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.

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.

On the theoretical investigation of the velocity of sound, as corrected from M. Dulong's recent experiments, compared with the results of the observations of Dr. Moll and Dr. Van Beek

1833 ◽  
Vol 2 ◽  
pp. 401-402
Keyword(s):  
Theoretical Investigation ◽  
Constant Pressure ◽  
Constant Volume ◽  
Velocity Of Sound ◽  
Great Probability ◽  
Atmospheric Air ◽  
Specific Heats ◽  
Actual Experiment

Laplace has demonstrated that Sir Isaac Newton’s formula for obtaining the velocity of sound, requires, in order to render it correct, that it be multiplied by a certain co-efficient, depending on the ratio between the specific heats of atmospheric air under a constant pressure, and under a constant volume. Laplace has endeavoured to deduce this coefficient, first from the experiments of MM. De la Roche and Berard; secondly, from those of MM. Clement and De-sormes; and lastly, from the more accurate investigations of MM. Gay-Lussac and Welter. By applying this correction, the velocity of sound, deduced from calculation, corresponded very nearly with the results of actual experiment. Still, however, a degree of discordance was always found to take place. With a view to perfect the theory still further, Dulong attempted, by reversing the process of Laplace, to deduce the coefficient by which the Newtonian formula is to be multiplied, directly from experiments themselves. The object of the present paper is to compare the investigation of Dulong with the experiments on the velocity of sound made by Drs. Moll and Van Beek, of which an account was lately published in the Philosophical Transactions. By-applying the values of the coefficients thus obtained, the computed velocities of sound came out much nearer to the observed velocities; and the author concludes by remarking, that such differences as yet remain between calculation and experiment, may with great probability be ascribed to the errors, which are unavoidable in observations of so complicated a nature.

scholarly journals XV. — On the theoretical investigation of the velocity of, as corrected from M. Dulong’s recent experiments, compared with the results the observations of Dr. Moll and Dr. Van Beek

1830 ◽  
Vol 120 ◽  
pp. 209-214
Keyword(s):  
Theoretical Investigation ◽  
Atmospheric Pressure ◽  
Constant Pressure ◽  
Constant Volume ◽  
Square Root ◽  
Velocity Of Sound ◽  
Atmospheric Air ◽  
Specific Heats

It has been demonstrated by the ever-to-be-lamented Laplace, that in order to obtain the velocity of sound by calculation, Sir Isaac Newton’s original expression†, V = √ g · p /D, must be multiplied by the square root of the ratio between the specific heats of atmospheric air under a constant pressure and under a constant volume. In this formula V is the velocity of sound, g the intensity of gravitating force, p the atmospheric pressure, and D the density of the medium through which sound is transmitted; the density of mercury being equal to 1. The coefficient, which is to multiply the Newtonian formula, has been deduced by M. Laplace, first from MM. Laroche and Berardo’s ‡ experiments, next from those of MM. Clement and Desormes§, and finally from the more accurate investigations of MM. Gay-Lussac and Welter.

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.

Surface pressures on a wing moving with supersonic speed

1974 ◽  
Vol 341 (1625) ◽  
pp. 177-193 ◽  
Keyword(s):  
Supersonic Flow ◽  
Delta Wing ◽  
Leading Edge ◽  
Ideal Gas ◽  
Numerical Results ◽  
Coordinate Surface ◽  
Supersonic Speed ◽  
Extrapolation Procedure ◽  
Specific Heats ◽  
Limiting Values

Estimates for pressures on the surface of a given delta wing at zero incidence in a steady uniform stream of air are obtained by numerically integrating two semi-characteristic forms of equations which govern the inviscid supersonic flow of an ideal gas with constant specific heats. In one form of the equations coordinate surfaces are fixed in space so that the surface of the wing, which has round sonic leading edges, is a coordinate surface. In the other, two families of coordinates are chosen to be stream-surfaces. For each form of the equations, a finite difference method has been used to compute the supersonic flow around the wing. Convergence of the numerical results, as the mesh is refined, is slow near the leading edge of the wing and an extrapolation procedure is used to predict limiting values for the pressures on the surface of the wing at two stations where theoretical and experimental results have been given earlier by another worker. At one station differences between the results given here and the results given earlier are significant. The two methods used here produce consistent values for the pressures on the surface of the wing and, on the basis of this numerical evidence together with other cited numerical results, it is concluded that the pressures given here are close to the true theoretical values.

Using Excel for the Thermodynamic Analysis of Air-Standard Cycles and Combustion Processes

2009 ◽  
Author(s):  
Amir Karimi
Keyword(s):  
Engineering Students ◽  
Solution Process ◽  
Ideal Gas ◽  
Power Cycles ◽  
Thermodynamic Cycles ◽  
Specific Heats ◽  
Property Evaluation ◽  
Difficult Time ◽  
Parametric Studies ◽  
Combustion Processes

In an undergraduate course or a course-sequence in thermodynamics mechanical engineering students are introduced to air-standard power cycles, refrigeration cycles, and the fundamentals of combustion processes. The analysis of air-standard thermodynamic cycles or solving problems involving combustion processes requires the evaluation of thermodynamic properties either from ideal gas tables or equations developed based on the assumption of constant specific heats. Many students have a difficult time to distinguish the differences between the two property evaluation methods. Also, solving problems involving power and refrigeration cycles or parametric studies of combustion processes involve several steps of property evaluation and some steps require interpolation of data listed in the thermodynamic property tables. Also solution to problems requiring trial and error iterative procedure makes the solution process tedious and time consuming, if it is done manually. This paper provides several examples to demonstrate the effectiveness of Excel in solving problems involving air-standard cycles and combustion processes.

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