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A polytropic process is one where the pressure and volume of a system is related by the equation | A polytropic process is one where the pressure and volume of a system is related by the equation PV<sup>n</sup>= C. Such processes are defined by what is constant in the process. | ||
In this equation, | In this equation, P represents the pressure, V represents the specific volume, n represents the polytropic index, and C is a constant. | ||
The equation can also be written as: PV<sup>n</sup>= K and as P=K/V<sup>n</sup>, where V<sup>n</sup>is the volume. To find the specific volume this term needs to be divided by the mass. | The equation can also be written as: PV<sup>n</sup>= K and as P=K/V<sup>n</sup>, where V<sup>n</sup>is the volume. To find the specific volume this term needs to be divided by the mass. | ||
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When n is equal to 1: A constant temperature, or isothermal process<br /> | When n is equal to 1: A constant temperature, or isothermal process<br /> | ||
When n is equal to infinity: Volume is constant, this is an isochoric process<br /><br /> | When n is equal to infinity: Volume is constant, this is an isochoric process<br /><br /> | ||
{| class="wikitable" | |||
! Constant | |||
! style="width: 45%" | n | |||
|- | |||
| Temperature | |||
|align="center"|1 | |||
|- | |||
| Pressure | |||
|align="center"|0 | |||
|- | |||
| Volume | |||
|align="center"|<big>∞</big> | |||
|- | |||
| Linear | |||
|align="center"|-1 | |||
|} | |||
== Isentropic Process == | == Isentropic Process == | ||
An isentropic process is a particular type of polytropic process, whereby n is the heat capacity ratio of an ideal gas and the system contains that ideal gas. | An isentropic process is a particular type of polytropic process, whereby n is the heat capacity ratio of an ideal gas and the system contains that ideal gas. | ||
Revision as of 00:11, 20 November 2018
A polytropic process is one where the pressure and volume of a system is related by the equation PVn= C. Such processes are defined by what is constant in the process.
In this equation, P represents the pressure, V represents the specific volume, n represents the polytropic index, and C is a constant.
The equation can also be written as: PVn= K and as P=K/Vn, where Vnis the volume. To find the specific volume this term needs to be divided by the mass.
For specific volume:
P= K/m / Vn/m
A polytropic process can be related to work by the equation:
W= P2V2-P1V1/ 1-n
These processes have shapes, and some of these shapes have names (such as linear, hyperbolic, etc.). Both open and closed systems can follow a polytropic path.
Polytropic Index
When n is less than 0: Negative n values represent a large amount of heat added to the system is much greater than the work done by the system
When n is equal to 0: A constant pressure, or isobaric process
When n is equal to 1: A constant temperature, or isothermal process
When n is equal to infinity: Volume is constant, this is an isochoric process
| Constant | n |
|---|---|
| Temperature | 1 |
| Pressure | 0 |
| Volume | ∞ |
| Linear | -1 |
Isentropic Process
An isentropic process is a particular type of polytropic process, whereby n is the heat capacity ratio of an ideal gas and the system contains that ideal gas.