Density Change under Pressure
With fixed mass and small hydrostatic compression, Delta rho/rho is approximately minus Delta V/V, so the density increase is rho Delta P/K to first order.
Why this shows up in the exam
Pressure correction of liquid density · Deep-ocean density estimates · Compressible material calculations
Learn the idea
Compression raises density because mass stays fixed while volume decreases. Squeezing a fixed amount of material into a slightly smaller volume increases its density by nearly the same fraction that its volume decreases.
🧠 Memory hook: Same mass, less volume, more density.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- rho = m/V — mass-conservation definition of density
- Delta rho/rho approximately -Delta V/V — first-order relation for a fixed mass
- Delta rho approximately rho Delta P/K — density increase under a small pressure rise
How to approach it
- 1State that mass is constant
- 2Use bulk modulus for the volume fraction
- 3Reverse the sign to obtain the density change
Common slip-ups that cost marks
- •Changing mass during compression
- •Using the exact reciprocal as a simple linear equality for large changes
- •Choosing the surrounding fluid's bulk modulus
🌟 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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