scholarly journals On the van der Waals Gas, Contact Geometry and the Toda Chain

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 554
Author(s):  
Diego Alarcón ◽  
P. Fernández de Córdoba ◽  
J. Isidro ◽  
Carlos Orea
Keyword(s):  
Van Der Waals ◽  
Toda Chain ◽  
Contact Geometry ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
The Ideal

A Toda–chain symmetry is shown to underlie the van der Waals gas and its close cousin, the ideal gas. Links to contact geometry are explored.

scholarly journals Increase in Axial Compressibility in a Spinning Van der Waals Gas

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 137
Author(s):  
Yun Liu ◽  
Hao Liu ◽  
Zhen-Guo Fu ◽  
Weimin Zhou
Keyword(s):  
Van Der Waals ◽  
Axial Direction ◽  
Md Simulations ◽  
High Energy ◽  
Ideal Gas ◽  
High Energy Density ◽  
Van Der Waals Gas ◽  
Equation Of States ◽  
Dense State ◽  
The Ideal

We investigated the adiabatic compression along the axial direction of a spinning Van der Waals gas by applying theoretical analysis and molecular dynamics (MD) simulations. Based on the analytical results, the rotation-induced compressibility increase effect is significant in a Van der Waals gas, while the attraction term in the Van der Waals equation of states (EOS) contributes significantly to the compressibility increase in a spinning system. We conducted MD simulations to the axial compression of a spinning gas, whose state is far from the ideal gas state, and further demonstrated that the rotation-induced compressibility increase effect in a dense state is robust, implying that such a phenomenon can be detected in experiments under high-energy-density conditions.

What Happens When We have Winter Heating of Our Rooms?

2020 ◽  
Vol 02 (01) ◽  
pp. 2020001
Author(s):  
Dulli C. Agrawal
Keyword(s):  
Internal Energy ◽  
Old Age ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
Constant Weight ◽  
Gas Laws ◽  
Ideal Gas Law ◽  
Marginal Change ◽  
Three Stages ◽  
The Ideal

The illustrious question by German Astrophysicist R. Emden, “Why do we have winter heating?” has been re-examined for air following both the ideal and imperfect gas laws; the internal energy of the air in the room remains unaffected in the former case whereas it increases marginally for the latter one. The findings corresponding to ideal gas law were correlated by Emden with the mass of a person which does not change even though food is constantly consumed. This example corresponds to adulthood when the mass of a person remains more or less constant. But the marginal change of internal energy in the case of van der Waals gas is consistent with three stages of a person — initially a person grows during childhood followed by adulthood when he has more or less constant weight and finally in old age, it deteriorates.

Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas

2019 ◽  
Vol 20 (3-4) ◽  
pp. 461-473 ◽  
Author(s):  
Jinhuan Wang ◽  
Yicheng Pang ◽  
Yu Zhang
Keyword(s):  
Euler Equations ◽  
Van Der Waals ◽  
Vacuum State ◽  
Ideal Gas ◽  
Transport Equations ◽  
Rarefaction Waves ◽  
Van Der Waals Gas ◽  
Riemann Solutions ◽  
Riemann Solution ◽  
Isentropic Euler Equations

AbstractIn this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

A notable difference between ideal gas and infinite molar volume limit of van der Waals gas

2010 ◽  
Vol 31 (3) ◽  
pp. 671-673
Author(s):  
Q H Liu ◽  
Y Shen ◽  
R L Bai ◽  
X Wang
Keyword(s):  
Molar Volume ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
Volume Limit

scholarly journals Thermal performance difference of ideal gas model and van der Waals gas model in gas-loaded accumulator

2018 ◽  
Vol 1 (3) ◽  
pp. 293 ◽  
Author(s):  
Shuce Zhang ◽  
Hiromu Iwashita ◽  
Kazushi Sanada
Keyword(s):  
Thermal Performance ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Performance Difference ◽  
Van Der Waals Gas ◽  
Ideal Gas Model

scholarly journals An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4537
Author(s):  
A. A. Avramenko ◽  
I. V. Shevchuk ◽  
Yu. Yu. Kovetskaya ◽  
N. P. Dmitrenko
Keyword(s):  
Natural Convection ◽  
Integral Method ◽  
Van Der Waals ◽  
Analytical Form ◽  
Ideal Gas ◽  
Heated Plate ◽  
Van Der Waals Gas ◽  
Transfer Coefficients ◽  
Nusselt Numbers ◽  
Energy Equations

This paper focuses on a study of natural convection in a van der Waals gas over a vertical heated plate. In this paper, for the first time, an approximate analytical solution of the problem was obtained using an integral method for momentum and energy equations. A novel simplified form of the van der Waals equation for real gases enabled estimating the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficients and Nusselt numbers in an analytical form. Trends in the variation of the Nusselt number depending on the nature of the interaction between gas molecules and the wall were analyzed. The results of computations for a van der Waals gas were compared with the results for an ideal gas.

scholarly journals On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Entropy ◽  
2018 ◽  
Vol 20 (4) ◽  
pp. 247 ◽  
Author(s):  
J.M. Isidro ◽  
P. de Córdoba
Keyword(s):  
Contact Geometry ◽  
Ideal Gas ◽  
Poisson Geometry ◽  
The Ideal

scholarly journals Economic Cycles of Carnot Type

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1344
Author(s):  
Constantin Udriste ◽  
Vladimir Golubyatnikov ◽  
Ionel Tevy
Keyword(s):  
Van Der Waals ◽  
Thermodynamic Cycle ◽  
Ideal Gas ◽  
Maximum Efficiency ◽  
Carnot Cycle ◽  
Refrigeration System ◽  
Classical Thermodynamic ◽  
Economic Cycles ◽  
Van Der Waals Surface ◽  
The Ideal

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a Q−P diagram and a E−I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.

scholarly journals An Efficient Analytical Solution of Blast Wave Problem in Real Gas Flow under the Influence of Dust-Laden Particles

2020 ◽  
Vol 9 (3) ◽  
pp. 2490-2494
Keyword(s):  
Hyperbolic System ◽  
Gas Flow ◽  
Van Der Waals ◽  
Unsteady Motion ◽  
Ideal Gas ◽  
Blast Waves ◽  
Dust Particles ◽  
Van Der Waals Gas ◽  
Real Gas ◽  
Flow Parameters

In the present paper, we investigated the problem of the propagation of blast waves governed by a nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs), describing one-dimensional unsteady motion with generalized geometries in a real gas flow (van der Waals gas) in which the influence of the dust particles is significant. An efficient analytical approach has been used to the governing hyperbolic system with respect to the Rankine-Hugoniot (RH) conditions to obtain an exact solution in terms of flow parameters density, velocity and the pressure, which exhibits space-time dependence. Further, an analytical expression for the total energy influenced by real gas effects (consisting of non-ideal gas and small solid dust-laden particles) is derived. The results obtained significantly explore the effect of dust-laden particles on the propagation of blast waves in a van der Waals gas.

scholarly journals Thermal performance difference of ideal gas model and van der Waals gas model in gas-loaded accumulator

2018 ◽  
Vol 1 (3) ◽  
pp. 293
Author(s):  
Kazushi Sanada ◽  
Hiromu Iwashita ◽  
Shuce Zhang
Keyword(s):  
Thermal Performance ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Performance Difference ◽  
Van Der Waals Gas ◽  
Ideal Gas Model
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