Polytropic Process

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Polytropic process

A process which occurs with an interchange of both heat and work between the system and its surroundings. The nonadiabatic expansion or compression of a fluid is an example of a polytropic process. The interrelationships between the pressure (P) and volume (V) and pressure and temperature (T) for a gas undergoing a polytropic process are given by Eqs. (1) and

(1) 
(2) 
(2), where a and b are the polytropic constants for the process of interest. These constants, which are usually determined from experiment, depend upon the equation of state of the gas, the amount of heat transferred, and the extent of irreversibility in the process. See Isentropic process, Isothermal process, Thermodynamic processes

Polytropic Process

 

a change in the state of a physical system where the system’s specific heat C remains constant. The curve representing a polytropic process on a thermodynamic diagram is called a polytropic curve.

A simple example of a reversible polytropic process is the polytropic change of an ideal gas. This process is defined by the equation pVn= const, where p is the pressure of the gas, V is the volume of the gas, and n = (C— CP)/(C— Cv) is the polytropic exponent (Cp and Cv are the specific heats of the gas at constant pressure and constant volume, respectively). By using the equation of state for an ideal gas, the equation of a polytropic curve can be written in a different form: pTn/(1-n)= const or VT1(1-n) = const, here T is the absolute temperature. Special cases of the equation of a polytropic process for an ideal gas are the equations for an isentropic curve, where C = 0 and n = Cp/cv (this ratio of specific heats is designated γ); an isobar, where C— Cp and n = 0; an isochor, where C= Cv and n = ∞; and an isotherm, where C= ∞ and n = 1. The work A done by an ideal gas against the ambient pressure is determined from the formula

where the subscripts 1 and 2 refer to the initial and final states of the gas.

Engineering thermodynamics makes extensive use of the concept of polytropic processes in investigating the operating cycles of heat engines.

polytropic process

[¦päl·i¦träp·ik ′prä·səs]
(thermodynamics)
An expansion or compression of a gas in which the quantity pV n is held constant, where p and V are the pressure and volume of the gas, and n is some constant.
References in periodicals archive ?
Higher in-cylinder pressures (polytropic index = 1.28) and advanced combustion in the case of MLLDI as against SLLDI were observed as shown in Figures 13a and 13b due to better combustion.
In [7], this discretization was generalized to the case of general state equations, and it was verified for the perfect polytropic gas and more complex state equations on a set of known tests.
Mu, "Critical blow-up and extinction exponents for non-Newton polytropic filtration equation with source," Bulletin of the Korean Mathematical Society, vol.
Caption: Figure 2: Steam turbine real (polytropic) and ideal (isentropic) expansion.
Sheng, "Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for polytropic gases," Journal of Mathematical Analysis and Applications, vol.
where [P.sub.r] is the pressure ratio (ratio of storage pressure to the atmospheric pressure) and n is a polytropic index of compression.
Secondly, if we consider the usual polytropic infiltration equation (6), i.e.,
A polytropic coefficient of 1.37 was used in the calculations for the compression and power stroke.
These are compared to the simple polytropic [GAMMA] = 2 EoS often employed in the literature.
Eid, "Stability of thin shell wormholes in Born-Infeld theory supported by polytropic phantom energy," The Korean Physical Society, vol.
where [P.sub.0] is the initial charge pressure of gas in reservoir tube; [V.sub.0] is the initial charge volume; [P.sub.g] and [V.sub.g] are, respectively, the gas pressure and volume after the fluid flows into reservoir tube; n is the gas polytropic index; v(t) is the velocity of piston.
Also it is assumed that the gas inside the vapor bubble satisfies the polytropic law with the polytropic exponent of [gamma], that [gamma] is the special heat ratio inside the vapor bubble.