Lithium-ion Batteries In Electric Vehicles Research Articles

A fuzzy adaptive sliding-mode-based SoC estimation for lithium-ion batteries in electric vehicles

A fuzzy adaptive sliding-mode-based SoC estimation for lithium-ion batteries in electric vehicles

Viable Alternatives to Lithium-Based Batteries

Developing sustainable and environmentally friendly energy storage technologies for electric vehicles has become increasingly important with the growing demand for electric vehicles and increasing climate concerns. Lithium-ion batteries have been the primary energy storage technology used in electric vehicles due to their high energy density, long cycle life, and relatively low cost compared to other options. However, safety concerns related to the flammability of liquid electrolytes have motivated research on alternative energy storage technologies, mainly Sodium-ion and solid-state batteries. This paper reviews the status of sodium-ion and solid-state batteries as viable alternatives to lithium-ion batteries for electric vehicles. Sodium-ion batteries have shown promising results regarding energy density, safety, and cost but face challenges related to their lower specific energy and power density. Solid-state batteries have the potential to overcome many of the safety concerns associated with liquid electrolytes and exhibit high energy density but are currently limited by their high cost and low cycle life.

The influence of tab overheating on thermal runaway propagation of pouch-type lithium-ion battery module with different tab connections

Thermal runaway (TR) of lithium-ion batteries is the main safety obstacle to the further development of electric vehicles (EVs) and electric energy storage systems (EESSs). Understanding the mechanism of TR propagation is one of the primary ways to improve the thermal safety of the lithium-ion battery. In this paper, an electro-thermal model coupled with the lumped thermal runaway model is applied to investigate the TR behaviors induced by tab overheating and the TR propagation in a battery module with different tab connection methods. The electro-thermal model is used to calculate the heat generation at tabs and the cell body during the normal charge/discharge process, and the lumped thermal runaway model is applied to calculate the TR behavior and TR propagation in the battery module. The results exhibit that the TR behavior and TR propagation are influenced by different aspects (C-rates, insulator, and tab connection modes) in the battery module. The largest quantity of heat generation is at 3C-rate, about 0.98 kJ, because of the heat accumulation in the battery. Besides, the quantity of heat generation that induce TR in lithium-ion batteries in this paper is lower than that from the reference, which means that tab overheating is more dangerous than other heating strategies for triggering the thermal runaway of batteries. The trigger time of TR decreases with the increasing C-rate and the tab connection modes mitigate the TR propagation in the battery module at a low C-rate because of the increasing heat dissipation rate, while the TR propagation is accelerated in the battery module at a high C-rate. At low C-rate conditions, the parallel tab connection exhibits a more significant effect on mitigating the TR behavior, and the effect of mitigation decreases with the increasing C-rate. At high C-rate conditions, the series tab connection accelerates the TR propagation to the adjacent battery, while the parallel tab connection speeds up the TR propagation of all the connected batteries. This work is important for understanding the TR propagation mechanism and improving the thermal safety of pouch-type lithium-ion batteries in EVs.

Effect of mechanical vibration on phase change material based thermal management system for a cylindrical lithium-ion battery at high ambient temperature and high discharge rate

The performance and safety of lithium-ion batteries (LIB) in electric vehicles (EV) depend strongly on the operating temperature, so an effective battery thermal management system (BTMS) is essential. Battery thermal management (BTM) technology based on phase change material (PCM) is currently considered to be one of the most promising approaches. Electric vehicles are inevitably affected by vibration during operation, and many studies have shown that mechanical vibration can enhance natural convection heat transfer. The effect of mechanical vibration on the PCM-based battery thermal management module of a single cylindrical lithium-ion battery at high ambient temperature and high discharge rate is studied by numerical simulation for the first time in this paper. N-octadecane is selected as the PCM application in the cylindrical battery's periphery. The results show that: (1) mechanical vibration enhances the heat transfer of natural convection to limit the excessive temperature rise and improve temperature uniformity of the lithium-ion battery, and when the PCM is 12 mm, the mechanical vibration has the most significant impact on the PCM-based BTMS (2) when the vibration frequency is 10 Hz, the cooling effect of the battery thermal management module is the best, which is 28.05% lower than when there is no vibration. when the vibration frequency is 50 Hz, the temperature uniformity of the battery is the best, with a maximum temperature difference of 3.86 K. (3) when the vibration amplitude is 100 mm, the maximum temperature difference of the battery is 1.89 K, and the maximum temperature decreases by 27.74%. This study provides a new perspective for the thermal management system of lithium-ion batteries for electric vehicles.

Analysis and Estimation of Internal Temperature Characteristics of Lithium-Ion Batteries in Electric Vehicles

To avoid thermal runaway in battery packs, it is necessary to estimate the internal temperature. Herein, the relationship between measurable electrical parameters and adjustable electrochemical parameters is first studied. Then, adjustable electrochemical parameters at different temperatures are rapidly calibrated. Based on this, an electrochemical-thermal coupling model is proposed. Second, the internal temperature field distribution is analyzed by the coupling model. It is found that the gradient of the radial temperature distribution is greater than that in the axial direction. Third, a radial thermodynamic reduced-order model is developed. The thermal parameters are calculated by the combination of the direct method and Variable Forgetting Factor Recursive Least Square (VFFRLS) algorithm. Finally, an internal temperature estimator based on the Kalman Filter algorithm is produced. Results show that the maximum estimated error is only 1.57 K under different working conditions. Furthermore, the results also validate the feasibility of thermal parameters obtained algorithm.

Online Parameter Identification for Lithium-Ion Batteries: An Adaptive Moving Window Size Design Methodology for Least Square Fitting

Online state-of-charge estimations are critical to lithium-ion batteries in electric vehicles for safe and reliable operations. To ensure accurate online state estimations, an online battery parameter identification algorithm, such as the least square fitting approach, along with a shifting moving window, was developed and implemented, while the decision of the moving window size for general purpose is a technical issue not yet been well-addressed. This paper proposes an adaptive moving window size design methodology that adjusts the moving window size considering three important factors: load profile, state-of-charge to open-circuit voltage profile, and condition of data. The simulation results show that the proposed methodology helps to identify the parameters of the battery electric circuit model with high accuracy, where the results are compatible to the results using fine-tuned fixed window sizes. Also, the proposed methodology is general to driving profiles from moderate to severe without extra algorithm redesign. In the three standard driving profile cases, the parameter identification error is reduced by 59.15%, 69.02%, and 75.14%, respectively, compared to the worst case in experiments, which are compatible with the results after fine-tuning the fixed window sizes. With accurately identified parameters, the modeling error is minimized, and three typical linear SOC estimation algorithms thus render accurate SOC estimation, rendering an average of 13.4%, 64.43% 57.48% reduction from the worst case in experiments, respectively.

Sensor fault diagnosis modeling of lithium-ion batteries for electric vehicles

Electric Vehicles (EVs) are considered the replacement for gas-emitting and environmentally polluting fuel vehicles. The development of EVs relies on electronic devices and communication circuits for ease of access. The heart of EVs is the battery that requires post-run-time charging and precise maintenance. Electronic sensors attached to the batteries monitor their health, discharging, and charging rate for user notification and prolonged functioning. Therefore, the operation of the sensors is to be monitored promptly for effective battery maintenance. This article introduces a Fault Detection Method (FDM) using Operational Data (OD) accumulated from the EV. This data is first split into active and passive that references the run-time and idle time of the vehicle. The sensor operations during the idle time are considered similar due to minimal or no sensing function. Contrarily the run-time observation shows up variations that are not huge compared to the previous history. In this data verification process, recurrent learning is employed for identifying variations in the active and passive states of the EVs. If variations are continuous regardless of the active and passive states, then the sensor is identified as faulty post the manual battery life assessment. The learning is trained using the current and previous sensor observations and batter health for identifying the variations.

Comments: Pricing Index Launched for “Black Mass”

As an indicator of the evolving global energy marketplace, recycled battery metals just earned their own spot pricing assessments for China and Europe. S&P Global Commodity Insights launched nine new daily “black mass” evaluations last month “to bring greater transparency to pricing of the battery raw materials market.” These complement its existing suite of daily battery metals assessments. The hunt is ongoing, and escalating, for virgin sources of metals such as lithium, manganese, cobalt, and nickel for use in lithium-ion batteries ranging from those in watches and devices to utility-scale storage, electric vehicles (EVs), and oil- and gas-related applications. In this issue of JPT, the use of oilfield technologies in deep-sea mining for these metals is highlighted. An ExxonMobil researcher, M. Stanley Whittingham, created the first examples of the rechargeable lithium-ion battery in the 1970s. He and two other researchers were awarded the 2019 Nobel Prize in Chemistry for the development of these batteries. For decades, lithium-ion batteries have been used in oil- and gas-related applications such as downhole tools related to drilling, measurement, testing, wireline, and well intervention. They can operate under extreme conditions and temperatures (from 220°C to –50°C, in the deep subsea) and are safe in potentially inflammable and explosive environments. Their long operation life and reliability are vital because of the high costs associated with downhole battery failures. More familiar to many is the use of lithium-ion batteries in EVs. The annual demand for EV batteries (in kilotonnes) is forecast to more than double from 2019 to 2030, according to the International Energy Agency’s Global EV Outlook 2020. The increased demand is due largely to their high energy density. They hold more energy in a smaller area than other types of batteries. New technologies enable the recovery and reuse of core components when these batteries reach the end of their useful lives. The battery pack can be collected, dismantled, and shredded. The shredded material is then processed to produce so-called “black mass” from which these high-value critical metals can be extracted and reused in new battery production. Although the demand is expected to mushroom, the global supply of these metals is finite. Their mining is energy- and labor-intensive. Mining the ore creates environmental effects such as land disruption and emissions; refining brine yields lower-grade lithium and recovers less of the metal present than is recovered from ore. Mining in Chile, a major lithium exporter, consumes 65% of the country’s water. In September 2022, the American Chemical Society estimated only 5% of the world’s lithium-ion batteries were recycled from the projected 8 million tons of waste. S&P Global expects recycled battery materials to make up an increasing share of the supply chain well beyond 2030. The potential availability of recycled materials would account for 30% of nickel, 27% of lithium, and 40% of cobalt demand between 2020 and 2050. Recycled metals have the potential to be cheaper than their virgin equivalents and provide supply in regions that do not have the natural resources available. In addition to reducing the need for virgin materials, recycling/reuse reduces the carbon emissions associated with new mining activities. But recycling of spent lithium-ion batteries, as a relatively nascent process, has its problems. Both physical and chemical processes are involved. Physical processes include pretreatment and recovery of electrode materials which include disassembly, crushing, screening, magnetic separation, washing, and heating treatment. Chemical processes involve leaching, separation, extraction, and chemical/electrochemical precipitation. Challenges remain to achieve the required “perfect” recovery in terms of safety, low cost, low energy consumption, and no pollution. Another challenge is to convince carmakers to use recycled materials. In an IEEE Spectrum article, Yan Wang, a professor of mechanical engineering at Worcester Polytechnic Institute, said, “Battery companies still hesitate to use recycled material in their batteries.” A study by Wang and researchers from the US Advanced Battery Consortium and A123 Systems, a battery company, concluded, “it becomes clear that recycled materials can be as good as or even better than the high-quality control materials.” As with most rapidly advancing technologies and processes, the concept must be proven, and the economics must make sense to increase widespread adoption. In the circular economy, the recycling and reuse of these high-value, limited-resource metals have the potential to be a shining star.

Research on pulse charging current of lithium-ion batteries for electric vehicles in low-temperature environment

The scale of the electric vehicle (EV) industry is expanding in the current new energy industry reform. Lithium-ion batteries (LIBs) have also gotten a lot of interest as the power source for EVs. However, the safety and remaining life of LIB are highly tied to the charging strategy adopted. Particularly, fast charging at low temperatures can cause lithium to deposit on the anode of the battery, intensifying heat production and even evolving into thermal runaway of the battery. Based on the simplified battery Alternating current (AC) impedance model, the optimal frequency of pulse current is analyzed. Considering the influence of state of charge (SOC) and temperature on the battery impedance, a three-dimensional response surface about the optimal frequency, temperature and SOC was established using Mendeley data. To simulate LIB pulse strategy charging in a cold environment, the equivalent circuit model (ECM) is coupled with a simple battery heating model. The three-dimensional response surface is employed to instantly determine the pulse frequency. The simulation results demonstrate that both the bi-directional pulse current charging strategy with optimal frequency and the positive pulse current charging strategy with optimal frequency have faster charging time and better temperature rise effect than the constant current (CC) charging strategy, and can significantly eliminate the polarization voltage of the battery at low temperatures.

State of Charge Estimation of Lithium-ion Battery in Electric Vehicles Using the Smooth Variable Structure Filter: Robustness Evaluation against Noise and Parameters Uncertainties

State of Charge (SoC) of Lithium-ion battery is a key parameter in battery management systems for electric vehicles. This paper uses the fundamental theory of the smooth variable structure filter (SVSF) and proposes a SoC estimation algorithm for a Manganese Cobalt (NMC) cell with a nominal capacity of 20 Ah. Several tests are conducted considering different types of noise and parameters variation. A nonrandom Gaussian noise is first added to the battery voltage. The maximum root mean square error (RMSE) of the estimated SoC is about for a standard deviation of the noise set to P.U. The same noise is applied to the battery current and the maximum RMSE of the SoC is obtained as 1.36%. Moreover, an EMI noise is added to the battery voltage and the obtained RMSE of the SoC is about 1.73% for a peak amplitude of the noise set to 0.07 P.U. The convergence of the algorithm is also confirmed under battery parameters variation due to the temperature change. However, its accuracy degrades considerably. Finally, a comparative study is carried out with the extended Kalman filter and shows the superiority of SVSF in terms of accuracy and robustness against measurement noise.

State-of-Charge and State-of-Health variable-gain estimation based on tracking sliding mode differentiators for an electric vehicle Lithium-ion battery

In this paper, new methods to provide on-line measures of the State-of-Charge and State-of-Health of Lithium-ion batteries intended for vehicular applications are presented. The proposal is based on an estimation methodology formulated to determine, and accurately track the variations of the time-varying parameters of an equivalent electric circuit model employed for system modelling during vehicle operation.The proposed Lithium-ion battery parameter estimation method successfully combines recently developed differentiation techniques, i.e. high-order Tracking Sliding Mode differentiators, with a recursive least squares with forgetting factor algorithm, that includes a variable-gain specifically designed for this application. The parameter estimates are employed to efficiently compute the evolution of the State-of-Charge and the State-of-Health.Finally, to assess the algorithms performance, in-silico evaluations are conducted utilising power profiles taken from standardised driving cycles.

Review on Thermal Management of Lithium-Ion Batteries for Electric Vehicles: Advances, Challenges, and Outlook

Due to strict regulations and the requirement to reduce greenhouse gas emissions, electric vehicles (BEVs) are a promising mode of transportation. The lithium battery is the most important power source for an electric vehicle, but its performance and life are greatly restricted by temperature. To ensure the safety of automobile operation and alleviate mileage anxiety, it is urgent to understand the current situation and predict the development and challenge of battery thermal management system. This work reviews the existing thermal management research in five areas, including cooling and heating methods, modeling optimization, control methods, and thermal management system integration for lithium batteries. Battery thermal management types include air-based, liquid-based, PCM-based, heat-pipe-based, and direct cooling. Designing a better battery thermal management system not only needs to be optimized using algorithms on the model but also it uses intelligent algorithms for precise control to achieve safety and reduce energy consumption. This work also reviews the differences in thermal management systems between square and cylindrical batteries and summarizes the development trend of modularity in battery thermal management systems.

Toward Improving the Thermal Stability of Negative Electrode Materials: Differential Scanning Calorimetry and In Situ High-Temperature X-ray Diffraction/X-ray Absorption Spectroscopy Studies of Li2ZnTi3O8 and Related Compounds

Negative electrode materials with high thermal stability are a key strategy for improving the safety of lithium-ion batteries for electric vehicles without requiring built-in safety devices. To search for crucial clues into increasing the thermal stability of these materials, we performed differential scanning calorimetry (DSC) and in situ high-temperature (HT)-X-ray diffraction (XRD)/X-ray absorption (XAS) up to 450 °C with respect to a solid-solution compound of Li4/3-2x/3ZnxTi5/3-x/3O4 with 0 ≤ x ≤ 0.5. The DSC profile of fully discharged x = 0.5 (Li2ZnTi3O8) with a LiPF6-based electrolyte could be divided into three temperature (T) regions: (i) T ≤ 250 °C for ΔHaccumi, (ii) 250 °C < T ≤ 350 °C for ΔHaccumii, and (iii) T > 350 °C for ΔHaccumiii, where ΔHaccumn is the accumulated change in enthalpy in region n. The HT-XRD/XAS analyses clarified that ΔHaccumi and ΔHaccumii originated from the decomposition of solid electrolyte interphase (SEI) films and the formation of a LiF phase, respectively. Comparison of the DSC profiles with x = 0 (Li[Li1/3Ti5/3]O4) and graphite revealed the operating voltage, i.e., amount of SEI films, and stability of the crystal lattice play significant roles in the thermal stability of negative electrode materials. Indeed, the highest thermal stability was attained at x = 0.25 using this approach.

Optimization Strategies for Lithium-Ion Batteries in Practical Electric Vehicles

As the environmental pollution caused by traditional fuel cars is becoming increasingly serious, electric vehicles (EVs) driven by green energy have become a new trend, and there is a growing demand for the energy source. Lithium-ion batteries (LIBs), the most widely used type, have become the ideal power source for practical EVs. However, although the superiorities of LIBs make them stand out in a crowd of EVs, several shortcomings still have not been solved, which hinder the further development of EVs to a certain extent. Firstly, this paper will briefly analyze the two most commonly used LIBs in EV at present- lithium iron phosphate and ternary lithium batteries. Secondly, the superiorities of the two types of batteries in performance, cost and fabrication will be pointed out separately. Considering the batteries' shortcomings and according to relevant professional literature, there will be detailed optimization strategies for electrodes and electrolytes as well as a description of recent advances in LIBs for EVs.

A bibliometric analysis of lithium-ion batteries in electric vehicles

As the ideal energy storage device, lithium-ion batteries (LIBs) are already equipped in millions of electric vehicles (EVs). The complexity of this system leads to the related research involving all aspects of LIBs and EVs. Therefore, the research hotspots and future research directions of LIBs in EVs deserve in-depth study. A bibliometric analysis is conducted according to the SCI-Expanded database in the Web of Science Core Collection. From 1993 to 2022, a total of 5187 articles or review articles related to LIBs and EVs have been published. The visualization means of geographical tool, software VOSviewer and CiteSpace help to visualize the structure network. The annual publications, countries, institutions, authors, terms, and references of the retrieved publications and the relation between them are analyzed comprehensively. This paper quantitatively analyzes the development tendency of LIBs in EVs, which provides experienced reference for researchers who want to engage in this domain.

Evaluating strategies for managing resource use in lithium-ion batteries for electric vehicles using the global MATILDA model

The exponential increase in lithium-ion battery (LIB) demand for electric vehicles (EVs) has sparked material supply concerns, which makes the understanding of the LIB system and its drivers a pertinent issue. To understand the uncertainty and sensitivity around these drivers, we introduce the MATerIaL Demand and Availability (MATILDA) model. We investigate resource use within the global LIB cycle in the context of EVs and the potential secondary material supply generated by alternative scenarios. Using this dynamic, multi-layer material flow analysis model, we conducted a detailed, time-explicit sensitivity analysis to broaden our understanding of the critical factors affecting resource supply. We identified potential problem shifts between Co, P, Ni, and Li and evaluated alternative strategies to mitigate their criticality over time. We show that social paradigm shifts such as using fewer, smaller vehicles as well as technological developments can play an important role in enabling a sustainable transition.

A Sensitivity Study of a Thermal Propagation Model in an Automotive Battery Module

Thermal runaway is a major concern for lithium-ion batteries in electric vehicles. A manufacturing fault or unusual operating conditions may lead to this event. Starting from a single battery cell, more cells may be triggered into thermal runaway, and the battery pack may be destroyed. To prevent this from happening, safety solutions need to be evaluated. Physical testing is an effective, yet costly, method to assessing battery safety performance. As such, the potential of a numerical tool, which can cut costs and reduce product development times, is investigated in terms of capturing a battery module’s tolerance to a single cell failure. A 3D-FE model of a battery module was built, using a commercial software, to study thermal runaway propagation. The model assumes that when the cell jelly roll reaches a critical value, thermal runaway occurs. This approach was considered to study the module’s tolerance to a single cell failure, which was in reasonable agreement with what had been observed in full-scale experiments. In addition, quantitative sensitivity study on the i) model input parameters, ii) model space, and iii) time resolutions on the computed start time instant and time duration of thermal runaway were performed. The critical temperature was found to have the greatest influence on thermal runaway propagation. The specific heat capacity of jelly roll was found to significantly impact the thermal runaway time duration. The multi-physics model for battery thermal propagation is promising and worth to be applied with care for designing safer batteries in combination with physical testing.

Electric Vehicle Lithium-ion Battery Ageing Analysis under Dynamic Condition: A Machine Learning Approach

Currently, the smart cities, smart vehicles, and smart gadgets will improve the way of living standard. Cloud connectivity of IoT sensed devices will capture real-time data in the cloud which helps to improve the system performance and quick response to queries. Electric Vehicle battery health diagnosis plays an important role in the proper functioning of the battery management system, guarantees safety, and warranty claim. Society 5.0 develops with the advancement in the road, infrastructure, better connectivity, transportation, and options available to purchase. Battery health cannot be measured directly. There are internal and external factors that affect battery health such as State of Charge, model parameters, charging/discharging method, temperature, Depth of Discharge, C-rate, battery chemistry, form factor, thermal management, and load change effect. Battery degrades due to both calendar ageing and cyclic ageing. Artificial Intelligence plays a significant role in Battery management system due to the nonlinear behavior of lithium-ion battery. Prediction of battery health accurately and in due time will reduce the risk of recklessness. Timely maintenance will reduce the risk of fatal accidents. This paper presents different batteries analysis under different discharge voltage and capacity conditions. Different machine learning algorithms such as Neural Network, Modified Support Vector Machine (M-SVM) and Linear Regression are used to predict state of health. The proposed M-SVM performs well with less error for all four-battery discharge data.

State of charge estimation of ternary lithium-ion batteries at variable ambient temperatures

Among the factors that affect lithium-ion batteries, ambient temperature has a great influence on the charge and discharge rate, general battery performance, and storage capacity of the battery, hence accurate state of charge (SOC) estimation over a wide range of temperatures is essential and necessary. In this paper, a Second-order Thevenin equivalent circuit model is established with ambient temperature compensation over varying ambient temperature conditions. An improved Fixed Range Forgetting Factor-Adaptive Extended Kalman Filtering (FRFF-AEKF) algorithm with the Saga-Husa Adaptive filter (SHAF) is proposed for the accurate estimation of SOC at variable ambient temperature. The temperatures −10°C, 10 °C, 25 °C, and 40 °C are set to depict low, normal, and high ambient temperatures in which lithium-ion batteries in electric vehicles (EVs) and most electronic devices usually operate. Tests conducted include the hybrid pulse power characterization (HPPC) for obtaining data required for parameterization, and for SOC estimation and verification, the Beijing Bus Dynamic stress (BBDST). The object of the tests was a ternary lithium-ion battery representing those used in electric vehicles (EVs). To improve adaptability, reduced noise, and achieve faster convergence with increased accuracy, the range of forgetting factor is fixed between a variable range of 0.997–1. To verify the performance of the proposed algorithm under varying conditions and different ambient temperatures, the SOC estimation result was compared with that of the adaptive extended Kalman filtering (AEKF) algorithm. The results show that the proposed improved algorithm implemented with the established Second-order Thevenin equivalent model has a 1.1 % better estimation accuracy compared to the results of the AEKF algorithm. This confirms that the proposed method can achieve accurate SOC estimation and is adaptive to variable ambient temperatures.

Performance evaluation with orthogonal experiment method of drop contact heat dissipation effects on electric vehicle lithium-ion battery

In order to solve the heat dissipation problem of lithium-ion power battery, a novel heat dissipation structure for lithium-ion power battery is proposed in this work, which is a drip contact heat dissipation method with transformer oil as the cooling medium. The effects of drip flow rate, drip temperature and drip position on the maximum temperature, temperature difference and energy consumption of a battery pack are investigated. The optimal scheme is obtained with orthogonal experimental design and the structure is then further optimized by the flow rate at the drip position adjustments. The results implicate that the optimal scheme is got when the drip flow rate, drip temperature of liquid are taken as 7 mL/min, 303.15 K with the drip position I at the battery cell center. The optimal structure conditions is the ratio of the liquid flow rate of the outermost ring to the inner of 0.4275:0.5725. The maximum temperature and the maximum temperature difference of the battery pack are lower than those before optimization when the battery pack are discharged in 1C, 1.5C and 2C.The time required to reach the maximum temperature of 313.15 K is increased.