A gas can expanding adiabatically might stop expanding either because it has filled a rigid container (known final volume) or it has equilibrated with an external pressure (known final volume). Derive the expression for the final pressure of an ideal gas after an adiabatic expansion. Begin with the simple expression derived using the ideal gas law: PiVi Ti PfVf Tf Then use the expression for the ratio of the final temperature R/C₂ (1) The final expression is Ti Tf Pƒ = P₁ * Cp Vi Cv SIS

Physical Chemistry
2nd Edition
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Author:Ball, David W. (david Warren), BAER, Tomas
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Chapter2: The First Law Of Thermodynamics
Section: Chapter Questions
Problem 2.30E: A piston reversibly and adiabatically contracts 3.88 moles of ideal gas to one-tenth of its original...
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A gas can expanding adiabatically might stop expanding either because it has filled a
rigid container (known final volume) or it has equilibrated with an external pressure
(known final volume).
Derive the expression for the final pressure of an ideal gas after an adiabatic expansion.
Begin with the simple expression derived using the ideal gas law:
PiVi Ti
Pf Vf Tf
Then use the expression for the ratio of the final temperature
R/C₂
The final expression is
Ti
Tf
=
=
(1)
Pf = Pi
- (²
*
Transcribed Image Text:A gas can expanding adiabatically might stop expanding either because it has filled a rigid container (known final volume) or it has equilibrated with an external pressure (known final volume). Derive the expression for the final pressure of an ideal gas after an adiabatic expansion. Begin with the simple expression derived using the ideal gas law: PiVi Ti Pf Vf Tf Then use the expression for the ratio of the final temperature R/C₂ The final expression is Ti Tf = = (1) Pf = Pi - (² *
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