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Adiabatic Process Equations for an Ideal Gas

An adiabatic process is one that occurs without transfer of heat or matter between a thermodynamic system and its surroundings. Energy is transferred only as work.

The equations relate initial and final pressure and temperature for an adiabatic process, including the net work done on or by the system. The equations also indicate no net change in the heat and entropy in the system.


{QuantityVariable[Subscript["p", "f"], "Pressure"]*QuantityVariable[Subscript["V", "f"], "Volume"]^QuantityVariable["γ", "HeatCapacityRatio"] == QuantityVariable[Subscript["p", "i"], "Pressure"]*QuantityVariable[Subscript["V", "i"], "Volume"]^QuantityVariable["γ", "HeatCapacityRatio"], QuantityVariable[Subscript["T", "f"], "Temperature"]*QuantityVariable[Subscript["V", "f"], "Volume"]^(-1 + QuantityVariable["γ", "HeatCapacityRatio"]) == QuantityVariable[Subscript["T", "i"], "Temperature"]*QuantityVariable[Subscript["V", "i"], "Volume"]^(-1 + QuantityVariable["γ", "HeatCapacityRatio"]), QuantityVariable["W", "Work"] == (QuantityVariable[Subscript["p", "f"], "Pressure"]*QuantityVariable[Subscript["V", "f"], "Volume"] - QuantityVariable[Subscript["p", "i"], "Pressure"]*QuantityVariable[Subscript["V", "i"], "Volume"])/(-1 + QuantityVariable["γ", "HeatCapacityRatio"]), QuantityVariable["Q", "Heat"] == 0, QuantityVariable["Δ​S", "Entropy"] == 0}

symbol description physical quantity
pf final pressure "Pressure"
Vf final volume "Volume"
γ heat capacity ratio "HeatCapacityRatio"
pi initial pressure "Pressure"
Vi initial volume "Volume"
Tf final temperature "Temperature"
Ti initial temperature "Temperature"
W work done on the system "Work"
Q heat transferred to the system "Heat"
Δ​S entropy change "Entropy"



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