Isentropic Expansion and the Three Isentropic Exponents of R152a

1999 ◽  
Author(s):  
D. A. Kouremenos ◽  
X. K. Kakatsios ◽  
O. E. Floratos ◽  
G. Fountis
Keyword(s):  
Specific Heat ◽  
Vapor Phase ◽  
Constant Pressure ◽  
Initial Pressure ◽  
Ideal Gas ◽  
Constant Volume ◽  
State Equations ◽  
Real Gas ◽  
Isentropic Expansion ◽  
The Ideal

Abstract The isentropic change of an ideal gas is described by the well known relations pvk = const., Tv(k-1) = const. and p(1-k)Tk = const., where the exponent k is defined as the ratio of the constant pressure to the constant volume specific heat, k = Cp/Cv. The same relations can be used for real gases only if the differential isentropic changes under consideration are small. A better examination of the differential isentropic change shows that for p, v, T systems, there are three different isentropic exponents corresponding to each pair formed out of the variables p, v, T. These three exponents noted kT,p, kT,v, kp,v after the corresponding pair of variables used, are interconnected by one relation, and accordingly only two out of the three are independent. The analysis of the present paper shows the numerical values of these exponents as well as the isentropic expansion ratios for R152a in the vapor phase, presented in diagram form. It can be seen that the deviations of the three isentropic exponents relative to the conventional k = Cp/Cv values are considerable and depend upon the initial pressure and the stage of the expansion. Additionally, the effect of the three isentropic exponents on the ideal gas relations describing the isentropic expansion ratios is examined, in order to develop simple yet more accurate relations without having to resort to the complex real gas state equations.

FALSIFICATIONS OF POISSON ADIABATE, HUGONIO ADIABATE, LAPLACE SOUND SPEEDS. MODERNIZATION OF FOUNDATIONS OF THERMODYNAMICS

2020 ◽  
Vol 5 (333) ◽  
pp. 58-67
Author(s):  
K.B. Jakupov ◽  
Keyword(s):  
Shock Wave ◽  
Heat Capacity ◽  
Specific Heat ◽  
Specific Heat Capacity ◽  
Speed Of Sound ◽  
Constant Pressure ◽  
Energy Balance Equation ◽  
Ideal Gas ◽  
Constant Volume ◽  
Capacity Coefficient

The inequality of the universal gas constant of the difference in the heat capacity of a gas at constant pressure with the heat capacity of a gas at a constant volume is proved. The falsifications of using the heat capacity of a gas at constant pressure, false enthalpy, Poisson adiabat, Laplace sound speed, Hugoniot adiabat, based on the use of the false equality of the universal gas constant difference in the heat capacity of a gas at constant pressure with the heat capacity of a gas at a constant volume, have been established. The dependence of pressure on temperature in an adiabatic gas with heat capacity at constant volume has been established. On the basis of the heat capacity of a gas at a constant volume, new formulas are derived: the adiabats of an ideal gas, the speed of sound, and the adiabats on a shock wave. The variability of pressure in the field of gravity is proved and it is indicated that the use of the specific coefficient of ideal gas at constant pressure in gas-dynamic formulas is pointless. It is shown that the false “basic formula of thermodynamics” implies the falseness of the equation with the specific heat capacity at constant pressure. New formulas are given for the adiabat of an ideal gas, adiabat on a shock wave, and the speed of sound, which, in principle, do not contain the coefficient of the specific heat capacity of a gas at constant pressure. It is shown that the well-known equation of heat conductivity with the gas heat capacity coefficient at constant pressure contradicts the basic energy balance equation with the gas heat capacity coefficient at constant volume.

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.

Supercooling in hypersonic nitrogen wind tunnels

1994 ◽  
Vol 269 ◽  
pp. 283-299 ◽  
Author(s):  
Wayland C. Griffith ◽  
William J. Yanta ◽  
William C. Ragsdale
Keyword(s):  
Vibrational Energy ◽  
Ideal Gas ◽  
Wind Tunnels ◽  
Pure Nitrogen ◽  
Real Gas ◽  
Absolute Limit ◽  
Real Gas Effects ◽  
Supercooled Region ◽  
The Ideal

Recent experimental observation of supercooling in large hypersonic wind tunnels using pure nitrogen identified a broad range of non-equilibrium metastable vapour states of the flow in the test cell. To investigate this phenomenon a number of real-gas effects are analysed and compared with predictions made using the ideal-gas equation of state and equilibrium thermodynamics. The observed limit on the extent of supercooling is found to be at 60% of the temperature difference from the sublimation line to Gibbs’ absolute limit on phase stability. The mass fraction then condensing is calculated to be 12–14%. Included in the study are virial effects, quantization of rotational and vibrational energy, and the possible role of vibrational relaxation and freezing in supercooling. Results suggest that use of the supercooled region to enlarge the Mach–Reynolds number test envelope may be practical. Data from model tests in supercooled flows support this possibility.

scholarly journals On the temperature variation of the specific heats of hydrogen and nitrogen

1930 ◽  
Vol 126 (801) ◽  
pp. 204-212 ◽  
Keyword(s):  
Kinetic Theory ◽  
Temperature Variation ◽  
Characteristic Equation ◽  
Constant Pressure ◽  
Ideal Gas ◽  
Constant Volume ◽  
Specific Heats

The energy of a gram molecule of an ideal gas can be calculated from the kinetic theory. From this, by the application of the Maxwell-Boltzmann hypothesis, the molecular specific heats at constant volume, S v , of ideal monatomic and diatomic gases are deduced to be 3R /2 and 5R/2 respectively at all temperatures. R is the gas constant per gram molecule = 1⋅985 gm. cal./° C. The corresponding molecular specific heats at constant pressure, S p , can be obtained by the addition of R. In the case of real gases, which obey some form of characteristic equation other than P. V = R. T, it can be shown from thermodynamical considera­tions that the value of S p depends upon the pressure, but as the term involving the pressure also includes the temperature, S p is not independent of the tempera­ture but it increases in value as the temperature is reduced. Assuming the characteristic equation proposed by Callendar, i. e. , v - b ­­= RT/ p - c (where b is the co-volume, c is the coaggregation volume which is a function of the temperature of the form c = c 0 (T 0 /T) n , n being dependent on the nature of the gas), it is easy to show from the relation (∂S p /∂ р ) T = -T(∂ 2 ν /∂Τ 2 ) р , hat S p = S p 0 + n (n + 1) cp /T; and, by combining this with S p – S v = T(∂ p /∂Τ) v (∂ v /∂Τ) p = R(1 + ncp /RT) 2 , the corresponding values of S v can be obtained.

Simple Predictions for the Sonic Conditions in a Real Gas

1977 ◽  
Vol 99 (1) ◽  
pp. 217-225 ◽  
Author(s):  
P. A. Thompson ◽  
D. A. Sullivan
Keyword(s):  
Equation Of State ◽  
Closed Form ◽  
Thermodynamic Parameters ◽  
Ideal Gas ◽  
Accurate Prediction ◽  
Bernoulli Equation ◽  
Real Gas ◽  
Similarity Principle ◽  
Isentropic Flow ◽  
The Ideal

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

Specific Heat of Natural Rubber

1951 ◽  
Vol 24 (2) ◽  
pp. 285-289 ◽  
Author(s):  
Hiroshi Ichimura
Keyword(s):  
Low Temperature ◽  
Natural Rubber ◽  
Specific Heat ◽  
Constant Pressure ◽  
Constant Volume ◽  
Theoretical Considerations

Abstract The constant volume specific heat of natural rubber is calculated from the constant pressure specific heat, which is measured experimentally, and it is shown that the low temperature part is expressed by a combination of the Debye and Einstein formulas. Some theoretical considerations on the transition phenomena at 200° K are included.

scholarly journals PENENTUAN JUMLAH MOL UDARA DALAM SELINDER DAN BOLA MENGGUNAKAN HUKUM BOYLE-MARIOTTE

2013 ◽  
Vol 5 (1) ◽  
pp. 41-45
Author(s):  
MATHEUS SOUISA
Keyword(s):  
Constant Temperature ◽  
Ideal Gas ◽  
Constant Volume ◽  
Ideal Gas Law ◽  
The Ideal

Has done research on different container and the syringe bulb to determine the number of moles of air. If the gas or air is introduced into the syringe or bulb then the more air is forced into it. The analysis uses Boyle-Mariotte law shows that the number of moles of air in the syringe with constant temperature and number of moles of air at constant volume is a sphere with eqqual 0.02 mol. Thus two different media (cylindrical and spherical), giving the same number of moles. Obtaining the number of moles show that the application of Boyle-Mariotte is derived from the ideal gas law is appropriate.

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