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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.
An isentropic process is customarily defined as an idealized quasi-static reversible adiabatic process, of transfer of energy as work. Otherwise, for a constant-entropy process, if work is done irreversibly, heat transfer is necessary, so that the process is not adiabatic, and an accurate artificial control mechanism is necessary; such is ...
The path between each state consists of some process (A through D) which alters the pressure or volume of the system (or both). Generalized PV diagram A key feature of the diagram is that the amount of energy expended or received by the system as work can be measured because the net work is represented by the area enclosed by the four lines.
A process during which the entropy remains constant is called an isentropic process, written = or =. [12] Some examples of theoretically isentropic thermodynamic devices are pumps, gas compressors, turbines, nozzles, and diffusers.
This Process Path is a straight horizontal line from state one to state two on a P-V diagram. Figure 2. It is often valuable to calculate the work done in a process. The work done in a process is the area beneath the process path on a P-V diagram. Figure 2 If the process is isobaric, then the work done on the piston
Polytropic compression will use a value of between 0 (a constant-pressure process) and infinity (a constant volume process). For the typical case where an effort is made to cool the gas compressed by an approximately adiabatic process, the value of n {\displaystyle n} will be between 1 and κ {\displaystyle \kappa } .
Neutron stars are well modeled by polytropes with index between n = 0.5 and n = 1. A polytrope with index n = 1.5 is a good model for fully convective star cores [5] [6] (like those of red giants), brown dwarfs, giant gaseous planets (like Jupiter). With this index, the polytropic exponent is 5/3, which is the heat capacity ratio (γ) for ...
Utilizing that, for the isobaric process, T 3 /T 1 = V 3 /V 1, and for the adiabatic process, T 2 /T 3 = (V 3 /V 1) γ−1, the efficiency can be put in terms of the compression ratio, = (), where r = V 3 /V 1 is defined to be > 1. Comparing this to the Otto cycle's efficiency graphically, it can be seen that the Otto cycle is more efficient at ...