PhysicsRankPREVIEWTry a problem

THE PRACTICE STUDIO

Go slowly. Ask why. Make it yours.

PRACTICE · MEMBERSIntermediate · Single correct

PRACTICE / Thermal expansion

Compare liquid growth with new capacity

A vessel initially holds exactly 250 mL of liquid to the brim. The liquid’s volume expansion coefficient is 250 × 10⁻⁶ K⁻¹. The free isotropic vessel’s linear coefficient is 20 × 10⁻⁶ K⁻¹. Both warm by 80 K; evaporation is negligible.

What overflow volume does the first-order model predict?

Organize the givens & assumptions
  • Initial volume = 250 mL
  • Liquid β = 250 × 10⁻⁶ K⁻¹
  • Vessel α = 20 × 10⁻⁶ K⁻¹
  • Rise = 80 K

Uniform temperatures and the stated expansion coefficients; small thermal strains and first-order expansion unless a retained ratio is explicitly requested. Free expansion except for the named axial constraints. Constrained rods remain straight and linearly elastic; no buckling, yielding or moving supports.

  1. A4.6 mL4.6\ \mathrm{mL}
  2. B6.2 mL6.2\ \mathrm{mL}
  3. C3.8 mL3.8\ \mathrm{mL}
  4. D5.0 mL5.0\ \mathrm{mL}

Try it on paper first. Free sample problems in every collection include the complete reasoning: find one in this collection →