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 air nitrogen helium argon xenon air nitrogen helium argon xenon 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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