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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.
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 ...
The model assumptions are: the uncompressed volume of the cylinder is one litre (1 L = 1000 cm 3 = 0.001 m 3); the gas within is the air consisting of molecular nitrogen and oxygen only (thus a diatomic gas with 5 degrees of freedom, and so γ = 7 / 5 ); the compression ratio of the engine is 10:1 (that is, the 1 L volume of uncompressed ...
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).
The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).
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 ...
Now inverting the equation for temperature T(e) we deduce that for an ideal polytropic gas the isochoric heat capacity is a constant: c v ≡ m ( ∂ e ∂ T ) v = m d e d T = 1 ( γ − 1 ) {\displaystyle c_{v}\equiv m\left({\partial e \over \partial T}\right)_{v}=m{de \over dT}={\frac {1}{(\gamma -1)}}}
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 ...