**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:**

**C**_{V,inner}dT_{inner}
= - P_{operating}dV_{inner} ,
C_{V,outer}dT_{outer} = - P_{operating}**dV**_{outer}

**with**

**
P**_{operating}
= P_{inner}**(1 - u/v**_{inner}**)**^{2}
, v_{inner}** = (RT**_{inner}**/M**_{inner}**)**^{1/2}

** P**_{operating}**
= P**_{outer}**(1 + u/v**_{outer}**)**^{2}**
, v**_{outer}** = (RT**_{outer}**/M**_{outer}**)**^{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:**

**C**_{V,inner}dT_{inner}
+ C_{V,outer}**dT**_{outer}**
= 0 and
dV**_{inner} + dV_{outer}**
= 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.**