.861%-2.314%, and the uncertainty is reduced.

[0022] 2. The present invention provides a gas specific heat ratio measuring device and method, which expands the measurement range, adopts a PID algorithm to measure the specific heat ratio of gas at different temperatures, and provides the possibility for exploring its relationship with temperature and verifying related theories; improves safety and stability, with electric gas pump controlling the flow to prevent overpressure, thickened high borosilicate bottle to enhance pressure and temperature change resistance, and automated operation to reduce intervention; and provides experimental optimization direction, revealing the influence mechanism of relevant parameters through machine learning analysis, and clarifying environmental conditions such as "low temperature and high humidity" that are conducive to stability.

[0023] 3. This invention provides a gas specific heat ratio measuring device and method. By improving the experimental setup and combining humidity correction and machine learning methods, the measurement accuracy of the gas specific heat ratio is improved; intelligent and automated measurement is achieved, reducing errors caused by manual operation, and providing visualization of data changes throughout the experimental process, making it easy for students to intuitively analyze the changes in various physical quantities; the measurement range is expanded, and the PID algorithm can be used to measure the gas specific heat ratio at different temperatures; it provides error tracing guidance for physics experiments in complex environments, verifies the effectiveness of machine learning in physical parameter correction, and explores the integrated application of multi-sensor technology.

[0024] 4. This invention provides a gas specific heat ratio measuring device and method. Using a novel sensor method to measure the specific heat ratio of air, it facilitates learning and mastering the principles and methods of air pressure and temperature sensors, and allows for the exploration of changes in the specific heat ratio of air at different temperatures. Therefore, this instrument is an ideal and high-quality instrument for physics experiments, representing a novel device for measuring the specific heat ratio of air. Specifically, it uses a BMP388 air pressure sensor to measure changes in air pressure and temperature within the bottle. This sensor has high sensitivity, good linearity and stability, and can display data in real time via a computer connection. Optimized sensor design and signal processing algorithms enable the measuring device to respond more quickly to changes in air temperature and pressure. A stepper motor controls the opening and closing of the piston, reducing human error. By changing the temperature, it allows for the exploration of changes in the specific heat ratio of air at different temperatures. Furthermore, some functions of the original experimental device were not used. This device uses more cost-effective materials and technologies compared to the original experimental device, reducing the overall cost of the measurement system. Humidity corrections have been made to the original experimental calculation formula, resulting in more accurate calculation results. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0026] Figure 1 : Schematic diagram of the overall structure of the present invention.

[0027] Figure 2 The feature influence of this invention on the sorting diagram.

[0028] Figure 3 Distribution diagram of the influence of the features of this invention.

[0029] Figure 4 WSS curve diagram of this invention.

[0030] Figure 5 The contour coefficient curve of this invention.

[0031] Figure 6 The statistical distribution characteristics and inter-group differences of parameters related to the specific heat ratio of gases in this invention.

[0032] Figure 7 The PCA dimensionality reduction diagram of this invention.

[0033] Figure 8 : Relationship diagram between γ and P1 in this invention.

[0034] Figure 9 : The γ distribution kernel density map of this invention.

[0035] Figure 10 : Flowchart of the operation of this invention.

[0036] Figure 11 This invention presents a multi-subplot showing the trends of pressure, temperature, and humidity over time.

[0037] Figure 12 : Physical sample image of the present invention.

[0038] Explanation of reference numerals in the attached figures:

[0039] 1. Power supply module; 2. Motor driver; 3. Arduino control board; 4. Stepper motor; 5. Coupling; 6. Venting valve; 7. Gas flow rate sensor; 8. Sensor; 9. Sealed container; 10. Heating element; 11. Inflation valve; 12. Drying tube; 13. Automated inflation device; 14. Data communication module. Detailed Implementation

[0040] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0041] Example 1:

[0042] This embodiment provides a gas specific heat ratio measuring device, such as... Figure 1As shown, the main components include: a sealed container 9, made of thickened high borosilicate glass with a low coefficient of thermal expansion, capable of withstanding large temperature and pressure changes; an internal heating element 10 and multi-parameter sensors 8 for measuring pressure, temperature, and humidity to ensure experimental safety and stability; an automated inflation device 13, consisting of an electric inflation pump and inflation valve 11, capable of rapidly inflating the sealed container in approximately 3 to 4 seconds, maximally simulating the adiabatic compression process; and an automated deflation device, including a gas flow rate sensor 7 and a stepper motor 4 for controlling the deflation valve 6. The gas flow rate sensor replaces traditional human judgment; when a change in gas flow rate is detected, it triggers the stepper motor to automatically close the valve, reducing human error. A temperature control module, consisting of a heating element 10, a MOS driver chip, and an Arduino control board 3 equipped with a PID algorithm, is used to precisely control the temperature inside the bottle within a preset value, with fluctuations within ±0.1℃, thereby enabling the measurement of the specific heat ratio of the gas at different temperatures. The data processing unit, connected to various sensors and control boards via a host computer, is equipped with a Python program for receiving sensor data, performing filtering and steady-state identification processing, and calculating the specific heat ratio based on a humidity correction formula. This program can also store and visualize data in real time and perform in-depth data analysis using machine learning models. The drying tube 12 is connected in series in the air path between the outlet of the automated inflation device 13 and the inlet of the inflation valve 11; it pre-treats the gas entering the sealed container 9 by adsorbing water vapor, reducing the interference of initial humidity on pressure measurement. Combined with the humidity correction algorithm, it improves the accuracy of dry air pressure calculation and reduces the dispersion of the specific heat ratio γ value caused by fluctuations in inflation water vapor content across different experimental batches, thus stabilizing the experimental data baseline.

[0043] The top of the borosilicate glass bottle is sealed, and its interior is connected to an electric air pump via a gas tube. An air filling valve 11 is installed between the electric air pump and the borosilicate glass bottle. A gas flow meter, i.e., a gas velocity sensor 7, is installed on the top of the borosilicate glass bottle. The gas flow meter communicates with the interior of the borosilicate glass bottle, and a venting valve 6 is installed between the gas flow meter and the borosilicate glass bottle. A heating element 10 is installed inside the borosilicate glass bottle. The electronic control section of the heating element 10 is connected to a MOS driver on the outside of the borosilicate glass bottle, and further communicates with a PID program through an Arduino control board 3. A BMP388 sensor is installed inside the borosilicate glass bottle, and its output terminal is connected to the control terminal of the Arduino control board 3 on the outside of the borosilicate glass bottle. The vent valve 6 is connected to the output shaft of the stepper motor 4 via a coupling 5. The electronic control drive end of the stepper motor 4 is connected to the input end of the motor driver 2, and the power module 1 is located at the bottom of the motor driver 2. The device is connected to a host computer via an Arduino control board, allowing the user to operate the measuring device through the host computer interface. The user can specify the temperature using a PID algorithm and directly measure and obtain real-time data and the final visualized results. Because the vent valve 6 closes randomly due to some degree of randomness—the pressure difference between the inside and outside gradually decreases as the venting process nears its end, making the venting sound difficult for the human ear to distinguish—a gas flow sensor 7 is selected to automatically close the valve by applying pulses to the stepper motor 4, reducing accidental errors caused by human intervention. Furthermore, since the experimental environment inevitably contains humid air, a humidity correction formula is used in the host computer calculation program to obtain more accurate experimental results. The operator can specify the number of experiments on the host computer and complete multiple measurements at once, which are automatically recorded in a table. After repeated experiments to obtain sufficient data, the machine learning component can learn the ranking of factors influencing the measurement results. This facilitates adjustments to the experimental environment for more accurate results in subsequent experiments. The data communication module 14 (e.g., a serial port module) connects the Arduino control board 3 to the host computer. It handles the real-time transmission of pressure, temperature, and humidity data collected by the sensor 8 to the host computer, supporting the visualization and analysis of experimental data. It also transmits control commands from the host computer (such as temperature settings and inflation time) to the Arduino control board 3, enabling remote automated control of the device. Furthermore, it provides a stable data channel for data filtering, model training, and other processing steps on the host computer, and feeds back calculation results to dynamically adjust device parameters.

[0044] During the inflation process, a rapid inflation speed is required to minimize heat exchange with the atmosphere. This can be approximated as an adiabatic compression process. To further approximate this process, the inflation device was improved by using an air pump, enabling rapid inflation. The BMP388 sensor is a 24-bit high-precision barometric pressure and temperature sensor capable of accurate altitude tracking, detecting atmospheric pressure and temperature. Its small size, low power consumption, low noise, and high precision make it particularly suitable for environmental monitoring and IoT applications. Integrating the BMP388 into this experiment allows for real-time measurement of pressure and temperature within the bottle, resulting in more accurate measurements. Finally, to analyze the data and study the effect of temperature on the specific heat ratio of air, a Python program was designed to help calculate and analyze the data more quickly and accurately. This program automates data processing and integrates hardware control logic through the Python main program, filtering and performing steady-state identification processing on the raw signals collected by the sensor. Based on the humidity correction formula, the specific heat ratio of the gas is calculated, and the data is stored and visualized in real time. Meanwhile, by combining random forest models and SHAP interpretability analysis from machine learning, the influence of each parameter on the specific heat ratio of the gas was quantified, providing data support for experimental optimization. Ordinary glass bottles were replaced with thickened high borosilicate glass bottles, which have a low coefficient of thermal expansion, can withstand large temperature and pressure changes, and have stable chemical properties, ensuring the safety and stability of the experiment.

[0045] Example 2:

[0046] This embodiment provides a measurement method based on the above-mentioned gas specific heat capacity ratio measuring device, specifically involving the measurement method of gas specific heat capacity ratio at room temperature and at different temperatures;

[0047] Measurement of the specific heat ratio of gases at room temperature:

[0048] Step 1: Turn on the air pump and the air filling / venting valve to pump air into the gas cylinder to relatively dry the gas inside the cylinder.

[0049] Step 2: Turn off the air pump and air valve, keep the vent valve open to allow the bottle to communicate with the atmosphere. After the gas state stabilizes, the system will automatically record the atmospheric pressure P0, room temperature T0 and bottle humidity B0 data.

[0050] Step 3: Close the vent valve, use the electric inflation pump to quickly inflate the bottle for about 3-4 seconds, and then close the inflation valve. When the temperature inside the bottle drops to room temperature and the pressure stabilizes, the system automatically marks it as steady-state region 1, and automatically measures and records the pressure P1.

[0051] Step 4: Start the switch module. The gas flow rate sensor triggers the stepper motor to automatically open and close the vent valve. After the gas state inside the bottle stabilizes again, the system automatically marks it as steady-state region 2 and automatically measures and records the pressure P2.

[0052] Step 5: Using the host computer program, calculate the dry air pressure based on the pressure, temperature and humidity data under each steady state using the humidity correction formula, and calculate the specific heat ratio γ using the corrected formula.

[0053] Step 6: Repeat the above steps multiple times to integrate the data into a dataset, and then analyze the data using clustering analysis and SHAP analysis in machine learning.

[0054] Measurement of the specific heat ratio of gases at different temperatures:

[0055] Step 1: Same as the method above, first dry the gas inside the bottle.

[0056] Step 2: Turn off the air pump and air filling / venting valve, turn on the heating device, and use the PID algorithm to stabilize the temperature inside the bottle at the preset temperature. After the temperature and pressure stabilize, the system automatically records the temperature T0, pressure P0, and humidity B0 at this time.

[0057] Step 3: Close the vent valve, and use the electric air pump to quickly inflate the bottle for about 3-4 seconds, then close the valve. When the temperature inside the bottle returns to the set temperature T0 and the pressure stabilizes, the system automatically marks it as steady-state region 1, and automatically measures and records the pressure P1.

[0058] Step 4: Start the switch module. The gas flow rate sensor triggers the stepper motor to automatically open and close the vent valve. When the temperature inside the bottle returns to the set temperature T0 and the pressure stabilizes, the system automatically marks it as steady-state region 2 and automatically measures and records the pressure P2.

[0059] Step 5: Using the host computer program, calculate the dry air pressure based on the pressure, temperature and humidity data under each steady state using the humidity correction formula, and calculate the specific heat ratio γ using the corrected formula.

[0060] Step 6: Repeat the above steps, change the preset temperature, measure multiple sets of data, and analyze the data using the SHAP analysis method.

[0061] This invention improves the formula for measuring the specific heat ratio of air;

[0062] Let the room temperature before inflation be T, and the room temperature when the gas in the bottle reaches equilibrium after inflation be T. ， The gas is initially in state I (P1, V1, T1). After venting, it undergoes adiabatic expansion, changing to state II (P0, V2, T0). When the gas in the isochoric endothermic bottle reaches equilibrium at room temperature T, the gas state changes to III (P2, V2, T2), where V is the volume of the storage bottle and V1 is the volume of the gas remaining in the bottle in state I (P1, T1). The gas state changes within the bottle are as follows:

[0063] I(P1,V1,T1)—II(P0,V2,T0)—III (P2,V2,T2).

[0064] I→II is an adiabatic process, which can be obtained from the adiabatic process equation:

[0065]

[0066] Combining the above three equations and eliminating V1 and V2, we get:

[0067]

[0068] Humidity Improvement: Since air itself contains a certain amount of humidity and is unstable, the error value of humidity in the experiment is removed, thereby improving the accuracy.

[0069] If the relative humidity is B (unit: %)

[0070] The saturated vapor pressure is calculated using the Antoine equation:

[0071]

[0072] Water vapor pressure value:

[0073]

[0074] because:

[0075]

[0076] Next, consider substituting the measured values ​​of P0, P1, and P2 into the formula and replacing them with P. 干0 P 干1 P 干2

[0077] Right now

[0078] Therefore, at this point, we only need to measure P1, P0, P2, T1, T2, B0, B1, and B2 to calculate the accurate specific heat ratio of air. In the gas specific heat ratio measurement scenario of this invention, the P 总 P w and P 干 All three are key barometric pressure parameters for achieving humidity correction and improving measurement accuracy, and they have a clear physical relationship and calculation logic: among them, P 总 This refers to the total pressure of the mixed gas (containing dry air and water vapor) inside a sealed container, directly acquired by a sensor (such as the BMP388 sensor). This parameter is the basic raw data for subsequent humidity correction, but because it contains water vapor, it cannot be directly used for accurate calculation of the gas specific heat ratio; P wThis refers to the water vapor pressure in the gas mixture inside a sealed container. Its calculation requires the relative humidity B (in %) synchronously collected by a sensor and the saturated vapor pressure P obtained using the Antoine equation (ln P_B = 58.430772 - 6750.4344 / T, where P_B is the saturated vapor pressure at the corresponding temperature and T is the measurement temperature). B Specifically, according to the formula "P" w = B×P B Calculations show that this parameter directly reflects the contribution of ambient humidity to the pressure of the mixed gas, and is the core factor causing P to deviate from the actual pressure of dry air; P 干 This refers to the actual pressure of dry air inside a sealed container, that is, the effective pressure parameter that can be used to calculate the specific heat ratio of a gas after correcting for the influence of water vapor. It is expressed as "P". 干 = P 总 - P w The relationship is derived by removing P. w Interference caused P 干 It can accurately characterize the thermodynamic state of dry air, and then combine the corresponding temperature data into the gas specific heat ratio calculation formula to ultimately optimize the accuracy of the measurement results, solving the calculation deviation problem caused by not considering humidity factors in traditional measurements.

[0079] Example 3:

[0080] This embodiment provides an experimental comparison between the experimental equipment used in this application and the original experimental equipment;

[0081] Data obtained from the original experimental equipment:

[0082]

[0083] The data obtained in this application are as follows:

[0084]

[0085] Data obtained after changing the temperature:

[0086]

[0087] The data table above shows that, in terms of relative error, the traditional device measures the gas specific heat ratio with a relative error range of 5.834%-7.896%. For example, when P0=101000Pa, the traditional device measures an average γ value of 1.3183, with a relative error of 5.834%. In contrast, the method of this patent, under room temperature conditions (T0≈25-27℃), has a minimum relative error of only 1.861% (e.g., when T0=25.04℃, the average γ value is 1.3739), and a maximum of only 1.970%, representing a maximum reduction of over 76% compared to the traditional device. Even when the temperature rises to 30-41℃, the relative error of this patent method can still be controlled within 2.128%-2.314%, consistently far lower than the minimum relative error of the traditional device, fully demonstrating that this patent method, through humidity correction (eliminating P... w For P 总 The system significantly reduces systematic and random errors by combining automated inflation / deflation control (which reduces human error) with automatic inflation / deflation control.

[0088] In terms of uncertainty, the traditional device exhibits a maximum uncertainty of 0.0441 (corresponding to an experimental group with a relative error of 7.896%) and a minimum uncertainty of 0.0092 (corresponding to an experimental group with a relative error of 5.834%), with significant data fluctuations. In contrast, the uncertainty of this patented method remains consistently low, with a minimum of 0.0181 at room temperature (T0≈26-27℃, mean γ value 1.3742) and a minimum of only 0.0164 at high temperatures (34-41℃) (T0≈34-35℃, mean γ value 1.3702), with a maximum of only 0.0186. Furthermore, the difference in uncertainty between different temperature groups is minimal, indicating that this patented method effectively reduces the dispersion of measurement data and improves the reliability of results through precise PID temperature control (temperature fluctuation within ±0.1℃) and high-precision BMP388 sensor acquisition (real-time capture of pressure / temperature changes).

[0089] In terms of data stability, the traditional device exhibits a large fluctuation range in γ value under the same P0 condition. For example, when P0 = 101000 Pa, the γ value ranges from a minimum of 1.2612 to a maximum of 1.3667, with a difference of 0.1055. In contrast, the method of this patent exhibits extremely small fluctuations in γ value within the same temperature group. For instance, in the room temperature group of 25-26℃, the γ value ranges from a minimum of 1.3664 to a maximum of 1.3794, with a difference of only 0.013. In the high temperature group of 39-41℃, the γ value ranges from a minimum of 1.3548 to a maximum of 1.3809, with a difference of only 0.0261.

[0090] This invention utilizes the random forest model and SHAP interpretability analysis from machine learning to perform in-depth analysis of experimental data. SHAP analysis revealed that humidity parameters (B1, B0, B2) are the most critical features affecting the measurement results, such as... Figure 2As shown; Figure 3 As shown in the bee colony diagram, the SHAP value distribution becomes more discrete as the B1 value increases, indicating that γ is significantly affected by the coupling of temperature and pressure under high humidity. P1 and γ show a positive correlation trend; SHAP values ​​are mostly positive when the standardized value is > 0, but a negative influence exists in the low P1 range. Through cluster analysis, the system automatically identifies the "low temperature and high humidity" environmental condition and finds that the average specific heat ratio under this condition is closest to the theoretical value with the smallest data dispersion and the best stability. These analytical results provide clear, but not obvious, guidance for experimental optimization; such as... Figure 4 As shown, a clear inflection point appears when the number of clusters is 3; further increasing the number of clusters slows the rate of decrease in WSS, indicating that 3 clusters is a reasonable division; as Figure 5 The coefficient was highest (0.68) when the number of clusters was 3, indicating high intra-cluster similarity and significant inter-cluster differences.

[0091] Cluster characteristics and physical association table:

[0092]

[0093] The cluster feature and physical correlation table shows that, based on multiple sets of experimental data obtained using the measurement method of this patent, cluster analysis clarifies the correspondence between different experimental environments (temperature, humidity, pressure) and the measurement results of the gas specific heat ratio (γ). From three core dimensions—"precisely locating the optimal experimental conditions," "quantifying the interference patterns of environmental parameters," and "guiding the tracing and control of experimental errors"—it provides crucial support for improving experimental accuracy. Its specific functions are as follows:

[0094] First, the table accurately identifies the optimal experimental environment of "low temperature and high humidity," directly reducing accuracy deviations caused by improper selection of environmental parameters. Cluster 0 (sample size 3) in the table clearly shows that under the conditions of "low temperature and high humidity" (T0=26.55℃, B0=48.19%, P0=101588Pa), the mean γ value is 1.3724, which is closest to the theoretical value of the gas specific heat ratio. Furthermore, the data in this cluster shows no significant dispersion, further demonstrating the optimal stability of the measurement results under this environment. This conclusion provides clear parameter guidance for experimental operations, avoiding the deviation of γ values ​​caused by blindly selecting the environment (such as ignoring the influence of humidity) in traditional experiments, thus improving measurement accuracy from the source of the experiment.

[0095] Secondly, the table quantifies the interference patterns of different combinations of environmental parameters on the measurement results, providing a basis for targeted error correction. The comparison between cluster 1 (sample size 11, T0=39.09℃, B0=43.46%) and cluster 2 (sample size 6, T0=27.92℃, B0=39.48%) shows that, under the "high temperature and medium humidity" environment, the mean γ value of 1.3679 is slightly lower than that of cluster 0, but the data distribution is stable, and accuracy can be further optimized through minor humidity adjustments. In contrast, under the "low temperature and low humidity" environment, the mean γ value is 1.3654 with large dispersion, clearly indicating that low humidity is the core factor causing the accuracy deviation in this group. This quantitative analysis allows the error correction of this patent to no longer rely on empirical judgment, but rather to formulate precise correction strategies for different combinations of environmental parameters. For example, for the "low temperature and low humidity" group, the humidity can be adjusted to 45%-50% (the humidity range of cluster 0) using a humidifier, directly reducing the accuracy loss caused by environmental interference.

[0096] Finally, the table provides a clear direction for tracing experimental errors and optimizing subsequent parameters, helping to form a closed loop of "measurement-analysis-optimization" for improving accuracy. The characteristic parameters (temperature, humidity, mean γ) of each cluster in the table correspond one-to-one with the experimental environment analysis, which not only quickly identifies the cause of accuracy deviations in a certain set of measurement data (e.g., if a group of γ values ​​has large dispersion, the table can be consulted to determine if it is due to being in the "low temperature and low humidity" environment of cluster 2), but also provides a basis for parameter optimization in subsequent experiments. For example, based on the "low temperature and high humidity" characteristic of cluster 0, a humidity control module can be added to the device to stably control the experimental environment within this optimal range. Simultaneously, combined with the consistency of the P0 parameter in the table (P0 for each cluster is close to 101500 Pa), the stability of the pressure control of the automated inflation device can be further verified, avoiding additional errors introduced by inflation pressure fluctuations. Ultimately, through continuous parameter optimization and error control, a steady improvement in experimental accuracy can be achieved.

[0097] like Figure 6 The distribution of γ values ​​in the three clusters (cluster 0, 1, and 2) shows significant differences. Cluster 0 exhibits a generally high γ value with relatively low data dispersion, indicating more concentrated and stable γ value measurements under the corresponding experimental conditions. Cluster 1 shows a γ value distribution in the middle range with increased dispersion. Cluster 2 shows a generally low γ value with the greatest dispersion, indicating more pronounced data fluctuations. This reflects the varying consistency and stability of the gas specific heat ratio γ measurement results under different combinations of experimental conditions, and also verifies the effectiveness of clustering. Further optimization of experimental parameters, such as humidity correction and precise pressure control methods described in the patent, can be used for clusters with high dispersion (e.g., cluster 2) to improve measurement accuracy. Figure 6The box plot clearly shows the statistical distribution characteristics and inter-group differences of gamma, a parameter related to the specific heat ratio of gases, in different clusters (cluster 0, 1, 2): the gamma of cluster 0 is generally positive and concentrated, the gamma of cluster 1 is mainly negative and has outliers, and the gamma of cluster 2 is generally in the lower range. This verifies that the clustering algorithm can effectively distinguish the differences in gamma performance under different experimental conditions (such as gas systems under different temperature control conditions), providing an intuitive basis for subsequent analysis of the specific heat ratio patterns of gases corresponding to each cluster; it also helps to check the reliability of experimental data by marking outliers, and by using the median and dispersion of gamma within clusters, it helps to interpret the gas thermal states represented by different clusters, promoting a deeper understanding of the changes in gas thermal properties with cluster categories in experiments.

[0098] like Figure 7 As shown, the three clusters are clearly distributed in 2D space, with cluster 0 and cluster 2 being clearly separated, verifying the effectiveness of clustering;

[0099] like Figure 8 As shown, cluster 0 corresponds to high P1 and high γ, while cluster 2 corresponds to low P1 and low γ, reflecting a positive correlation between pressure and γ.

[0100] like Figure 9 As shown, cluster 0 is concentrated at 1.37, while clusters 1 and 2 shift to lower values, which is related to physical characteristics;

[0101] like Figure 11 As shown, the trends of pressure, temperature, and humidity over time are illustrated, divided into three stages: initial stability, dynamic regulation, and subsequent stability. In the initial stage, all three remain stable. In the dynamic regulation stage, pressure rises rapidly and is maintained, temperature rises rapidly due to pressure changes and then fluctuates before falling back, and humidity increases. In the subsequent stability stage, pressure fluctuates slightly before stabilizing, temperature converges and stabilizes, and humidity decreases before stabilizing. These changes visually demonstrate the control effect of the experimental operation on the thermodynamic state of the gas, providing dynamic data support for subsequent analysis of the relationship between the specific heat ratio of the gas and temperature and pressure, and for verifying the effectiveness of the experimental operation. This graph shows the trends of pressure, temperature, and humidity over time for measurement number 1, including specific data: initial steady state P0 = 100342.11 Pa, T ≈ 26.1℃, B0 = 43.32%; during the dynamic adjustment phase, P rises to P1 = 104801.43 Pa, T reaches 26.41℃, and B rises to B1 = 43.72%; subsequently, in the steady state, P falls to P2 = 101486.41 Pa, T stabilizes, and B decreases to B2 = 42.92%, with the original formula yielding a γ value of 1.377 and a humidity-corrected value of 1.3840. The data clearly demonstrates the control of the gas state by the experimental operation, providing precise dynamic support for analyzing the relationship between γ and temperature and pressure, and verifying the effectiveness of the operation.

[0102] This multi-subplot of "Pressure, Temperature, and Humidity Changes Over Time (Measurement No. 1)" uses green, blue, and red backgrounds to divide the experiment into three stages: "Initial Stability - Dynamic Regulation - Subsequent Stability." It simultaneously displays the dynamic evolution of the three key parameters of gas pressure, temperature, and humidity, providing intuitive support for analyzing the correlation between the thermodynamic state of the gas and the operation during the experiment.

[0103] Pressure changes (top sub-graph): Green indicates the initial stage, where the pressure stabilizes at approximately... The blue indicator reflects the initial pressure baseline of the experiment; during the blue control phase, the pressure rises rapidly and remains at approximately [value missing]. This corresponds to the active control of gas pressure in the experiment (such as the operation of compressing gas); in the subsequent red phase, the pressure stabilizes at approximately [value missing] after a small fluctuation. This provides stable pressure conditions for subsequent thermal parameter measurements. The "stabilization-regulation-restabilization" process of pressure directly reflects the effectiveness of experimental operations in controlling gas pressure.

[0104] Temperature change (middle subplot, purple curve): The temperature stabilizes in the green phase. This represents the initial thermal equilibrium state of the experiment; during the blue control phase, the temperature rapidly rises to... The subsequent fluctuations and subsequent drop reflect the dynamic response of gas temperature to pressure changes (or external thermal intervention) (such as the temperature rise when the gas is compressed and the subsequent cooling caused by heat transfer); during the red phase, the temperature gradually converges and stabilizes at approximately [temperature value missing]. This indicates that the system has regained thermal stability, laying the foundation for temperature-based measurements of thermal quantities such as the specific heat ratio of gases. The dynamic evolution of temperature clearly demonstrates the changing patterns of the gas's thermodynamic state with experimental operations.

[0105] Humidity changes (subplot below, cyan curve): In the initial green phase, humidity stabilizes at approximately... The blue area represents the initial humidity level of the experimental environment; the humidity in the blue phase first rises and then stabilizes at approximately [value missing]. This may be related to the relative change in water vapor content in the gas after the pressure increases; during the red phase, the humidity drops rapidly and stabilizes at approximately [value missing]. This reflects the diffusion and equilibrium process of water vapor in the subsequent stages (after pressure and temperature stabilize). Humidity, as an auxiliary parameter, can be used to help verify the airtightness of the experimental system (abnormal fluctuations in humidity may indicate system leakage) or to analyze the interference of water vapor on gas thermal measurements.

[0106] In summary, this figure clearly presents the coupling law of "active pressure regulation - dynamic temperature response - coordinated humidity change" through multi-parameter, phased synchronous visualization. It provides intuitive and comprehensive dynamic data support for subsequent analysis of the relationship between gas specific heat ratio and temperature and pressure, as well as verification of the control effect of experimental operation on the thermodynamic state of gas.

[0107] The comparison shows that the experimental data are complete, with γ measurements concentrated at 1.37. The random forest model has basic predictive capabilities, and SHAP analysis reveals humidity as the core influencing factor. In various experimental environments, γ stability is best under "low temperature and high humidity" conditions; it is recommended to control humidity at 45%-50% using a drying tube and humidifier. Outliers in pressure parameters (P1, P2) require precise control using an automatic air pump to reduce human error. SHAP and cluster analysis provide a data-driven optimization path for complex physics experiments and can be further extended to multi-parameter collaborative control scenarios.

[0108] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A gas specific heat capacity ratio measuring device, characterized by, The application relates to a sealed container (9) provided with a heating sheet (10) and a sensor (8) inside the sealed container (9); an automatic inflation device (13) connected with the inside of the sealed container (9) through an inflation valve (11); an automatic deflation device connected with the sealed container (9) through a deflation valve (6), wherein the automatic deflation device comprises a gas flow rate sensor (7) for measuring the gas flow rate and a stepping motor (4) for controlling automatic opening and closing of the deflation valve (6), and the control of the stepping motor (4) is triggered by the gas flow rate sensor (7); a temperature control module comprising a MOS driving sheet electrically connected with the heating sheet (10) and an Arduino control board (3) provided with a PID algorithm for accurately controlling the temperature in the sealed container (9); and a data processing unit connected with the sensor (8), the temperature control module, the automatic inflation device and the automatic deflation device through an upper computer. The data processing unit is provided with a program for receiving pressure, temperature and humidity data collected by the sensor (8), filtering and steady-state identification processing the received data; calculating dry air pressure in each steady state by using a humidity correction formula according to the pressure, temperature and humidity data in different steady states; and calculating the specific heat capacity of the gas by using the corrected dry air pressure and temperature data. The program of the data processing unit is also used for real-time storage and visual display of the data collected by the sensor (8) and the calculation results. The sealed container (9) is a high borosilicate glass bottle, and the automatic inflation device (13) is an electric inflation pump. The sensor (8) is a BMP388 sensor. The electric control driving end of the stepping motor (4) is connected with the input end of a motor driver (2), and the motor driver (2) is provided with a power module (1) at the bottom.

2. The specific gas heat capacity ratio measuring apparatus according to claim 1, characterized by The application further comprises the following steps: S1: the electric inflation pump is used to rapidly inflate the sealed container (9), then the inflation valve (11) is closed and the deflation valve (6) is opened, so that the gas in the container is communicated with the atmosphere, and the gas pressure P0, the temperature T0 and the humidity B0 data at the time are automatically collected when the gas state in the container is stable; S2: the deflation valve (6) is closed, the electric inflation pump is used to rapidly inflate the container again, the inflation time is about 3-4 seconds, then the inflation valve (11) is closed, and the gas pressure P1, the temperature T1 and the humidity B1 data in the container are automatically collected when the gas state in the container is stable; this period of time is marked as steady state region 1; 3. The gas specific heat ratio measuring device according to claim 2, wherein S3: the switching module is started, the stepping motor is triggered to automatically open and close the deflation valve through the gas flow rate sensor, and the gas pressure P2, the temperature T2 and the humidity B2 data in the container are automatically collected when the gas state in the container is stable; this period of time is marked as steady state region 2; 4. The specific gas heat capacity ratio measuring apparatus according to claim 3, wherein S6: the gas pressure, the temperature and the humidity data in different steady states and the calculated specific heat capacity of the gas are integrated into a data set, and the data set is analyzed by using a machine learning model, so as to reveal the influence of each parameter on the specific heat capacity.

5. The specific gas heat capacity ratio measuring apparatus according to claim 4, wherein ​ 6. The specific heat ratio measuring device of claim 5, wherein ​ 7. A measuring method based on the gas specific heat ratio measuring device according to any one of claims 1 to 6, characterized by, ​ ​ ​ ​ S4: According to the pressure, temperature and humidity data under the different steady states, the dry air pressure P under each steady state is calculated by using a humidity correction formula 干0 , P 干1 , P 干2 ; S5: Using the corrected dry air pressure and temperature data, calculate the gas specific heat ratio according to the following equation : ； ​ 8. The measurement method according to claim 7, characterized in that, The machine learning model is a random forest model, and the analysis method is SHAP explainability analysis and cluster analysis.

9. The measurement method according to claim 8, characterized in that, In the step S1, when measuring the air specific heat capacity ratio at different high temperatures, the gas in the container is communicated with the outside atmosphere, and then the gas exhaust valve (6) is closed, the heating sheet (10) is opened, and the heating sheet (10) is controlled to stabilize the temperature in the bottle at different preset temperatures.

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