Polytropic processes on a PV plot

The conversation discusses the isochoric heat addition, polytropic expansion, and isobaric compression back to the initial state in a cycle on a pressure-volume plot. The question is raised about why the polytropic process is concave up on the plot, which can vary depending on the value of n in the equation PV^n = K. Different values of n will result in different processes on the PV graph, such as adiabatic, isothermal, and isobaric processes, but none of them will produce a convex curve.
  • #1
1 -> 2 : Isochoric heat addition
2 -> 3 : Polytropic expansion
3 -> 1 : Isobaric compression back to the initial state

Sketch this cycle on a pressure-volume plot in relation to the saturation curve.
Now, my question is, why is the polytropic process on the PV plot concave up and not down, as shown on http://imageshack.us/photo/my-images/685/unledmhi.png/ ?
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  • #2
The plot of the polytropic process depends on the value of n in [itex]PV^n = K[/itex]. If n = Cp/Cv it is an adiabatic process. If n = 1 then it is an isothermal process (PV = nRT = constant). If n=0 it is an isobaric process. None of those will provide a convex PV graph.


What is a polytropic process on a PV plot?

A polytropic process is a thermodynamic process in which the relationship between pressure (P) and volume (V) can be described by the equation P*V^n = constant, where n is a constant known as the polytropic index. On a PV plot, this process appears as a curved line.

What is the significance of the polytropic index (n) in a polytropic process?

The polytropic index represents the ratio of heat added or removed during the process to the change in internal energy of the system. It also indicates the type of process that is occurring - for example, a polytropic index of 1 represents an isothermal process, while a polytropic index of 0 represents an isobaric process.

How is work calculated for a polytropic process on a PV plot?

The work done in a polytropic process can be calculated by taking the integral of the pressure-volume curve on a PV plot. The formula for work is W = P*dV, where P is the pressure at a given point on the curve, and dV is the change in volume between two points on the curve.

What are some real-life examples of polytropic processes?

Polytropic processes can be observed in many natural and artificial systems, such as in the compression and expansion of gases in an internal combustion engine, the expansion and contraction of air in a bicycle pump, and the expansion and cooling of air in a refrigerator.

What are some ideal gas laws that can be applied to polytropic processes?

The ideal gas law (PV = nRT) and the combined gas law (P1V1/T1 = P2V2/T2) can both be applied to polytropic processes, as long as the process is reversible and the gas behaves ideally. Additionally, the adiabatic equation (P1V1^gamma = P2V2^gamma) can be used for polytropic processes with a constant heat capacity ratio (gamma).

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