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.

Effects of Constitutive Properties on Pressure and Extent of Reaction

2016 ◽  
Vol 230 (10) ◽  
Author(s):  
Elisabetta Arato ◽  
Angelo Morro
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Chemical Potential ◽  
Ideal Gas ◽  
Thermodynamic Relation ◽  
Chemical Potentials ◽  
Theory Of Mixtures ◽  
Low Pressures ◽  
Ideal Gas Model ◽  
The Ideal

AbstractThe paper applies the theory of mixtures to the chemical reaction rate. Concerning the time dependence of pressure, it is shown that pressure increases, is constant or decreases depending on the analogous behaviour of mole numbers. The results are established analytically and then numerically for the ideal gas, the van der Waals and the truncated virial equations. Next, in connection with the ideal gas model, Denbigh assumption is established by starting from the thermodynamic relation between (partial) pressure and Helmholtz free energy. Moreover, it is pointed out that the chemical potential does not exactly equal the partial derivative of the Gibbs free energy with respect to the corresponding mole number. This in turn is shown to imply that the evolution of a reaction is provided by the chemical potentials rather than by the derivative of the Gibbs free energy. Subject to the assumption of ideal gas for the constituents, as a thermodynamic requirement it is shown that if the number of moles increases the reaction is favoured by low pressures, and viceversa, and explicit estimates are established.

In-Cylinder Temperature Measurements in a 55-cm3 Two-Stroke Engine Via Tunable Laser Absorption Spectroscopy

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Joseph K. Ausserer ◽  
Marc D. Polanka ◽  
Matthew J. Deutsch ◽  
Jacob A. Baranski ◽  
Keith D. Rein
Keyword(s):  
Absorption Spectroscopy ◽  
Ideal Gas ◽  
Operating Conditions ◽  
Temperature Measurements ◽  
Cylinder Pressure ◽  
Laser Absorption Spectroscopy ◽  
Laser Absorption ◽  
Ideal Gas Model ◽  
Stroke Engine ◽  
The Ideal

Abstract In-cylinder temperature is a critical quantity for modeling and understanding combustion dynamics in internal combustion engines (ICEs). It is difficult to measure in small, two-stroke engines due to high operational speeds and limited space to install instrumentation. Optical access was established in a 55-cm3 displacement two-stroke engine using M4 bolts as carriers for sapphire rods to establish a 1.5-mm diameter optical path through the combustion chamber. Temperature laser absorption spectroscopy was successfully used to measure time varying in-cylinder temperature clocked to the piston position with a resolution of 3.6 crank angle degrees (CAD) at 6000 rpm. The resulting temperature profiles clearly showed the traverse of the flame front and were qualitatively consistent with in-cylinder pressure, engine speed, and delivery ratio. The temperature measurements were compared to aggregate in-cylinder temperatures calculated using the ideal gas model using measured in-cylinder pressure and trapped mass calculated at exact port closure as inputs. The calculation was sensitive to the trapped mass determination, and the results show that using the ideal gas model for in-cylinder temperature calculations in heat flux models may fail to capture trends in actual in-cylinder temperature with changing engine operating conditions.

Particle Entropies and Entropy Quanta. I. The Ideal Gas

2000 ◽  
Vol 214 (2) ◽  
Author(s):  
Helmuth W. Zimmermann
Keyword(s):  
Chemical Potential ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Translational Energy ◽  
Quantum Numbers ◽  
De Broglie Wavelength ◽  
Bose Einstein ◽  
Particle Statistics ◽  
The Ideal

We consider an ideal gas of monatomic independent particles, which is enclosed in a cubic box. At temperature T the particles are in thermal equilibrium. All relevant properties of the gas can be deduced from the particle statistics on the assumption that each particle of the ensemble has the particle entropy σ = ε/T = ka. ε is the translational energy of the particle. The non-dimensional number a measures the particle entropy σ in multiples of the Boltzmann constant k, which acts as an atomic entropy unit. a obeies an eigenvalue equation and satisfies boundary conditions. Eigenvalues and eigenfunctions are determined by the translational quantum numbers. Using particle entropies it is easy to calculate the Bose-Einstein and the Boltzmann distribution; and in combination with the density function we immediately get the internal energy E and the Helmholtz free energy F, the total entropy S, the chemical potential μ, the equation of state of the ideal gas at ordinary temperatures and at low temperatures near absolute zero, inclusively Bose-Einstein condensation. Entropy quanta are used to introduce the temperature into the equations of statistical thermodynamics and to calculate the thermal and the actual de Broglie wavelength at temperature T.

Thermodynamic Property Models for Moist Air and Combustion Gases

2002 ◽  
Vol 125 (1) ◽  
pp. 374-384 ◽  
Author(s):  
D. Bu¨cker ◽  
R. Span ◽  
W. Wagner
Keyword(s):  
Ideal Gas ◽  
Moist Air ◽  
Combustion Gas ◽  
Real Gas ◽  
New Model ◽  
Combustion Gases ◽  
Dissociation Model ◽  
The Individual ◽  
Ideal Gas Model ◽  
The Ideal

A new model for the prediction of caloric properties of moist air and combustion gases has been developed. The model very accurately predicts ideal gas caloric properties of undissociated gas mixtures at temperatures from 200 K to 3300 K. In addition, a simple model has been developed to account for caloric effects of dissociation at temperatures up to 2000 K. As a part of the project, scientific equations for the ideal gas isobaric heat capacity of the individual combustion gas components have been established. Based on this reference, an assessment and comparison of the new model with the most common technical models have been carried out. Results of the simplified dissociation model are compared to the results of complex chemical equilibrium programs. To mark out the limits of the ideal gas hypothesis, some sample calculations are given, which compare results of the new ideal gas model to results from sophisticated real gas models.

AN APPLICATION OF NONEXTENSIVE PARAMETER: THE NONEXTENSIVE GAS AND REAL GAS

2007 ◽  
Vol 21 (06) ◽  
pp. 947-953 ◽  
Author(s):  
YAHUI ZHENG ◽  
JIULIN DU
Keyword(s):  
Heat Capacity ◽  
Second Virial Coefficient ◽  
Ideal Gas ◽  
Quasi Equilibrium ◽  
Equilibrium System ◽  
Real Gas ◽  
Nonextensive Statistics ◽  
Thomson Coefficient ◽  
Ideal Gas Model ◽  
The Ideal

By application of the nonextensive statistics to the ideal gas model, we establish a nonextensive gas model. If we regard the nonextensive gas as a real gas, we can use the nonextensive parameter q ∈ ℝ in Tsallis statistics to describe Joule coefficient, Joule–Thomson coefficient, second virial coefficient and etc. We also derive an expression, with a multiplier T1-q, of the heat capacity of the nonextensive gas. We can prove that in the quasi-equilibrium system there is 1 - q > 0, 2 so the heat capacity still vanishes if temperature tends to zero, just as that in Boltzmann-Gibbs statistics.

CFD-Simulation of Centrifugal Fan Performance Characteristics Using Ideal and Real Gas Models for Air and Organic Fluids

2019 ◽  
Author(s):  
Manuel Fritsche ◽  
Philipp Epple ◽  
Karsten Hasselmann ◽  
Felix Reinker ◽  
Robert Wagner ◽  
...  
Keyword(s):  
Cfd Simulation ◽  
Ideal Gas ◽  
High Tech ◽  
Test Case ◽  
Centrifugal Fan ◽  
Real Gas ◽  
The Real ◽  
Organic Fluids ◽  
Ideal Gas Model ◽  
The Ideal

Abstract Efficient processes with organic fluids are becoming increasingly important. The high tech fluid Novec™ is such an organic fluid and is used, for example, as a coolant for highperformance electronics, low-temperature heat transfer applications, cooling of automotive batteries, just to mention a few. Thus, efficient designed fans for the transport of organic fluids are becoming more and more important in the process engineering. CFD-simulations are nowadays integral part of the design and optimization process of fans. For air at the most usual application conditions, i.e. no extreme temperatures or pressures, the ideal gas model is in good agreement with the real gas approach. In the present study, this real gas approach for organic fluids have been investigated with CFD methods and, the deviation from the ideal gas model has been analyzed. For this purpose, a simulation model of a centrifugal fan with volute has been designed as a test case. First, the ideal gas model approach has been compared with the real gas approach model of Peng-Robinson for air using the commercial solver ANSYS CFX. Thereafter, the same comparison has been performed using the organic fluid Novec™. After a detailed grid study, the entire fan characteristics, i.e. the design point and the off-design points, have been simulated and evaluated for each fluid (air and Novec™) and gas model (ideal gas and Peng-Robinson real gas). The steady state simulations of the centrifugal fan have been performed using the Frozen Rotor model. The simulation results have been compared, discussed and presented in detail.

scholarly journals IGE Model: An Extension of the Ideal Gas Model to Include Chemical Composition as Part of the Equilibrium State

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Christopher P. Paolini ◽  
Subrata Bhattacharjee
Keyword(s):  
Thermodynamic Properties ◽  
Equilibrium State ◽  
Major Change ◽  
Equilibrium Composition ◽  
Ideal Gas ◽  
The State ◽  
State Evaluation ◽  
Pure Substances ◽  
Ideal Gas Model ◽  
The Ideal

The ideal gas (IG) model is probably the most well-known gas models in engineering thermodynamics. In this paper, we extend the IG model into an ideal gas equilibrium (IGE model) mixture model by incorporating chemical equilibrium calculations as part of the state evaluation. Through a simple graphical interface, users can set the atomic composition of a gas mixture. We have integrated this model into a thermodynamic web portal TEST (http://thermofluids.sdsu.edu/) that contains Java applets for various models for properties of pure substances. In the state panel of the IGE model, the known thermodynamic properties are entered. For a given pressure and temperature, the mixture's Gibbs function is minimized subject to atomic constraints and the equilibrium composition along with thermodynamic properties of the mixture are calculated and displayed. What is unique about this approach is that equilibrium computations are performed in the background, without requiring any major change in the familiar user interface used in other state daemons. Properties calculated by this equilibrium state daemon are compared with results from other established applications such as NASA CEA and STANJAN. Also, two different algorithms, an iterative approach and a direct approach based on minimizing different thermodynamic functions in different situation, are compared.

scholarly journals Real Gas Models in Coupled Algorithms Numerical Recipes and Thermophysical Relations

2020 ◽  
Vol 5 (3) ◽  
pp. 20
Author(s):  
Lucian Hanimann ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Damian Vogt ◽  
Marwan Darwish
Keyword(s):  
Gas Flow ◽  
Measurement Data ◽  
Ideal Gas ◽  
Computational Time ◽  
State Equations ◽  
Cfd Simulations ◽  
Real Gas ◽  
Standard Ideal ◽  
Ideal Gas Model ◽  
The Ideal

In the majority of compressible flow CFD simulations, the standard ideal gas state equation is accurate enough. However, there is a range of applications where the deviations from the ideal gas behaviour is significant enough that performance predictions are no longer valid and more accurate models are needed. While a considerable amount of the literature has been written about the application of real gas state equations in CFD simulations, there is much less information on the numerical issues involved in the actual implementation of such models. The aim of this article is to present a robust implementation of real gas flow physics in an in-house, coupled, pressure-based solver, and highlight the main difference that arises as compared to standard ideal gas model. The consistency of the developed iterative procedures is demonstrated by first comparing against results obtained with a framework using perfect gas simplifications. The generality of the developed framework is tested by using the parameters from two different real gas state equations, namely the IAPWS-97 and the cubic state equations state equations. The highly polynomial IAPWS-97 formulation for water is applied to a transonic nozzle case where steam is expanded at transonic conditions until phase transition occurs. The cubic state equations are applied to a two stage radial compressor setup. Results are compared in terms of accuracy with a commercial code and measurement data. Results are also compared against simulations using the ideal gas model, highlighting the limitations of the later model. Finally, the effects of the real gas formulations on computational time are compared with results obtained using the ideal gas model.

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