Search results
Results from the WOW.Com Content Network
A polytropic process is a thermodynamic process that obeys the relation: = where p is the pressure , V is volume , n is the polytropic index , and C is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer.
[2] [3] The equation of state of a polytropic fluid is general enough that such idealized fluids find wide use outside of the limited problem of polytropes. The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus [ 4 ] where its relation to the Murnaghan equation of state has also ...
The particular choice of a polytropic gas as given above makes the mathematical statement of the problem particularly succinct and leads to the Lane–Emden equation. The equation is a useful approximation for self-gravitating spheres of plasma such as stars, but typically it is a rather limiting assumption.
The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). For a linear triatomic molecule such as CO 2 , there are only 5 degrees of freedom (3 translations and 2 rotations), assuming vibrational modes are not ...
In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n × n real or complex matrix . The exponential of X , denoted by e X or exp( X ) , is the n × n matrix given by the power series
A highly detailed study on the Tait-Tammann equation of state with the physical interpretation of the two empirical parameters and is given in chapter 3 of reference. [2] Expressions as a function of temperature for the two empirical parameters C {\displaystyle C} and B {\displaystyle B} are given for water, seawater, helium-4, and helium-3 in ...
In 2017, it was proven [14] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
The largest Lyapunov exponent is as follows [2] = (()). Lyapunov proved that if the system of the first approximation is regular (e.g., all systems with constant and periodic coefficients are regular) and its largest Lyapunov exponent is negative, then the solution of the original system is asymptotically Lyapunov stable .