Crystal structure,phase transitions,and thermodynamic properties of magnesium metavanadate(MgV_(2)O_(6))

As a promising anode material for magnesium ion rechargeable batteries,magnesium metavanadate(MgV_(2)O_(6))has attracted considerable research interest in recent years.A MgV_(2)O_(6)sample was synthesized via a facile solid-state reaction by multistep-firing stoichiometric mixtures of MgO and V2O5 powder under an air atmosphere.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)occurred at 841 K and the enthalpy change was 4.37±0.04 kJ/mol.The endothermic effect at 1014 K and the enthalpy change was 26.54±0.26 kJ/mol,which is related to the incongruent melting ofβ-MgV_(2)O_(6).In situ XRD was performed to investigate phase transition of the as-prepared MgV_(2)O_(6)at high temperatures.The cell parameters obtained by Rietveld refinement indicated that it crystallizes in a monoclinic system with the C2/m space group,and the lattice parameters of a=9.280 A°,b=3.501 A°,c=6.731 A°,β=111.76°.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)was further studied by thermal kinetics,indicating that this process is controlled first by a fibril-like mechanism and then by a spherulitic-type mechanism with an increasing heating rate.Additionally,the enthalpy change of MgV_(2)O_(6)at high temperatures was measured utilizing the drop calorimetry,heat capacity was calculated and given as:Cp=208.3+0.03583T-4809000T^(−2)(298-923 K)(J mol^(−1)K^(−1)),the high-temperature heat capacity can be used to calculate Gibbs free energy of MgV_(2)O_(6)at high temperatures.

Recent progress in thermodynamic and kinetics modification of magnesium hydride hydrogen storage materials

Hydrogen energy has emerged as a pivotal solution to address the global energy crisis and pave the way for a cleaner,low-carbon,secure,and efficient modern energy system.A key imperative in the utilization of hydrogen energy lies in the development of high-performance hydrogen storage materials.Magnesium-based hydrogen storage materials exhibit remarkable advantages,including high hydrogen storage density,cost-effectiveness,and abundant magnesium resources,making them highly promising for the hydrogen energy sector.Nonetheless,practical applications of magnesium hydride for hydrogen storage face significant challenges,primarily due to their slow kinetics and stable thermodynamic properties.Herein,we briefly summarize the thermodynamic and kinetic properties of MgH2,encompassing strategies such as alloying,nanoscaling,catalyst doping,and composite system construction to enhance its hydrogen storage performance.Notably,nanoscaling and catalyst doping have emerged as more effective modification strategies.The discussion focuses on the thermodynamic changes induced by nanoscaling and the kinetic enhancements resulting from catalyst doping.Particular emphasis lies in the synergistic improvement strategy of incorporating nanocatalysts with confinement materials,and we revisit typical works on the multi-strategy optimization of MgH2.In conclusion,we conduct an analysis of outstanding challenges and issues,followed by presenting future research and development prospects for MgH2 as hydrogen storage materials.

Temperature-dependent solubility of Rebaudioside A in methanol/ethanol and ethyl acetate mixtures:Experimental measurements and thermodynamic modeling

The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The experimental findings indicate a positive correlation between the solubility of Reb A(FormⅡ)and both the temperature and the methanol/ethanol content in the solvent system.To describe the solubility data,six distinct models were employed:the modified Apelblat equation,theλh model,the combined nearly ideal binary solvent/Redlich—Kister(CNIBS/R—K)model,the van't HoffJouyban-Acree(VJA)model,the Apelblat-Jouyban-Acree(AJA)model,and the non-random two-liquid(NRTL)model.The combined nearly ideal binary solvent/Redlich—Kister model exhibited the most precise fit for solubility in methanol+ethyl acetate mixtures,reflected by an average relative deviation(ARD)of 0.0011 and a root mean square deviation(RMSD)of 12×10^(-7).Conversely,for ethanol+ethyl acetate mixtures,the modified Apelblat equation provided a superior correlation(ARD=0.0014,RMSD=4×10^(-7)).Furthermore,thermodynamic parameters associated with the dissolution of Reb A(FormⅡ),including enthalpy,entropy,and the Gibbs energy change,were inferred from the data.The findings underscore that the dissolution process is predominantly endothermic across the solvent systems examined.Notably,the entropy changes appear to have a significant influence on the Gibbs free energy associated with the dissolution of Reb A(FormⅡ),suggesting that entropic factors may play a pivotal role in the studied systems.

Composition optimization and performance prediction for ultra-stable water-based aerosol based on thermodynamic entropy theory

Water-based aerosol is widely used as an effective strategy in electro-optical countermeasure on the battlefield used to the preponderance of high efficiency,low cost and eco-friendly.Unfortunately,the stability of the water-based aerosol is always unsatisfactory due to the rapid evaporation and sedimentation of the aerosol droplets.Great efforts have been devoted to improve the stability of water-based aerosol by using additives with different composition and proportion.However,the lack of the criterion and principle for screening the effective additives results in excessive experimental time consumption and cost.And the stabilization time of the aerosol is still only 30 min,which could not meet the requirements of the perdurable interference.Herein,to improve the stability of water-based aerosol and optimize the complex formulation efficiently,a theoretical calculation method based on thermodynamic entropy theory is proposed.All the factors that influence the shielding effect,including polyol,stabilizer,propellant,water and cosolvent,are considered within calculation.An ultra-stable water-based aerosol with long duration over 120 min is obtained with the optimal fogging agent composition,providing enough time for fighting the electro-optic weapon.Theoretical design guideline for choosing the additives with high phase transition temperature and low phase transition enthalpy is also proposed,which greatly improves the total entropy change and reduce the absolute entropy change of the aerosol cooling process,and gives rise to an enhanced stability of the water-based aerosol.The theoretical calculation methodology contributes to an abstemious time and space for sieving the water-based aerosol with desirable performance and stability,and provides the powerful guarantee to the homeland security.

Thermodynamics-directed bulk/grain-boundary engineering for superior electrochemical durability of Ni-rich cathode

Introducing high-valence Ta element is an essential strategy for addressing the structu ral deterioration of the Ni-rich LiNi_(1-x-y)Co_(x)Mn_(y)O_(2)(NCM)cathode,but the enlarged Li/Ni cation mixing leads to the inferior rate capability originating from the hindered Li~+migration.Note that the non-magnetic Ti~(4+)ion can suppress Li/Ni disorder by removing the magnetic frustration in the transition metal layer.However,it is still challenging to directionally design expected Ta/Ti dual-modification,resulting from the complexity of the elemental distribution and the uncertainty of in-situ formed coating compounds by introducing foreign elements.Herein,a LiTaO_3 grain boundary(GB)coating and bulk Ti-doping have been successfully achieved in LiNi_(0.834)Co_(0.11)Mn_(0.056)O_(2) cathode by thermodynamic guidance,in which the structural formation energy and interfacial binding energy are employed to predict the elemental diffusion discrepancy and thermodynamically stable coating compounds.Thanks to the coupling effect of strengthened structural/interfacial stability and improved Li~+diffusion kinetics by simultaneous bulk/GB engineering,the Ta/Ti-NCM cathode exhibits outstanding capacity retention,reaching 91.1%after 400 cycles at 1 C.This elaborate work contributes valuable insights into rational dual-modification engineering from a thermodynamic perspective for maximizing the electrochemical performances of NCM cathodes.

Comparative analysis of thermodynamic and mechanical responses between underground hydrogen storage and compressed air energy storage in lined rock caverns

Underground hydrogen storage(UHS)and compressed air energy storage(CAES)are two viable largescale energy storage technologies for mitigating the intermittency of wind and solar power.Therefore,it is meaningful to compare the properties of hydrogen and air with typical thermodynamic storage processes.This study employs a multi-physical coupling model to compare the operations of CAES and UHS,integrating gas thermodynamics within caverns,thermal conduction,and mechanical deformation around rock caverns.Gas thermodynamic responses are validated using additional simulations and the field test data.Temperature and pressure variations of air and hydrogen within rock caverns exhibit similarities under both adiabatic and diabatic simulation modes.Hydrogen reaches higher temperature and pressure following gas charging stage compared to air,and the ideal gas assumption may lead to overestimation of gas temperature and pressure.Unlike steel lining of CAES,the sealing layer(fibre-reinforced plastic FRP)in UHS is prone to deformation but can effectively mitigates stress in the sealing layer.In CAES,the first principal stress on the surface of the sealing layer and concrete lining is tensile stress,whereas UHS exhibits compressive stress in the same areas.Our present research can provide references for the selection of energy storage methods.

TP-PROFILE: Monitoring the Thermodynamic Structure of the Troposphere over the Third Pole

Ground-based microwave radiometers(MWRs)operating in the K-and V-bands(20–60 GHz)can help us obtain temperature and humidity profiles in the troposphere.Aside from some soundings from local meteorological observatories,the tropospheric atmosphere over the Tibetan Plateau(TP)has never been continuously observed.As part of the Chinese Second Tibetan Plateau Scientific Expedition and Research Program(STEP),the Tibetan Plateau Atmospheric Profile(TPPROFILE)project aims to construct a comprehensive MWR troposphere observation network to study the synoptic processes and environmental changes on the TP.This initiative has collected three years of data from the MWR network.This paper introduces the data information,the data quality,and data downloading.Some applications of the data obtained from these MWRs were also demonstrated.Our comparisons of MWR against the nearest radiosonde observation demonstrate that the TP-PROFILE MWR system is adequate for monitoring the thermal and moisture variability of the troposphere over the TP.The continuous temperature and moisture profiles derived from the MWR data provide a unique perspective on the evolution of the thermodynamic structure associated with the heating of the TP.The TP-PROFILE project reveals that the low-temporal resolution instruments are prone to large uncertainties in their vapor estimation in the mountain valleys on the TP.

Thermodynamic theory of flotation for a complex multiphase solid -liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involve interactions among multiple components,the core problem facing flotation theory.Meanwhile,the combined use of multicomponent flotation reagents to improve mineral flotation has become an important issue in studies on the efficient use of refractory mineral resources.However,studying the flotation of complex solid–liquid systems is extremely difficult,and no systematic theory has been developed to date.In addition,the physical mechanism associated with combining reagents to improve the flotation effect has not been unified,which limits the development of flotation theory and the progress of flotation technology.In this study,we applied theoretical thermodynamics to a solid–liquid flotation system and used changes in the entropy and Gibbs free energy of the reagents adsorbed on the mineral surface to establish thermodynamic equilibrium equations that de-scribe interactions among various material components while also introducing adsorption equilibrium constants for the flotation reagents adsorbed on the mineral surface.The homogenization effect on the mineral surface in pulp solution was determined using the chemical potentials of the material components of the various mineral surfaces required to maintain balance.The flotation effect can be improved through synergy among multicomponent flotation reagents;its physical essence is the thermodynamic law that as the number of compon-ents of flotation reagents on the mineral surface increases,the surface adsorption entropy change increases,and the Gibbs free energy change of adsorption decreases.According to the results obtained using flotation thermodynamics theory,we established high-entropy flotation theory and a technical method in which increasing the types of flotation reagents adsorbed on the mineral surface,increasing the adsorption entropy change of the flotation reagents,decreasing the Gibbs free energy change,and improving the adsorption efficiency and stability of the flotation reagents improves refractory mineral flotation.

A thermodynamics-consistent spatiotemporally-nonlocal model for microstructure-dependent heat conduction

The spatiotemporally-nonlocal phenomena in heat conduction become significant but challenging for metamaterials with artificial microstructures.However,the microstructure-dependent heat conduction phenomena are captured under the hypothesis of spatiotemporally local equilibrium.To capture the microstructure-dependent heat conduction phenomena,a generalized nonlocal irreversible thermodynamics is proposed by removing both the temporally-local and spatially-local equilibrium hypotheses from the classical irreversible thermodynamics.The generalized nonlocal irreversible thermodynamics has intrinsic length and time parameters and thus can provide a thermodynamics basis for the spatiotemporally-nonlocal law of heat conduction.To remove the temporallylocal equilibrium hypothesis,the generalized entropy is assumed to depend not only on the internal energy but also on its first-order and high-order time derivatives.To remove the spatially local equilibrium hypothesis,the thermodynamics flux field in the dissipation function is assumed to relate not only to the thermodynamics force at the reference point but also to the thermodynamics force of the neighboring points.With the developed theoretical framework,the thermodynamics-consistent spatiotemporally-nonlocal models can then be developed for heat transfer problems.Two examples are provided to illustrate the applications of steady-state and transient heat conduction problems.

FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

View of thermodynamic phase transition of the charged Gauss-Bonnet AdS black hole via the shadow

We examine thermodynamic phase transition(PT)of the charged Gauss-Bonnet Ad S black hole(BH)by utilizing the shadow radius.In this system,we rescale the corresponding Gauss-Bonnet coefficientαby a factor of 1/(D-4),and ensure thatαis positive to avoid any singularity problems.The equation derived for the shadow radius indicates that it increases as the event horizon radius increases,making it an independent variable for determining BH temperature.By investigating the PT curve in relation to shadows,we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT.Furthermore,the results indicate that an increase in the parameterαcorresponds to a decrease in the temperature of the BH.By utilizing the relationship between the temperature and the shadow radius,it is possible to obtain the thermal profile of the Gauss-Bonnet AdS BH.It is evident that there is an N-type variation in temperature for pressures P<P_(c).Additionally,as the parameterαincreases,the region covered by shadow expands while the temperature decreases.The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.

Homochiral metalated tetraphenylethylene-based organic cages: Unusual chiral and luminescent behavior depending on thermodynamic and kinetic aggregation

Chirality and luminescence are important for both chemistry and biology,which are highly influenced by aggregation.In this work,a pair of metalated tetraphenylethylene(TPE)-based organic cage enantiomers are reported,which fea-ture a quadrangular prismatic cage structure.These homochiral cages exhibit concentration-dependent chiral behaviors alongside a propensity for thermodynamic aggregation.Aggregation caused quench effect is found for these cages accom-panying the increasing of the concentrations.When a poor solvent is added to produce a kinetical aggregation,the aggregation-annihilation circular dichroism and aggregation-induced emission behaviors are observed for these enantiomeric cages.By comparing these observations with the photophysical behaviors of a pair of structurally similar organic molecular enantiomers,the unique photophysical proper-ties observed are intricately linked to the metal-integrated TPE-functionalized cage structures.

Improving hydrogen storage thermodynamics and kinetics of Ce-Mg-Ni-based alloy by mechanical milling with TiF_(3)

Mg-based hydrides are too stable and the kinetics of hydrogen absorption and desorption is not satisfactory.An efficient way to improve these shortcomings is to employ reactive ball milling to synthesize the nanocomposite materials of Mg and additives.In this experiment,TiF_(3)was selected as an additive,and the mechanical milling method was employed to prepare the experimental alloys.The alloys used in this experiment were the as-cast Ce_(5)Mg_(85)Ni_(10),as-milled Ce_(5)Mg_(85)Ni_(10)and Ce_(5)Mg_(85)Ni_(10)+3 wt.%TiF3.The phase transformation,structural evolution,isothermal and non-isothermal hydrogenation and dehydrogenation performances of the alloys were inspected by XRD,SEM,TEM,Sievert apparatus,DSC and TGA.It revealed that nanocrystalline appeared in the as-milled samples.Compared with the as-cast alloy,ball milling made the particle dimension and grain size decrease dramatically and the defect density increase significantly.The addition of TiF_(3)made the surface of ball milling alloy particles markedly coarser and more irregular.Ball milling and adding TiF_(3)distinctly improved the activation and kinetics of the alloys.Moreover,ball milling along with TiF_(3)can decrease the onset dehydrogenation temperature of Mg-based hydrides and slightly ameliorate their thermodynamics.

Thermodynamic model for deoxidation of liquid steel considering strong metal-oxygen interaction in the quasichemical model framework

Herein,a thermodynamic model aimed at describing deoxidation equilibria in liquid steel was developed.The model provides explicit forms of the activity coefficient of solutes in liquid steel,eliminating the need for the minimization of internal Gibbs energy preliminarily when solving deoxidation equilibria.The elimination of internal Gibbs energy minimization is particularly advantageous during the coupling of deoxidation equilibrium calculations with computationally intensive approaches,such as computational fluid dynamics.The model enables efficient calculations through direct embedment of the explicit forms of activity coefficient in the computing code.The proposed thermodynamic model was developed using a quasichemical approach with two key approximations:random mixing of metallic elements(Fe and oxidizing metal) and strong nonrandom pairing of metal and oxygen as nearest neighbors.Through these approximations,the quasichemical approach yielded the activity coefficients of solutes as explicit functions of composition and temperature without requiring the minimization of internal Gibbs energy or the coupling of separate programs.The model was successfully applied in the calculation of deoxidation equilibria of various elements(Al,B,C,Ca,Ce,Cr,La,Mg,Mn,Nb,Si,Ti,V,and Zr).The limitations of the model arising from these assumptions were also discussed.

Parameterization, sensitivity, and uncertainty of 1-D thermodynamic thin-ice thickness retrieval

Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.

Solvation dynamics of furazolidone in pure organic solvents and aqueous EDTA disodium salt mixtures:molecular interactions and thermodynamic insights

This study systematically examined the dissolution behavior of furazolidone in 12 different pure solvents and in aqueous solutions containing ethylenediaminetetraacetic acid disodium salt(EDTA-2Na).The solubility data indicated that polar aprotic solvents demonstrated a marginally higher solubility of furazolidone compared to alcohols and water.Interestingly,a co-solvency effect was observed in the aqueous solutions of EDTA-2Na,where the solubility of furazolidone initially increased and then decreased with the gradual addition of EDTA-2Na,peaking at a mass fraction of 0.03(1.949×10^(–5)at 323.15 K).The analysis using the Kamlet-Abboud-Taft Linear Solvation Energy Relationship(KAT-LSER)model suggested that the dissolution of furazolidone in these systems was predominantly influenced by non-specific solute-solvent and solvent-solvent interactions.Furthermore,Hansen solubility parameter calculations revealed that N,N-dimethylformamide(DMF)and N,N-dimethylacetamide(DMAC)exhibited superior dissolution capabilities compared to other solvents.It was also found that the partial solubility parameters played a crucial role in determining the overall solubility behavior.

A thermodynamic view on the in-situ carbon dioxide reduction by biomass-derived hydrogen during calcium carbonate decomposition

In the carbonate industry,deep decarbonization strategies are necessary to effectively remediate CO_(2).These strategies mainly include both sustainable energy supplies and the conversion of CO_(2)in downstream processes.This study developed a coupled process of biomass chemical looping H2 production and reductive calcination of CaCO_(3).Firstly,a mass and energy balance of the coupled process was established in Aspen Plus.Following this,process optimization and energy integration were implemented to provide optimized operation conditions.Lastly,a life cycle assessment was carried out to assess the carbon footprint of the coupled process.Results reveal that the decomposition temperature of CaCO_(3)in an H_(2)atmosphere can be reduced to 780℃(generally around 900℃),and the conversion of CO_(2)from CaCO_(3)decomposition reached 81.33%with an H2:CO ratio of 2.49 in gaseous products.By optimizing systemic energy through heat integration,an energy efficiency of 86.30%was achieved.Additionally,the carbon footprint analysis revealed that the process with energy integration had a low global warming potential(GWP)of-2.624 kg·kg^(-1)(CO_(2)/CaO).Conclusively,this work performed a systematic analysis of introducing biomass-derived H_(2)into CaCO_(3)calcination and demonstrated the positive role of reductive calcination using green H_(2)in mitigating CO_(2)emissions within the carbonate industry.

Thermodynamics in a quantum corrected Reissner-Nordstr?m-AdS black hole and its GUP-corrections

We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.

Two innovative equivalent statements of the third law of thermodynamics

It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.

A New Class of Simple,General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems

In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.