Example 1 — Follow the energy, not the thermometer
EasyProblem
Ice at 0 °C is warmed until it has all melted into water at 0 °C. The thermometer does not move the whole time. Say what the added energy did.
Solution
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Compare the two panels: the particles are the same, but the lattice has broken up.
A phase change rearranges particles. It does not create, destroy, or alter them.
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Note that both panels are labelled 0 °C.
Temperature measures the average motion of the particles. During a melt that average holds steady, so the thermometer sits still.
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Account for the energy: it went into separating particles, not into speeding them up.
Pulling particles out of a fixed lattice costs energy. That is what the absorbed heat paid for.
Answer
The energy went into breaking the fixed arrangement holding the particles in place, so the ice became water at the same temperature.
Takeaway: A flat thermometer during a phase change means energy is going into arrangement, not motion.