Adiabatic Calculations of A Gas Expanding Against A Gas
Gary L Bertrand, Professor Emeritus of Chemistry
Missouri University of Science and Technology

Inner Gas       Outer Gas 



Volume(L)  Volume (L) 
Temperature (K)  Temperature (K) 
Pressure (bar)  Pressure (bar) 

orifice    cm2



instructions/discussion


final temperature  

    reversible temp 

     isobaric temp 








This calculator performs thermodynamic calculations for adiabatic expansion of an Inner ideal gas against an Outer ideal gas, separated by a massless, frictionless piston.  These are numerical integrations of the relationships:

CV,innerdTinner = - PoperatingdVinner   ,  CV,outerdTouter = - PoperatingdVouter
with
    Poperating = Pinner(1 - u/vinner)2    ,    vinner = (RTinner/Minner)1/2
    Poperating = Pouter(1 + u/vouter)2    ,    vouter = (RTouter/Mouter)1/2

in which u is the velocity of the piston, and v is the mean velocity of the gas molecules in the direction of the piston’s movement.  These relationships are subject to the restraints:

CV,innerdTinner + CV,outerdTouter = 0     and  dVinner  + dVouter = 0 .

The calculator operates in two modes:
1. Infinite volume of outer gas (default): The temperature and pressure of the outer gas are essentially unchanged during the expansion.  The calculation shows the final temperature of the inner gas, the calculated temperature for a reversible expansion of the inner gas to the pressure of the outer gas, and the calculated temperature for a constant-pressure expansion of the inner gas to the pressure of the outer gas.  The program also shows P-V-T data for the inner gas at 10 points during the expansion.

2. Finite volume of outer gas (replace “infinite” volume of the outer gas with a numerical value for its volume in liters):  The inner gas gets colder and the outer gas gets warmer in this expansion/compression of the two gases.  P-V-T data are shown for both gases at 10 points during the process, plus entropy changes for both gases.

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