Irreversible, Sudden, and Free Adiabatic Changes
For an irreversible adiabatic process Q = 0 but generally PV^γ is not constant; boundary work is evaluated from the external pressure, and ideal-gas free expansion into vacuum has W = 0, ΔU = 0, and ΔT = 0.
Why this shows up in the exam
Partition removal into vacuum · Sudden piston loading or release · Distinguishing adiabatic from isentropic motion
Learn the idea
Adiabatic does not imply reversible: sudden motion and free expansion require external-pressure energy accounting. An insulated gas can change without following a Poisson curve; in vacuum it does no boundary work and an ideal gas keeps the same temperature.
🧠 Memory hook: No heat is not enough for Poisson; reversibility is the missing key.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_by = ∫ P_ext dV — irreversible boundary work determined by external, not equilibrium gas, pressure
- Q = 0 => ΔU = -W_by — first-law result with work by the system positive
- free expansion into vacuum: W = 0, ΔU = 0 — ideal-gas result for an insulated rigid outer container
How to approach it
- 1Decide whether the path is quasistatic
- 2Write work using external pressure
- 3Use Q = 0 in the first law before invoking any gas relation
Common slip-ups that cost marks
- •Applying PV^γ to every insulated process
- •Using gas pressure instead of external pressure for sudden motion
- •Assuming all adiabatic changes alter temperature
🌟 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 absorbs 500 J of heat and does 200 J of work. What is the change in its internal energy?
More from Thermodynamics
Thermodynamic Processes and P-V Diagrams
Study different thermodynamic processes (isothermal, isobaric, isochoric, adiabatic, polytropic, cyclic), their definitions, characteristics, and graphical representation on P-V diagrams.
Laws of Thermodynamics
Understand the zeroth and first laws of thermodynamics, including their statements, implications, and applications to physical systems.
Internal Energy, Heat, and Work
Explore the concepts of internal energy, heat, and work, including their definitions, relationships, and how they change during various thermodynamic processes.
Ideal Gas Law and Equation
Learn the ideal gas equation, its relation to physical quantities like pressure, volume, temperature, and density, and its use in describing the behavior of ideal gases.
Gibbs Free Energy and Spontaneity
Learn how Gibbs free energy determines spontaneity, how to calculate it, and its dependence on temperature, pressure, and other thermodynamic parameters.
Entropy and Its Changes
Understand entropy as a measure of disorder, how it changes in physical and chemical processes, and its calculation in various scenarios including phase transitions and isothermal processes.