Polytropic processes on a PV plot

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SUMMARY

The discussion focuses on the characteristics of polytropic processes depicted on a pressure-volume (PV) plot. It establishes that the shape of the polytropic process curve is concave up due to the relationship defined by the equation PV^n = K, where 'n' influences the curve's orientation. Specifically, when n equals Cp/Cv, the process is adiabatic; when n equals 1, it is isothermal; and when n equals 0, it is isobaric. None of these conditions yield a convex PV graph, confirming the concave nature of the polytropic process.

PREREQUISITES
  • Understanding of thermodynamic processes, specifically polytropic, isothermal, and adiabatic processes.
  • Familiarity with the ideal gas law and its applications in thermodynamics.
  • Knowledge of pressure-volume (PV) diagrams and their significance in thermodynamic cycles.
  • Basic grasp of specific heat capacities, Cp and Cv, and their roles in thermodynamic equations.
NEXT STEPS
  • Study the derivation and applications of the polytropic process equation PV^n = K.
  • Explore the implications of varying 'n' in polytropic processes and its effect on the PV plot.
  • Investigate the differences between adiabatic, isothermal, and isobaric processes in detail.
  • Learn how to sketch and interpret various thermodynamic cycles on PV diagrams.
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, mechanical engineers, and anyone involved in analyzing thermodynamic cycles and processes.

eurekameh
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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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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.

AM
 

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