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The article presents a continuation of research carried out to determine the effect of input parameters (changes in engine structure parameters) on selected output parameters (diagnostic measures), based on quickly changing exhaust gas temperature. A method of determining the simultaneous influence of two input factors (the structure parameter and the engine load) on one output factor was presented, as well as an evaluation of which of the analysed input factors has a stronger influence on the output parameter. The article presents the stages of the experimental research conducted and statistical inference based on the results. Three changing parameters for the structure were reviewed: the active cross-sectional area of the inlet air channel, the injector opening pressure and the compression ratio. Based on the quickly changing temperatures of the exhaust gases, three diagnostic measures were defined and subjected to statistical tests. The following data were averaged over one cycle for a 4-stroke engine operation: the intensity of changes, the specific enthalpy and the peak-to-peak value of the exhaust gas temperature. The results of the two-factor analysis are presented. Conclusions on the analysis are given and a criterion for the selection of a diagnostic measure, depending on the analysed parameter of the structural design of the diesel engine, is proposed.

The monitoring of sintering bed temperature is crucial for controlling physical and chemical reactions during the sintering process and achieving low carbonization trends. However, accurately monitoring this temperature is challenging due to the ''black box'' nature of the sintering bed, which includes the sintering trolley and cup. As a result, a theoretical model needs to be developed urgently to predict the sintering bed's temperature profile. In this investigation, we propose a mathematical model that utilizes the characteristic value of the lognormal distribution to estimate indirectly the temperature of the sintering bed based on the measured temperature of the sintering exhaust gas. The sintering exhaust gas temperature and sintering bed temperature conform to the function: T=T0+A2πw⋅te−(ln(t−tc))2w22. To further enhance the accuracy of the sintering bed temperature prediction, the longitudinal positions of the sintering bed were expanded from three points to multiple points, enabling the construction of a temperature prediction function for the entire sinter bed and obtaining a cloud map of the sintering bed temperature. By determining the sintering terminal point and controlling the sintering machine's speed according to the location of the high-temperature region on the cloud map, the performance of the temperature prediction model was optimized. Through an analysis of the mathematical model and construction of the sintering temperature profile, a predictive route of exhaust gas temperature → three-point sintering bed → total sintering bed was established. This predictive method can significantly enhance the understanding of the sintering process and can be employed in industrial plants.

In this paper the performance and emission characteristics of thermal energy storage integrated micro-cogeneration system was investigated. This system was developed by connecting the vapor absorption refrigeration (VAR) system and thermal energy storage (TES) system with the exhaust gas pipe of a single-cylinder diesel engine. The vapor absorption refrigeration system has the cooling capacity of 500 W. A cabin of 1500 mm length, 1200 mm width and 1500 mm height was fabricated with proper insulation as space for cooling. The cabin temperature drop of 8.6 ℃ was achieved in 45 min. The cooling capacity of the VAR system was 302 W, and the COP of the VAR system was 0.398. The cabin temperature drop decrease with decrease in engine RPM but it was maintain stable (8.6℃) for 25 min by using TES. The overall efficiency of the cogeneration system was 1.79 % higher than the single generation. Hence, the result showed that the small capacity (5 kW) stationary diesel can be successfully converted into a cogeneration system to produce power and space cooling simultaneously.

A significant obstacle to creating efficient machine health monitoring systems is estimating performance degradation in dynamic systems, like aero plane engines. In exceedingly complex systems with many components, states, and parameters, conventional model-based and data-driven methods fall short of producing satisfactory results. While traditional methods had several drawbacks, deep learning has emerged as a viable computational tool for dynamic system prediction. In order to track system deterioration and estimate the EGT, a novel technique based on the Long Short-Term Memory (LSTM) network, (an architecture created to find the hidden patterns hidden in time series data) is provided in this research. The health monitoring information of aircraft turbofan engines is used to assess the effectiveness of the proposed strategy. As a result of this network’s ability to recognize the input data as a real-time series, the output in the following step can be predicted. Results of the suggested study show a significant ability to anticipate the output in the following time step. Additionally, the proposed model has a shorter learning curve and is more accurate.

In this paper, attention was paid to the problem of low controllability of marine medium- and high-speed engines during operation, which significantly limits the parametric diagnosis. The measurement of quickly changing temperature of engine exhaust gas was proposed, the courses of which can be a source of diagnostic information. The F statistic of the Fisher-Snedecor distribution was chosen as a statistical tool. Laboratory tests were carried out on the bench of a Farymann Diesel engine. The tests consisted of introducing the real changes in the constructional structure of the considered functional systems of the engine. Three changed parameters for the structure were reviewed: the active cross-sectional area of the inlet air channel, injector opening pressure and compression ratio. Based on the recorded plots of the quick-changing temperatures of the exhaust gases, three diagnostic measures were defined and subjected to statistical tests. The following data were averaged over one cycle for a 4-stroke piston engine operation, (1) the peak-to-peak value of the exhaust gas temperature, (2) the specific enthalpy of the exhaust gas, and (3) the rate of increase and decrease in the values for the quick-changing exhaust gas temperature.

The paper discusses the impact of changes in the compression ratio on the operating parameters of a diesel engine, e.g. on the temperature of exhaust gases. It presents the construction of the laboratory test stand, on which experimental measurements were realized. It is characterized how the actual changes of the compression ratio were introduced to the existing engine. The program of experimental investigations taking into account the available test stand and measurement possibilities was described. A statistical and qualitative analysis of the obtained measurement results was made. The use of F statistics of the Fisher-Snedecor distribution was proposed to assess the significance of the effect of compression ratio changes on the specific enthalpy of the exhaust gas stream. The specific enthalpy of exhaust gases was analysed for one cycle of diesel engine work, determined on the basis of the course of quickly varying temperature of exhaust gases. The results of these analyses are discussed and the utilitarian purpose of this type of evaluation in parametric diagnostics of piston engines is presented.

Aiming at engine health management, a novel hybrid prediction method is proposed for exhaust gas temperature (EGT) prediction of gas turbine engines. This hybrid model combines a nonlinear autoregressive with exogenous input (NARX) model and a moving average (MA) model. A feature attention mechanism-enhanced long short-term memory network (FAE-LSTM) is first developed to construct the NARX model, which is used for identifying the aircraft engine using condition parameters and gas path measurement parameters that correlate to the EGT. A vanilla LSTM is then used for constructing the MA model, which is used for improving the difference between the actual EGT and the predicted EGT given by the NARX model. The proposed method is evaluated using real flight process data and compared to several dynamic prediction techniques. The results show that our hybrid model reduces the predicted RMSE and MAE by at least 13.23% and 18.47%, respectively. The developed FAE-LSTM network can effectively deal with dynamic data. Overall, the present work demonstrates a promising performance and provides a positive guide for predicting engine parameters.

Low load is one of the most challenging combustion stages for a fixed-speed diesel electric generator. Due to incomplete combustion during this phase, a significant proportion of contaminants form inside the cylinder. This can lead to numerous chemical and mechanical harms to the diesel engine, resulting in friction, efficiency reduction, increased fuel consumption, and prematurely ending the generator’s life. These phenomena are qualified as underperformance, possibly due to a misfire and/or a low-efficiency value (air fuel–fuel ratio). Therefore, detecting and preventing underperformance and reducing its extended operation is crucial. This paper deals with the performance and emission analysis of a multicylinder fixed-speed diesel engine driving an electric generator (300 kW) fueled with ultra-low sulfur diesel (≤15 mg/kg) to provide energy in an isolated Canadian community. The tests were carried out according to ISO 3046-1:2002 standard in a remote site to identify clues that can prevent prolonged operation in underperformance. Among the tests conducted, emissions such as sulfur (S), carbon dioxide (CO2), nitrogen oxide (NOx), and exhaust gas temperature are considered the best indices for detecting the underperformance of a fixed-speed diesel–electric generator under very-low and low load (0–30%) with the following registered values: 18 ppm for S, 4% for CO2, 150 ppm for NOx, and 210 °C for the temperature.

The 21st century aviation and aerospace technologies have evolved and become more complex and technical. Turbofan jet engines as well as their cousins, the rocket engines (liquid/solid) have gone through several design upgrades and enhancements during the course of their design and exploitation. These technological upgrades have made engines very complex and expensive machines which need constant monitoring during their working phase. As the demand and use of such engines is growing steadily, both in the civilian and military sectors, it becomes necessary to monitor and predict the behavior of parametric data generated by these complex engines during their working phases. In this paper flight parameters such as Exhaust Gas Temperature (EGT), Engine Fan Speeds (N1 and N2), Fuel Flow (FF), Oil Temperature (OT), Oil Pressure (OP), Vibration and others where used to determine engine fault. All turbo fan engines go through several distinctly different working phases: Take-off phase, Cruise phase and Landing phase. Recording generated parametric data during these different phases leads to a massive amount of in-flight data and maintenance reports, which makes the task of designing and developing a fault diagnostic system highly challenging. It becomes imperative to use modern techniques in data analysis that can handle large volumes of generated data and provide clear visual results for determining the technical status of the engine under investigation/monitoring. These modern techniques should be able to give clear and objective assessment of the object under investigation. Cluster analysis methods based on Neural Networks such as c-means, k-means, self-organizing maps and DBSCAN algorithm have been used to build clusters. Differences in cluster groupings/patterns between healthy engine and engine with degraded performance are compared and used as the bases for defining faults. Fault diagnosis plays a crucial role in aircraft engine management. Timely and accurate detection of faults is the foundation on which maintenance turnaround times, operational costs and flight safety are based. The data used in this paper for analysis was obtained from flight data recorder during one flight cycle. The final decision on a fault is taken by an engineer.

This paper presents the application of Fisher-Snedecor distribution F statistics to assess the significance of the influence of changes in the active cross-sectional area of the inlet air channel (Adol) flow in a diesel engine on the observed diagnostic parameter determined on the basis of measurements of the quick changing exhaust gas temperature in the outlet channel, which is the specific enthalpy of the exhaust gas stream within one engine operating cycle (hspal). A plan of experimental tests carried out on the laboratory stand of a single-cylinder Farymann Diesel type D10 laboratory engine was presented and the method of determination of F statistics values for the obtained measurement results was characterized. Representative results of calculations were presented and the strength of Adol input parameter influence on the determined diagnostic parameter hspal simplified physical model of the working process of a compression ignition engine as the object of diagnosis was evaluated. It is planned to further develop the experimental research program to determine the significance of the influence of changes in the values of selected parameters of the engine structure on other diagnostic measures determined from the exhaust gas temperature signal, i.e. the mean peak-to-peak value as well as the rate (intensity) of increase and decrease in its value for individual engine cycles.

Current on-road vehicles are generally outfitted with exhaust after-treatment (EAT) systems to meet the stringent emission regulations. At cold start and low-loaded operations, those systems need to be warmed up above a threshold temperature (generally 250oC) for effective performance. High exhaust temperatures and high exhaust flow rates are required to accelerate the EAT warm up which are mostly not available at low-loaded diesel vehicle operations. Therefore, the objective of this work is to improve EAT warm up at low loads through utilizing exhaust valve opening (EVO) modulation which allows both elevated exhaust temperatures and exhaust flow rates. A 1-D engine simulation program is used to model the system which is set to operate at 1200 RPM engine speed and at 2.5 bar brake mean effective pressure (BMEP) engine load. Exhaust temperature can be increased above 250oC via either early or late EVO timings. Reduced expansion work in advanced EVO timings and increased pumping loss in retarded EVO timings require higher fuel consumption (up to 15 % and 20 %, respectively) to keep engine load constant. Those high fuel penalties reduce engine air-to-fuel ratio and rise exhaust temperature more than 55oC. Exhaust mass flow rate is improved up to 9 % in the system as well. The method increases exhaust gas energy up to 40 % and rises heat transfer rate to the EAT system up to 140 % compared to nominal condition. The technique is highly effective at heating up EAT systems, however, it also causes high fuel inefficiency which needs to be considered.

The exhaust gas temperature (EGT) baseline of an aeroengine is key to accurately analyzing engine health, formulating maintenance decisions and ensuring flight safety. However, due to the complex performance characteristics of aeroengine and the constraints of many external factors, it is difficult to obtain accurate non-linear features between various operating factors and EGT. In order to diagnose and forecast aeroengine performance quickly and accurately, four data-driven baseline prediction frameworks for EGT are proposed. These baseline frameworks took engine operating conditions and operating state control parameters as input variables and EGT as predicted output variables. The original data were collected from CFM56-5B engine ACARS flight data. Four typical machine learning methods, including Generalized Regression Neural Network (GRNN), Radial Basis Neural Network (RBF), Support Vector Regression (SVR) and Random Forest (RF) are trained to develop the models. Four aeroengine EGT baseline models were validated by comparing the after-flight data of another engine. The results show that the developed GRNN models have the best accuracy and computational efficiency compared with other models, and their RE and CPU calculation time on the verification set are 1.132 × 10−3 and 3.512 × 10−3 s, respectively. The developed baseline prediction frameworks can meet the needs of practical engineering applications for airlines. The methodologies developed can be employed by airlines to predict the EGT baseline for the purpose of engine performance monitoring and health management.

Data-driven condition-based maintenance (CBM) and predictive maintenance (PdM) strategies have emerged over recent years and aim at minimizing the aviation maintenance costs and environmental impact by the diagnosis and prognosis of aircraft systems. As the use of data and relevant algorithms is essential to AI-based gas turbine diagnostics, there are different technical, operational, and regulatory challenges that need to be tackled in order for the aeronautical industry to be able to exploit their full potential. In this work, the machine learning (ML) method of the generalised additive model (GAM) is used in order to predict the evolution of an aero engine’s exhaust gas temperature (EGT). Three different continuous synthetic data sets developed by NASA are employed, known as New Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS), with increasing complexity in engine deterioration. The results show that the GAM can be predict the evolution of the EGT with high accuracy when using several input features that resemble the types of physical sensors installed in aero gas turbines currently in operation. As the GAM offers good interpretability, this case study is used to discuss the different data attributes a data set needs to have in order to build trust and move towards certifiable models in the future.

Catalytic converter (CATCO) and its effect on engine performance and exhaust gas temperature became an exciting field in automotive research. In this study purposed to compare existing CATCO which is ceramic and metallic with FeCrAl CATCO that treated with a combination of ultrasonic bath and electroplating technique in 30 minutes holding time (UB+EL 30 min). This study proposed to select an appropriate CATCO that used in a gasoline engine to increase the performance and to reduce the exhaust gas temperature as well as its potential to reduce the exhaust gas emission. Mitsubishi 4G93 conducted this analysis with 1.8 L and 10.5 compression ratio with a variable speed of 100, 2000 and 3000 rpm and different engine load of 10, 20 and 30%. The result shows that the FeCrAl CATCO was more useful to reduce fuel consumption up to 66.42% and increase torque up to 15.79% as well as reduce exhaust gas temperature up to 30.11% as compared to ceramic and metallic CATCO. It can be concluded that FeCrAl CATCO coated by UB+EL 30 min was recommended to increase engine performance and to reduce exhaust gas emission.

The creation of modern high-powered gas and gas-diesel engines is associated with the solution of two main tasks – the elimination of abnormal combustion and reduction of engine thermal factor. The paper discusses ways to reduce exhaust gas temperatures, methods to eliminate hot-tube ignition and detonation in single fuel gas engines. The ways of reducing exhaust gas temperatures, reducing the thermal factor of diesel injectors (pressure, duration of injection) and detonation issues in two-fuel gas-diesel engines are considered. The results of computational and experimental studies are presented. It is shown that due to the optimization of intake systems, fuel supply and control algorithms it is possible to significantly reduce the thermal stress of gas and gas-diesel engines, while ensuring the achievement of high values of the average effective cycle pressure up to 28 bar and the achievement of high volume power up to 43 kW/l.

Modern automotive gasoline engines have highly efficient after-treatment systems that reduce exhaust gas emissions. However, this efficiency greatly depends on the conditions of the exhaust gas, mainly the temperature and air–fuel ratio. The temperature instability during transient conditions may cause a reduction in the efficiency of the three-way catalyst (TWC). By using a thermal energy storage system before TWC, this negative effect can be suppressed. In this paper, the effects of the temperature stabilization on the efficiency of the three-way catalyst were investigated on a 1-D turbocharged gasoline engine model, with a focus on fuel consumption and emissions. The thermal energy storage system (TESS) was based on PCM materials and was built in the exhaust between the turbine and TWC to use the energy of the exhaust gas. Three different materials were picked up as possible mediums in the storage system. Based on the results, the usage of a TESS in a gasoline after-treatment system has shown great potential in improving TWC efficiency. This approach can assist the catalyst to operate under optimal conditions during the drive. In this study, it was found that facilitating the heat transfer between the PCM and the catalyst can significantly improve the emissions’ reduction performance by avoiding the catalyst to light out after the cold start. The TESS with PCM H430 proved to reduce the cumulative CO and HC emissions by 8.2% and 10.6%, respectively, during the drive. Although a TES system increases the after-treatment cost, it can result in emission reductions and fuel consumption over the vehicle’s operating life.

In this study, balanites Aegyptiaca (L.) Del biodiesel was blended in proportions of 10% and 20% on the volume basis with diesel fuel and tested in a single cylinder, VCR diesel engine under measured load conditions with varied EGR rates (0, 10 and 20%). The results showed that B10 and B20 blends shown a significant reduction rate in terms of NOx emissions that were familiar with biodiesel blends. At peak load conditions, BTE increased slightly for test fuel blends compared with pure diesel fuel while the BSFC rate and EGT suffered from increasing and decreasing nature with respect to blending percentage. From the emissions point of view, with the increase in blends percentage, a significant reduction rate is observed in terms of CO and HC concentrations (up to 12.34 and 17.5%, respectively) while NOx emissions decreased at peak load conditions (up to 24.34%). HC and CO emissions decreased with increase in blends percentage. However, lower levels of NOx and EGT (up to 21.37 and 8.47%, respectively) and the average increase in terms of BTE and BSFC (up to 2.83 and 2.9%, respectively) can be realised with B20 test fuel blend under 20% EGR rate.

In recent years, ethanol has attracted attention as an environmentally substitute fuel because of exhaustion of petroleum resources and environmental issues. In this study, we investigated emission by using the ethanol water solution from 45 to 60 vol.% concentrations under continuous combustion region by using the swirl burner. In addition, we investigated the flame behavior, influence of flame shape and flame length on the exhaust gas temperature and reduction of emission such as CO and NOX. Furthermore, the influence of the swirl flow by the supply air on the spray shape and the influence of the liquid film on the combustion characteristics were also examined. The exhaust gas temperature was measured in a combustion chamber and exhaust pipe by using K type thermocouples. The main conclusion are as follows: 1) The liquid film/liquid column ratio near the nozzle increases with decreasing the spray angle and the fuel flow rate at the low ethanol water solution (E45). 2) The continuous combustible regions are bigger with increasing the fuel flow rate at the low ethanol water solution (E45). 3) The exhaust gas temperature decreases monotonically with increasing the air ratio in spite of the spray angle and the fuel flow rate at low ethanol water solution (E45, E60). 4) The CO emission of high fuel flow rate remarkably decreases than that of low fuel flow rate at any spray angle for the ethanol water solution (E60) under the air ratio λ from 1 to 1.4. 5) It is possible to realize the less than 10 ppm NOX emission by using the ethanol water solution of E60 under the wide range of air ratios. 6) It is possible to reduce the simultaneous reduction of CO and NOX emissions for the ethanol water solution (E60) under the high air ratio.

A truly universal system to optimize consumptions, monitor operation and predict maintenance interventions for internal combustion engines must be independent of onboard systems, if present. One of the least invasive methods of detecting engine performance involves the measurement of the exhaust gas temperature (EGT), which can be related to the instant torque through thermodynamic relations. The practical implementation of such a system requires great care since its torque-predictive capabilities are strongly influenced by the position chosen for the temperature-detection point(s) along the exhaust line, specific for each engine, the type of installation for the thermocouples, and the thermal characteristics of the interposed materials. After performing some preliminary tests at the dynamometric brake on a compression-ignition engine for agricultural purposes equipped with three thermocouples at different points in the exhaust duct, a novel procedure was developed to: (1) tune a CFD-FVM-model of the exhaust pipe and determine many unknown thermodynamic parameters concerning the engine (including the real EGT at the exhaust valve outlet in some engine operative conditions), (2) use the CFD-FVM results to considerably increase the predictive capability of an indirect torque-detection strategy based on the EGT. The joint use of the CFD-FVM software, Response Surface Method, and specific optimization algorithms was fundamental to these aims and granted the experimenters a full mastery of systems’ non-linearity and a maximum relative error on the torque estimations of 2.9%.

The second part of the article describes the technology of marine engine diagnostics making use of dynamic measurements of the exhaust gas temperature. Little-known achievements of Prof. S. Rutkowski of the Naval College in Gdynia (now: Polish Naval Academy) in this area are presented. A novel approach is proposed which consists in the use of the measured exhaust gas temperature dynamics for qualitative and quantitative assessment of the enthalpy flux of successive pressure pulses of the exhaust gas supplying the marine engine turbocompressor. General design assumptions are presented for the measuring and diagnostic system which makes use of a sheathed thermocouple installed in the engine exhaust gas manifold. The corrected thermal inertia of the thermocouple enables to reproduce a real time-history of exhaust gas temperature changes.

Bioethanol is a well-known oil-alternate fuel for automobiles as a carbon neutral fuel adapted to environmental problems. Furthermore, ethanol water solution is thought to be effective to the depletion of problems of fossil fuel resources. Continuous combustion is achieved in a wide range of air ratios using low concentration ethanol water solution in previous research. This study aims to examine the influences on spray combustion characteristics by using a swirl burner. The images of flame structure for ethanol water solution was visualized for various air ratio and water contents by using a glass tube. The exhaust gases (CO, NOx, O2) and exhaust gas temperature are measured in a combustion chamber and exhaust pipe by using N type thermocouples. The main conclusions are as follows: 1) The brightness and length of flame for ethanol water solution at low ethanol concentration (E45) decreases compared to the other ethanol water concentrations (E60, E80 E95). 2) The exhaust temperature decreases with decreasing the air ratio at any ethanol concentration under constant ethanol flow rate conditions. 3) The CO emission decreases with increasing the air ratio at the low ethanol concentration (E45). 4) The NOx emission decreases with decreasing the ethanol concentration at any air ratios. 5) Fuel flow rate has a small influence for NOx emission under high air ratios at any ethanol water concentration.

The article discusses the problem of diagnostic informativeness of exhaust gas temperature measurements in turbocharged marine internal combustion engines. Theoretical principles of the process of exhaust gas flow in turbocharger inlet channels are analysed in its dynamic and energetic aspects. Diagnostic parameters are defined which enable to formulate general evaluation of technical condition of the engine based on standard online measurements of the exhaust gas temperature. A proposal is made to extend the parametric methods of diagnosing workspaces in turbocharged marine engines by analysing time-histories of enthalpy changes of the exhaust gas flowing to the turbocompressor turbine. Such a time-history can be worked out based on dynamic measurements of the exhaust gas temperature, performed using a specially designed sheathed thermocouple.

This paper describes the process of the M337 engine monitoring by the Engine Data Management 800 which is mounted on six aircraft of Air Training and Education Centre. This is the most advanced and accurate piston engine-monitoring system on the market that uses the latest microprocessor technology to monitor critical engine parameters in order to measure parameters as cylinder head temperature and exhaust gas temperature to evaluate each cylinder performance alone. These parameters are monitored during these flight regimes – take off, climb and cruise. Monitoring of the mentioned parameters will help us to increase the economy of the aircraft and also its operation’s reliability.

Waste heats of an internal combustion engine (ICE) are recovered by a dual-loop organic Rankine cycle (DORC). Thermodynamic performance analyses and optimizations are conducted with 523.15⁻623.15 K exhaust gas temperature (Tg1). Cyclopentane, cyclohexane, benzene, and toluene are selected as working fluids for high-temperature loop (HTL), whereas R1234ze(E), R600a, R245fa, and R601a are selected as working fluids for low-temperature loop (LTL). The HTL evaporation temperature, condensation temperature, and superheat degree are optimized through a genetic algorithm, and net power output is selected as the objective function. Influences of Tg1 on system net power output, thermal efficiency, exergy efficiency, HTL evaporation temperature, HTL condensation temperature, HTL superheat degree, exhaust gas temperature at the exit of the HTL evaporator, heat utilization ratio, and exergy destruction rate of the components are analyzed. Results are presented as follows: the net power output is mainly influenced by HTL working fluid. The optimal LTL working fluid is R1234ze(E). The optimal HTL evaporator temperature increases with Tg1 until it reaches the upper limit. The optimal HTL condensation temperature increases initially and later remains unchanged for a cyclopentane system, thus keeping constant for other systems. Saturated cycle is suitable for cyclohexane, benzene, and toluene systems. Superheat cycle improves the net power output for a cyclopentane system when Tg1 is 568.15⁻623.15 K.