Read Melting Spheres: Cancel the Area Carefully
This short read prepares one exact NSEP pattern: spherical ice melting at surface-limited heating. Identify the physical condition before calculating.
A phase change alters the arrangement and motion of particles without creating a new substance.
Particles change their freedom of movement
Heat → particles move more freely
Heating increases particle motion: solid → liquid → gas. During a phase-change plateau, energy separates particles instead of raising temperature.
Start with the physical model
Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.
Build the relation
Let the instantaneous radius be r.
Hence k(4πr2) = -ρL(4πr2)dr/dt, giving dr/dt = -k/(ρL). Therefore r decreases linearly with time with slope -k/(ρL).
Check before selecting
Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.
OlympIQ exam lens
- ✓Name the governing law before using a formula.
- ✓Keep the stated geometry and direction information explicit.
- ✓Use one unit or limiting-case check.
Do not assume shrinking area automatically makes the radius change nonlinearly; compare heat input and latent heat for the same thin shell.
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