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== Polytropic Index == | == Polytropic Index == | ||
Polytropic processes are usually categorized either by what variable remains constant in the process, or by the shape of its corresponding graph (e.g. linear) | |||
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 /> | ||
{| class="wikitable" | {| class="wikitable" | ||
! Constant | ! Constant | ||
! style="width: | ! style="width: 20%" | n | ||
! | ! Equation | ||
! | ! Associated with | ||
|- | |- | ||
| Temperature | | Temperature (Isothermic) | ||
|align="center"|1 (unless saturated) | |align="center"|1 (unless saturated) | ||
| | |align="center"|PV<sup>1</sup>= C | ||
|align="center"|Non-insulated systems | |||
|- | |- | ||
| Pressure | | Pressure (Isobaric) | ||
|align="center"|0 (unless saturated) | |align="center"|0 (unless saturated) | ||
|align="center"|PV<sup>0</sup>= C | |||
|align="center"|Pistons/Cylinders | |||
|- | |- | ||
| Volume | | Volume (Isochoric) | ||
|align="center"|<big>∞</big> | |align="center"|<big>∞</big> | ||
|align="center"|PV<sup><big>∞</big></sup>= C | |||
|align="center"|Rigid containers | |||
|- | |- | ||
| Linear | | Linear | ||
|align="center"|-1 | |align="center"|-1 | ||
|align="center"|PV<sup>-1</sup>= C | |||
|align="center"|Pistons/Cylinders | |||
|- | |- | ||
| Heat and mass flow | | Heat and mass flow (Adiabatic) | ||
|align="center"|γ | |align="center"|γ | ||
|align="center"|PV<sup>γ</sup>= C | |||
|align="center"|Pistons/Cylinders | |||
|} | |} | ||
== 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 04:11, 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
Polytropic processes are usually categorized either by what variable remains constant in the process, or by the shape of its corresponding graph (e.g. linear)
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
| Constant | n | Equation | Associated with |
|---|---|---|---|
| Temperature (Isothermic) | 1 (unless saturated) | PV1= C | Non-insulated systems |
| Pressure (Isobaric) | 0 (unless saturated) | PV0= C | Pistons/Cylinders |
| Volume (Isochoric) | ∞ | PV∞= C | Rigid containers |
| Linear | -1 | PV-1= C | Pistons/Cylinders |
| Heat and mass flow (Adiabatic) | γ | PVγ= C | Pistons/Cylinders |
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.