A liquid with volume expansion coefficient gamma is filled to the brim of a container made of material with linear expansion coefficient alpha. On heating, the liquid overflows. Which condition must hold?

gamma = 3*alpha
gamma > 3*alpha
gamma < 3*alpha
gamma = 3*alpha³

Correct answer: gamma > 3*alpha

Solution

For an isotropic solid container, the volume expansion coefficient is 3*alpha. On heating by DT, the container volume increases by a fraction 3*alpha*DT, while the liquid volume increases by gamma*DT. For the liquid to overflow, its expansion must exceed the container's expansion: gamma*DT > 3*alpha*DT => gamma > 3*alpha.

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