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A polytropic process is one where the pressure and volume of a system | A polytropic process is one where the pressure and volume of a system are related by the equation PV<sup>n</sup>= C. | ||
Where P represents the pressure, V represents the volume, n represents the polytropic index, and C is a constant. | Where P represents the pressure, V represents the volume, n represents the polytropic index, and C is a constant. | ||
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These processes have shapes | These processes have unique shapes (linear, hyperbolic, etc.). Both open and closed systems can follow a polytropic path. | ||
== Polytropic Index == | == Polytropic Index == | ||
Such processes are defined by what is constant in the process. | |||
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<br /> | 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<br /> | ||
When n is equal to 0: A constant pressure, or isobaric process<br /> | When n is equal to 0: A constant pressure, or isobaric process<br /> | ||
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{| class="wikitable" | {| class="wikitable" | ||
! Constant | ! Constant | ||
! style="width: | ! style="width: 15%" | n | ||
! Explanation | |||
! Association | |||
|- | |- | ||
| Temperature | | Temperature | ||
|align="center"|1 | |align="center"|1 (unless saturated) | ||
|A constant temperature, or isothermal, polytropic process is modeled by the equation PV<sup>1</sup>= C | |||
|- | |- | ||
| Pressure | | Pressure | ||
|align="center"|0 | |align="center"|0 (unless saturated) | ||
|- | |- | ||
| Volume | | Volume | ||
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| Linear | | Linear | ||
|align="center"|-1 | |align="center"|-1 | ||
|- | |||
| Heat and mass flow | |||
|align="center"|γ | |||
|} | |} | ||
== 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 02:19, 20 November 2018
A polytropic process is one where the pressure and volume of a system are related by the equation PVn= C.
Where P represents the pressure, V represents the 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)
Where P2V2 and P1V1 represent pressure and volume at two different time-steps of a process.
These processes have unique shapes (linear, hyperbolic, etc.). Both open and closed systems can follow a polytropic path.
Polytropic Index
Such processes are defined by what is constant in the process.
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 | Explanation | Association |
|---|---|---|---|
| Temperature | 1 (unless saturated) | A constant temperature, or isothermal, polytropic process is modeled by the equation PV1= C | |
| Pressure | 0 (unless saturated) | ||
| Volume | ∞ | ||
| Linear | -1 | ||
| Heat and mass flow | γ |
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.