scholarly journals Completeness of Classical Thermodynamics: The Ideal Gas, the Unconventional Systems, the Rubber Band, the Paramagnetic Solid and the Kelly Plasma

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 398 ◽  
Author(s):  
Karen Arango-Reyes ◽  
Gonzalo Ares de Parga
Keyword(s):  
Equations Of State ◽  
Fundamental Equation ◽  
Rubber Band ◽  
Thermodynamic System ◽  
Ideal Gas ◽  
Entropy Method ◽  
Complete Set ◽  
Classical Thermodynamics ◽  
Original Approach ◽  
The Ideal

A method is developed to complete an incomplete set of equations of state of a thermodynamic system. Once the complete set of equations is found, in order to verify the thermodynamic validity of a system, the Hessian and entropy methods are exposed. An original approach called the completeness method in order to complete all the information about the thermodynamic system is exposed. The Hessian method is improved by developing a procedure to calculate the Hessian when it is not possible to have an expression of the internal energy as a fundamental equation. The entropy method is improved by showing how to prove the first-degree homogeneous property of the entropy without having a fundamental expression of it. The completeness method is developed giving a total study of the thermodynamic system by obtaining the set of independent T d S equations and a recipe to obtain all the thermodynamics identities. In order to show the viability of the methods, they are applied to a typical thermodynamic system as the ideal gas. Some well-known and unknown thermodynamic identities are deduced. We also analyze a set of nonphysical equations of state showing that they can represent a thermodynamic system, but in an unstable manner. The rubber band, the paramagnetic solid and the Kelly equation of state for a plasma are corrected using our methods. In each case, a comparison is made between the three methods, showing that the three of them are complementary to the understanding of a thermodynamic system.

scholarly journals Modification of the Electron Entropy Production in a Plasma

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 935
Author(s):  
Juan F. García-Camacho ◽  
Gonzalo Ares de Parga ◽  
Karen Arango-Reyes ◽  
Encarnación Salinas-Hernández ◽  
Samuel Domínguez-Hernández
Keyword(s):  
Entropy Production ◽  
Equations Of State ◽  
Hermite Polynomials ◽  
Ideal Gas ◽  
Modified Equations ◽  
Modified Entropy ◽  
The Ideal

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1…rm(m) by means of the irreducible tensorial Hermite polynomials.

Temperature and heat

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Equations Of State ◽  
Open Systems ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Heat Energy ◽  
Conservation Of Energy ◽  
Temperature Scales ◽  
Ideal Gas Law ◽  
Molecular Interpretation ◽  
The Ideal

Concepts of temperature, temperature scales and temperature measurement. The ideal gas law, Dalton’s law of partial pressure. Assumptions underlying the ideal gas, and distinction between ideal and real gases. Introduction to equations-of-state such as the van der Waals, Dieterici, Berthelot and virial equations, which describe real gases. Concept of heat, and distinction between heat and temperature. Experiments of Rumford and Joule, and the principle of the conservation of energy. Units of measurement for heat. Heat as a path function. Flow of heat down a temperature gradient as an irreversible and unidirectional process. ‘Zeroth’ Law of Thermodynamics. Definitions of isolated, closed and open systems, and of isothermal, adiabatic, isobaric and isothermal changes in state. Connection between work and heat, as illustrated by the steam engine. The molecular interpretation of heat, energy and temperature. The Boltzmann distribution. Meaning of negative temperatures.

On a Scale-Invariant Model of Statistical Mechanics and the Laws of Thermodynamics

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Statistical Mechanics ◽  
Thermal Energy ◽  
Thermodynamic System ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Scale Invariant ◽  
Invariant Model ◽  
Definition Of ◽  
Classical Thermodynamics ◽  
Total Thermal Energy

A scale-invariant model of statistical mechanics is applied to describe modified forms of zeroth, first, second, and third laws of classical thermodynamics. Following Helmholtz, the total thermal energy of the thermodynamic system is decomposed into free heat U and latent heat pV suggesting the modified form of the first law of thermodynamics Q = H = U + pV. Following Boltzmann, entropy of ideal gas is expressed in terms of the number of Heisenberg–Kramers virtual oscillators as S = 4 Nk. Through introduction of stochastic definition of Planck and Boltzmann constants, Kelvin absolute temperature scale T (degree K) is identified as a length scale T (m) that is related to de Broglie wavelength of particle thermal oscillations. It is argued that rather than relating to the surface area of its horizon suggested by Bekenstein (1973, “Black Holes and Entropy,” Phys. Rev. D, 7(8), pp. 2333–2346), entropy of black hole should be related to its total thermal energy, namely, its enthalpy leading to S = 4Nk in exact agreement with the prediction of Major and Setter (2001, “Gravitational Statistical Mechanics: A Model,” Classical Quantum Gravity, 18, pp. 5125–5142).

scholarly journals Adsorption of an Ideal Gas on a Small Spherical Adsorbent

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 431 ◽  
Author(s):  
Bjørn Strøm ◽  
Dick Bedeaux ◽  
Sondre Schnell
Keyword(s):  
Surface Area ◽  
Chemical Potential ◽  
Ideal Gas ◽  
Surface Thermodynamics ◽  
Small Systems ◽  
Adsorbed Phase ◽  
Thermodynamic Variables ◽  
Classical Thermodynamics ◽  
Ideal Gas Model ◽  
The Ideal

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs’ surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics.

Computational fluid dynamics simulation of the supersonic steam ejector. Part 1: Comparative study of different equations of state

2011 ◽  
Vol 226 (3) ◽  
pp. 709-714 ◽  
Author(s):  
H T Zheng ◽  
L Cai ◽  
Y J Li ◽  
Z M Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Flow Field ◽  
Equations Of State ◽  
Ideal Gas ◽  
Dynamics Simulation ◽  
Real Gas ◽  
Steam Ejector ◽  
Ideal Gas Model ◽  
The Ideal

The aim of this study is to investigate the use of computational fluid dynamics in predicting the performance and geometry of the optimal design of a steam ejector used in a steam turbine. Many scholars have analysed the steam ejector using the ideal gas model, which lacks accuracy in terms of calculating the flow field of the ejector. This study is reported in a series of two papers. The first part covers the validation of CFX 11.0 results using different equations of state (EOS) on the converging–diverging nozzle flow field carried out with the experimental value. The IAPWS IF97 real gas model works well with the experimental value. The flow field of the ejector was analysed using different EOS after grid-dependent learning. The results show that the performance of the ejector was underestimated under the ideal gas model; the entrainment ratio was 20–40 per cent lower than when using the real gas model. The effect of the optimal geometrical design and operating conditions will be discussed in Part 2.

Effect of Using Different Equations of State in the Analysis of Rotary Displacer Stirling Engine

2018 ◽  
Author(s):  
AmirHossein Bagheri ◽  
Pavlina J. I. Williams ◽  
Phillip R. Foster ◽  
Huseyin Bostanci
Keyword(s):  
Equations Of State ◽  
Compressibility Factor ◽  
Ideal Gas ◽  
Stirling Engine ◽  
Operating Conditions ◽  
Distributed Power Generation ◽  
Realistic Representation ◽  
Isothermal Analysis ◽  
Ideal Gas Model ◽  
The Ideal

The ideal gas equation of state is defined for a theoretical gas composed of molecules that have perfect elastic collisions and no intermolecular interchange forces. However, it has been widely reported that such an ideal model may not be a realistic representation under certain circumstances, in particular when the compressibility factor (Z) is not close to unity, and the consideration of other equations of state (real models) is imperative. This study investigates the effect of using different equations of state, namely, the van der Waals, Redlich-Kwong, and Peng-Robinson equations, in the ideal isothermal analysis of a rotary displacer Stirling engine with the most commonly used gases, helium and air. The results are obtained numerically considering two major SE applications (cryocooling and distributed power generation) and two sets of operating conditions, and plotted in the form of Pressure-Volume diagrams. The amount of work per cycle based on the ideal gas model is taken as reference to compare the results from other models. The data show that at low pressure or high temperature conditions (corresponding to low density), the ideal gas equation is suitable for both gases, and using different models has no significant impact in the overall analysis. Additionally, while the use of ideal gas model is rather practical and fast, implementation of other models necessitate intensive computational processes.

scholarly journals Solutions of the Noh problem for various equations of state using LIE groups

2000 ◽  
Vol 18 (1) ◽  
pp. 93-100 ◽  
Author(s):  
ROY A. AXFORD
Keyword(s):  
Equation Of State ◽  
Lie Groups ◽  
Equations Of State ◽  
Spherical Geometry ◽  
Ideal Gas ◽  
Explicit Solutions ◽  
Special Case ◽  
General Method ◽  
The Ideal

A method for developing invariant equations of state (EOS) for which solutions of the Noh problem will exist is developed. The ideal gas EOS is shown to be a special case of the general method. Explicit solutions of the Noh problem in planar, cylindrical, and spherical geometry are determined for a Mie–Gruneisen and the stiff gas equation of state.

scholarly journals Heating in ultraintense laser-induced shock waves

2017 ◽  
Vol 35 (2) ◽  
pp. 304-312 ◽  
Author(s):  
Shalom Eliezer ◽  
Shirly Vinikman Pinhasi ◽  
José Maria Martinez Val ◽  
Erez Raicher ◽  
Zohar Henis
Keyword(s):  
Shock Wave ◽  
Degrees Of Freedom ◽  
Equations Of State ◽  
Ideal Gas ◽  
Planar Geometry ◽  
Binary Collisions ◽  
Shock Wave Formation ◽  
Work Done ◽  
Three Degrees Of Freedom ◽  
The Ideal

AbstractThis paper considers the heating of a target in a shock wave created in a planar geometry by the ponderomotive force induced by a short laser pulse with intensity higher than 1018 W/cm2. The shock parameters were calculated using the relativistic Rankine–Hugoniot equations coupled to a laser piston model. The temperatures of the electrons and the ions were calculated as a function of time by using the energy conservation separately for ions and electrons. These equations are supplemented by the ideal gas equations of state (with one or three degrees of freedom) separately for ions and electrons. The efficiency of the transition of the work done by the laser piston into internal thermal energy is calculated in the context of the Hugoniot equations by taking into account the binary collisions during the shock wave formation from the target initial condition to the compressed domain. It is shown that for each laser intensity there is threshold pulse duration for the formation of a shock wave. The explicit calculations are done for an aluminum target.

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