Pistons, Partitions, Springs, and Mechanical Equilibrium
For a quasistatic frictionless piston of area A, mechanical equilibrium requires (P_left-P_right)A plus all other signed external forces to vanish.
Why this shows up in the exam
Weighted and spring-loaded pistons · Thermally conducting movable partitions · Coupled gas-buoyancy arrangements
Learn the idea
A movable partition stops where gas-pressure forces balance weight, atmosphere, spring force, and the opposing gas. Treat the piston as a free body first; only after the force balance is clear should gas laws determine each chamber pressure.
🧠 Memory hook: Free-body the piston before gas-law algebra.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum F_piston = 0 — mechanical equilibrium condition for a stationary frictionless piston
- (P1-P2)A = mg + kx — representative vertical spring-loaded balance with signs set by the diagram
- P_i V_i = n_i RT_i — gas constraint applied separately to each chamber
How to approach it
- 1Draw piston forces with signs
- 2Express each chamber volume geometrically
- 3Combine force balance with gas equations
Common slip-ups that cost marks
- •Setting chamber pressures equal despite piston weight or spring force
- •Using spring length instead of extension
- •Forgetting volumes change in opposite directions
🌟 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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