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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.
In contrast, free expansion is an isothermal process for an ideal gas. Adiabatic compression occurs when the pressure of a gas is increased by work done on it by its surroundings, e.g., a piston compressing a gas contained within a cylinder and raising the temperature where in many practical situations heat conduction through walls can be slow ...
Compression efficiency is then the ratio of temperature rise at theoretical 100 percent (adiabatic) vs. actual (polytropic). 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 ...
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).
Absolute cylinder pressure is used to calculate the dynamic compression ratio, using the following formula: = where is a polytropic value for the ratio of specific heats for the combustion gases at the temperatures present (this compensates for the temperature rise caused by compression, as well as heat lost to the cylinder)
Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead center (BDC) to top dead center (TDC). Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead center.
where P is the pressure, V is volume, n is any real number (the "polytropic index"), and C is a constant. This equation can be used to accurately characterize processes of certain systems , notably the compression or expansion of a gas , but in some cases, liquids and solids .
Specifically, the polytropic gas is a gas for which the specific heat is constant. [2] [3] The equation of state of a polytropic fluid is general enough that such idealized fluids find wide use outside of the limited problem of polytropes. The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the ...