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:
= - PoperatingdVinner ,
CV,outerdTouter = - PoperatingdVouter
= Pinner(1 - u/vinner)2
, vinner = (RTinner/Minner)1/2
in which u
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:
= Pouter(1 + u/vouter)2
, vouter = (RTouter/Mouter)1/2
= 0 and
dVinner + dVouter
= 0 .
The calculator operates in two modes:
1. Infinite volume of outer gas (default): The temperature and
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
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