- #31
C.E
- 100
- 0
I got if from when you said "(v-Ax)^{\gamma}\approx v^\gamma-Ax\gamma" in post 8.
Thermodynamics: Horizontal Tube w/ Sliding Piston - Q&A
- Thread starter C.E
- Start date
-
- Tags
- Thermodynamics
Click For Summary
SUMMARY
The discussion focuses on the dynamics of a thermally insulating horizontal tube containing gas and a sliding piston. The force on the piston is derived as F = -2xpA²/γV, where γ = Cₚ/Cᵥ. Participants explore the nature of motion, confirming it as simple harmonic, and derive the frequency of oscillation as ω = √(k/m). The conversation emphasizes the importance of using Taylor series for approximating gas behavior under small displacements and clarifies the assumptions necessary for analyzing non-ideal gas behavior in adiabatic processes.
PREREQUISITES- Understanding of thermodynamics principles, particularly adiabatic processes.
- Familiarity with Taylor series expansions and their applications in physics.
- Knowledge of gas laws and the relationships between pressure, volume, and temperature.
- Basic concepts of harmonic motion and oscillation frequency calculations.
- Study the derivation of the adiabatic process equations for non-ideal gases.
- Learn about the application of Taylor series in physics, particularly in thermodynamic contexts.
- Explore the principles of simple harmonic motion and its mathematical representation.
- Investigate the implications of using non-ideal gas equations in thermodynamic calculations.
Students and professionals in physics, particularly those focusing on thermodynamics, mechanical engineering, and anyone interested in the dynamics of gas systems and oscillatory motion.