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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.
A polytropic process, in particular, causes changes to the system so that the quantity is constant (where is pressure, is volume, and is the polytropic index, a constant). Note that for specific polytropic indexes, a polytropic process will be equivalent to a constant-property process.
An adiabatic process (adiabatic from Ancient Greek ἀδιάβατος (adiábatos) 'impassable') is a type of thermodynamic process that occurs without transferring heat between the thermodynamic system and its environment. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work and/or mass flow.
where is the specific energy, is the specific volume, is the specific entropy, is the molecular mass, here is considered a constant (polytropic process), and can be shown to correspond to the heat capacity ratio. This equation can be shown to be consistent with the usual equations of state employed by thermodynamics.
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (C P) to heat capacity at constant volume (C V).
Isentropic process: a reversible adiabatic process, occurs at a constant entropy; Isobaric process: occurs at constant pressure; Isochoric process: occurs at constant volume (also called isometric/isovolumetric) Isothermal process: occurs at a constant temperature; Steady state process: occurs without a change in the internal energy
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 } .
The dependence of work on the path of the thermodynamic process is also unrelated to reversibility, since expansion work, which can be visualized on a pressure–volume diagram as the area beneath the equilibrium curve, is different for different reversible expansion processes (e.g. adiabatic, then isothermal; vs. isothermal, then adiabatic ...