Adiabatic Ideal-Gas Processes
For a quasistatic reversible adiabatic process of an ideal gas with constant gamma, PV^gamma, TV^(gamma-1), and T^gamma P^(1-gamma) are constants.
Why this shows up in the exam
Adiabatic bubble motion · Rapid compression or expansion · Multistage P-V paths
Learn the idea
An adiabatic ideal gas changes temperature because boundary work changes its internal energy without heat transfer. Expansion spends molecular internal energy on work and cools the gas; compression does work on it and heats it.
🧠 Memory hook: No heat: expansion cools because the gas pays the work.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- PV^gamma = constant — reversible adiabatic ideal-gas relation with constant gamma
- TV^(gamma-1) = constant — temperature-volume form under the same assumptions
- Q = 0; Delta U = -W — first-law balance when W is work done by the gas
How to approach it
- 1Confirm the process is adiabatic and quasistatic
- 2Choose the relation containing the requested variables
- 3Check that expansion lowers T
Common slip-ups that cost marks
- •Applying PV^gamma to irreversible free expansion
- •Using isothermal PV=constant instead
- •Forgetting gamma belongs to the gas or mixture
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
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Ideal-Gas Equation and Molecular Form
For a dilute ideal gas in thermal equilibrium, the state variables satisfy PV = nRT = Nk_B T, where intermolecular potential energy and molecular volume are neglected.