Apparent Expansion, Density, and Buoyancy
For fixed mass and small temperature change, density varies as rho approximately rho_0(1-gamma Delta T); an apparent liquid expansion coefficient is the liquid's real volume coefficient minus that of its container.
Why this shows up in the exam
Liquid-in-glass thermometers · Temperature correction of hydrometers and sinkers · Overflow and constant-vacant-volume problems
Learn the idea
Observed liquid expansion and buoyancy depend on the competing expansion of both liquid and container or immersed body. A rising liquid level or changing apparent weight is a comparison, not a one-material effect: the liquid density changes while the vessel, float, or sinker also changes size.
🧠 Memory hook: Apparent change equals what the liquid gains minus what the vessel gains.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- gamma_apparent = gamma_liquid - gamma_container — small apparent overflow or level-change coefficient
- rho(T) approximately rho₀/(1+gamma Delta T) — density change of a fixed mass under volumetric expansion
- F_b = rho_liquid(T) V_displaced(T) g — buoyant force when both density and displaced volume may vary
How to approach it
- 1Write mass conservation for each material
- 2Expand volumes only to the required order
- 3Apply buoyancy or vacant-volume constraints after temperature correction
Common slip-ups that cost marks
- •Changing density without conserving mass
- •Ignoring expansion of the sinker or container
- •Using a linear coefficient directly for a liquid volume
🌟 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 wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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