• id: JME-10-N03
• title: How Holes Expand
• tags: hole, cavity, ring, expansion

A hole or cavity in a heated solid expands exactly as if it were filled with the same material. When a metal ring is heated, its inner diameter increases (not decreases). Proof: imagine the hole filled with a solid plug of the same material. When heated uniformly, the plug and the ring expand identically — the plug exactly fills the expanded hole. Remove the plug, and the hole size must be the same. This means: (1) Heated metal rings are easier to slip over objects. (2) A heated ring can be shrink-fitted onto a shaft by cooling. (3) The volume of a cavity increases with the same $\gamma$ as the solid material.