Coupled Pistons, Partitions, and Multistage Processes
For gases separated by a frictionless piston or subjected to staged constraints, each compartment obeys its own equation of state and first law, while piston equilibrium imposes force balance and shared boundary displacement with equal-and-opposite intercompartment work.
Why this shows up in the exam
Adiabatic pistons between two gases · Spring-loaded cylinders · Sequential sudden, isochoric, and isothermal stages
Learn the idea
Coupled compartments require simultaneous mechanical balance, gas laws, and energy accounting for each subsystem. A moving partition transfers work between gases, so solve the two sides together instead of treating either side as an isolated one-step process.
🧠 Memory hook: One moving boundary couples two energy balances.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P_L A - P_R A = F_external — quasistatic piston force balance with a consistent positive direction
- V_L + V_R = constant — volume constraint for a movable partition in a rigid outer cylinder
- ΔU_i = Q_i - W_i — separate first-law balance for each compartment using work-by convention
How to approach it
- 1Separate the system into compartments and stages
- 2Write geometry and force constraints
- 3Apply the appropriate process law and first law to each part, then solve together
Common slip-ups that cost marks
- •Applying one gas law to the combined gases when states differ
- •Forgetting equal-and-opposite partition work
- •Using final mechanical equilibrium throughout a sudden stage
🌟 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?
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