Isoprocesses in an ideal gas as special cases of a polytropic process

2021 ◽  
pp. 22-26
Author(s):  
S.V. Sobolev ◽  
A.N. Kutuev
Keyword(s):  
Ideal Gas ◽  
Special Cases ◽  
Polytropic Process

scholarly journals Maximum Power Point Characteristics of Generalized Heat Engines with Finite Time and Finite Heat Capacities

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Abhishek Khanna ◽  
Ramandeep S. Johal
Keyword(s):  
Heat Transfer ◽  
Ideal Gas ◽  
Heat Capacities ◽  
Working Fluid ◽  
Maximum Power Point ◽  
Power Extraction ◽  
Heat Engines ◽  
Special Cases ◽  
Polytropic Process ◽  
Power Point

We revisit the problem of optimal power extraction in four-step cycles (two adiabatic and two heat-transfer branches) when the finite-rate heat transfer obeys a linear law and the heat reservoirs have finite heat capacities. The heat-transfer branch follows a polytropic process in which the heat capacity of the working fluid stays constant. For the case of ideal gas as working fluid and a given switching time, it is shown that maximum work is obtained at Curzon-Ahlborn efficiency. Our expressions clearly show the dependence on the relative magnitudes of heat capacities of the fluid and the reservoirs. Many previous formulae, including infinite reservoirs, infinite-time cycles, and Carnot-like and non-Carnot-like cycles, are recovered as special cases of our model.

Polytropic solutions to the problem of spherically symmetric flow of an ideal gas

1980 ◽  
Vol 58 (8) ◽  
pp. 1085-1092 ◽  
Author(s):  
D. Summers
Keyword(s):  
Differential Equations ◽  
Fluid Dynamic ◽  
Mass Density ◽  
Ideal Gas ◽  
Radial Coordinate ◽  
Polytropic Index ◽  
Spherically Symmetric ◽  
Polytropic Model ◽  
Special Cases ◽  
Complete Set

An ideal, compressible gas is considered in steady, spherically symmetric, purely radial motion in the presence of a gravitating point mass situated at the origin of coordinates. The gas pressure p and mass density ρ are assumed to satisfy a simple polytrope law, [Formula: see text], where β is the polytropic index which is assumed to take on any real value; the self-gravitation of the gas is neglected. The model equations, which are expressed in a form appropriate to both the expansion and accretion cases, reduce to two non-linear ordinary differential equations, for which Bernoulli integrals are readily found. Singular points of the differential equations are analyzed, and the complete set of asymptotic solutions for the velocity, temperature and Mach number are given for λ → 0 and λ → ∞, where λ [Formula: see text] (radial coordinate)−1, as well as a special class of solutions valid for λ → constant (≠ 0). Families of velocity profiles are sketched which are representative of the complete range of β. The polytropic model, special cases of which have been used successfully in astrophysics in stellar wind and accretion problems, is here cast in general fluid-dynamic terms so that the complete set of solutions obtained may be applicable to a wide class of gas expansion and accretion problems.

Generalized aerofoil theory

1957 ◽  
Vol 238 (1214) ◽  
pp. 358-388 ◽  
Keyword(s):  
Integral Equation ◽  
Incompressible Flow ◽  
Leading Edge ◽  
Porous Wall ◽  
Inviscid Flow ◽  
Ideal Gas ◽  
Point Sources ◽  
Surface Distribution ◽  
Limited Region ◽  
Special Cases

A theory is developed enabling the flow of an inviscid compressible gas at subsonic speeds past a porous aerofoil, with a given pressure on the inside of the porous surface, to be calculated. The assumptions made in the paper are ( a ) that the ideal gas can be replaced by a Kármán-Tsien tangent gas, ( b ) that the mass flow through the porous wall is linearly related to the pressure difference across the wall, and ( c ) that the mass of air sucked into the aerofoil is relatively small; no restrictions are placed on the magnitude of the aerofoil incidence or thickness. Generalized forms of Blasius’s well-known formulae for the lift and moment in incompressible flow are obtained for the tangent gas, and applied to the porous aerofoil problem. The theory is shown to yield as special cases ( a ) the flow about a given aerofoil, ( b ) the design of an aerofoil for a given pressure distribution, ( c ) the flow about a given aerofoil with point sources or sinks on the surface, or with a surface distribution of these (distributed suction), ( d ) the flow about a thin aerofoil with a limited region of flow separation, such as occurs in 'thin-aerofoil' stall, and ( e ) the flow about bluff bodies (two-dimensional) to which finite bubbles or cavities adhere. By 'flow’ here is meant, of course, the inviscid flow external to the bubble or boundary later. The paper contains incidentally a new treatment of the solid lifting aerofoil in a tangent gas; this treatment does not follow the usual method of first finding the incompressible flow about a profile—which must be distorted from the original shape in a manner initially unknown—but is based on an integral equation directly applicable to the given circulation and profile shape. As an integral equation must be solved in any case, to determine the in­compressible flow about the distorted profile, the direct treatment of the compressible flow problem, given in the paper, is simpler than the usual treatment. The paper includes a discussion of the problems of 'thin-aerofoil' and 'leading-edge' stall.

scholarly journals General forms of statistical mechanics with special reference to the requirements of the new quantum mechanics

1926 ◽  
Vol 113 (764) ◽  
pp. 432-449 ◽  
Keyword(s):  
Statistical Mechanics ◽  
Equations Of Motion ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Coupled Systems ◽  
Light Quantum ◽  
Classical Form ◽  
Special Cases ◽  
New Form ◽  
Temperature Radiation

It is well known that a new form of statistical mechanics has been recently developed by Einstein for an ideal gas of structureless mass-points. This starts from a discussion by Bose of the laws of temperature radiation based on the light quantum hypothesis, and has been further analysed by Schrödinger. Yet another new form has been proposed independently by Fermi and Dirac. The latter based his theory on a discussion of lightly coupled systems with the help of Schrödinger’s equation. Combined with Heisenberg’s work on the many-body problem, Dirac’s work forces us to conclude at least that the classical form of statistical mechanics must be changed. It indicates that the true form, which satisfies the laws of the new mechanics, is almost certainly that of Fermi and Dirac, which is the natural generalization of Pauli’s principle of exclusion for electronic orbits in an atom. The work of Heisenberg and Dirac already quoted has shown that Pauli’s principle and its extension are satisfied in the new mechanics by a complete self-consistent solution of the equations of motion. So far as I am aware, the discussions of the new forms have as yet dealt only with the statistics of a gas of structureless mass-points (and, of course, temperature radiation). There has, moreover, been as yet no attempt to define the entropy (and the absolute temperature) in strict analogy with rational thermodynamics by means of the equation d Q = T d S. If another definition is preferred, then this equation must be deduced from it. It has, therefore, seemed worth while to reopen the discussion by examining ab initio a quite general form of statistical mechanics of which the classical form and instein’s and Fermi-Dirac’s are special cases. This is rendered possible by using the powerful method of complex integration already applied to the classical form. The sequence of the argument is then to take the general form, which covers a very large range of ways of assigning possibilities and counting complexions, and construct on that basis exact integral expressions for the number of complexions possible to the assembly and for the average number of systems of the assembly in their various quantum states. We then derive from these the average energies and external reactions and so the form of d Q, deduce from d Q the existence of S and so define S and T. This can be done in the general form for assemblies of ideal systems just as general as can be handled in the classical way—ideal gases of molecules of any structure and crystals and radiation. Such assemblies are in all cases thermodynamical systems.

scholarly journals Simple analytic solution of fireball hydrodynamics

Open Physics ◽  
2004 ◽  
Vol 2 (4) ◽  
Author(s):  
Tamás Csörgő
Keyword(s):  
Equation Of State ◽  
Temperature Profile ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
New Family ◽  
Special Cases ◽  
Rotationally Symmetric

AbstractA new family of simple analytic solutions of hydrodynamics is found for slowly expanding, rotationally symmetric fireballs assuming an ideal gas equation of state. The temperature profile is position-independent only in the collisionless gas limit. The Zimányi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamic particle sources are recovered as special cases. The results are applied to predict new features of proton correlations and spectra for 1.93 AGeV Ni+Ni collisions.

scholarly journals SIMILARITY SOLUTIONS FOR STRONG SHOCKS IN A NON-IDEAL GAS

2012 ◽  
Vol 17 (3) ◽  
pp. 351-365 ◽  
Author(s):  
Rajan Arora ◽  
Amit Tomar ◽  
Ved Pal Singh
Keyword(s):  
Power Law ◽  
Initial Density ◽  
Similarity Solutions ◽  
Ideal Gas ◽  
Spherically Symmetric ◽  
State Dependent ◽  
Group Theoretic Method ◽  
Special Cases ◽  
Dependent Form ◽  
Flow Variables

A group theoretic method is used to obtain an entire class of similarity solutions to the problem of shocks propagating through a non-ideal gas and to characterize analytically the state dependent form of the medium ahead for which the problem is invariant and admits similarity solutions. Different cases of possible solutions, known in the literature, with a power law, exponential or logarithmic shock paths are recovered as special cases depending on the arbitrary constants occurring in the expression for the generators of the transformation. Particular case of collapse of imploding cylindrically and spherically symmetric shock in a medium in which initial density obeys power law is worked out in detail. Numerical calculations have been performed to obtain the similarity exponents and the profiles of the flow variables behind the shock, and comparison is made with the known results.

The Performance Analysis of a Quantum Brayton Refrigeration Cycle with an Ideal Bose Gas

2003 ◽  
Vol 10 (02) ◽  
pp. 147-157 ◽  
Author(s):  
Bihong Lin ◽  
Jincan Chen
Keyword(s):  
Constant Pressure ◽  
Pressure Ratio ◽  
Bose Gas ◽  
Ideal Gas ◽  
Coefficient Of Performance ◽  
Refrigeration Cycle ◽  
Special Cases ◽  
Work Input ◽  
Brayton Refrigeration Cycle ◽  
Ideal Bose Gas

A Brayton refrigeration cycle using an ideal Bose gas as the working substance is simply referred to as a quantum Brayton refrigeration cycle, which consists of two constant-pressure and two adiabatic processes. The influence of quantum degeneracy on the performance of the cycle is investigated, based on the correction equation of state of an ideal Bose gas. The general expressions of the coefficient of performance, refrigeration load and work input of the cycle are calculated. The lowest temperature of the working substance and the minimum pressure ratio of the two constant-pressure processes for a quantum Brayton refrigeration cycle are determined. The variations of the relative refrigeration load with the temperature of the cooled space and the pressure of the low constant-pressure process are discussed for three special cases. Some curves related to the important performance parameters are given. The results obtained here are compared with those of a classical Brayton refrigeration cycle using an ideal gas as the working substance. Some significant conclusions are obtained.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

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