The first law of thermodynamics relates internal energy
to heat added
and work added
For an adiabatic system, heat transfer is zero:
By the first law, applied to both tanks together, no work is done across the system boundary (the walls of the tanks):
represents the number of moles,
is the constant-volume heat capacity,
is absolute temperature,
is a reference temperature and
is the ideal gas constant. Subscript
represents initial conditions, and subscripts
represent the final conditions in tanks A and B.
Equation (6) simplifies to
Equation (7) means the average temperature of the system (
) does not change, so the final pressure (
) is determined from the ideal gas law:
where the initial volume of tank A is 22.4 L.
The total moles in the system does not change:
The expansion of the gas that remains in tank A is modeled as a reversible adiabatic expansion. This gas does work in pushing the rest of the gas out of tank A and through the valve. For an ideal gas, the final temperature in tank A is related to its initial temperature
and its final pressure
, the heat capacity ratio.