Q153
General SciencePhysics
A metallic ball has a spherical cavity at its centre. If the ball is heated what happens to the cavity?
- a.Its volume decreases.
- b.Its volume increases.
- c.Its volume remains unchanged.
- d.Its volume may increase or decrease depending upon the nature of the metal.
Answer: (B) Its volume increases.
Thermal expansion works like a photographic enlargement: every linear dimension of the body grows in the same proportion, including the dimensions of a cavity or hole. The cavity therefore expands exactly as if it were filled with the same metal, and its volume increases by $\Delta V=\gamma V\Delta T$, whatever the metal. This is why a hole in a metal plate gets bigger on heating, an iron tyre is heated before being fitted on a cart wheel, and a tight metal lid loosens under hot water. The coefficients are related as $\alpha:\beta:\gamma=1:2:3$.