A solid metal sphere has a spherical cavity inside it. When the entire metal ball is heated uniformly, what happens to the volume of the internal cavity?

Introduction / Context:
Thermal expansion is a key concept in physics and engineering. When a solid is heated, its dimensions usually increase. A classic conceptual question asks what happens to a cavity inside a solid object when the object is heated. Many learners incorrectly imagine that the cavity shrinks because the surrounding material expands inward. This question tests whether you understand that thermal expansion is a uniform scaling effect that affects the entire body, including the space of the cavity.

Given Data / Assumptions:

• We have a solid ball of metal with a spherical cavity inside.
• The metal sphere is heated uniformly, so its temperature increases throughout.
• The material of the metal expands when heated, following its coefficient of linear or volumetric expansion.
• No external constraints are applied that would prevent free expansion.

Concept / Approach:
Thermal expansion in solids causes each linear dimension to increase proportionally to the temperature rise. For an unconstrained body, every length scale expands outward from the centre. If you imagine the cavity as if it were filled with the same metal and then removed after expansion, the expansion would have increased its size as well. Therefore, the cavity also grows in volume when the metal expands. The correct view is that the entire object, including the shape of the cavity, scales up. The cavity does not behave independently or shrink; instead, it expands along with the rest of the solid.

Step-by-Step Solution:
Step 1: Recall that for a solid with coefficient of linear expansion α, each linear dimension L changes approximately by ΔL = α L ΔT. Step 2: When the metal sphere is heated, all distances measured within the metal, including distances that define the boundary of the cavity, increase. Step 3: Consider a thought experiment where the cavity is initially filled with the same metal. After heating, that imaginary metal region would expand outward. Step 4: If we then remove that imaginary metal filling, the space that remains as the cavity must be larger than before heating. Step 5: Because volume is related to the cube of linear dimensions, any increase in linear size leads to a larger volume for both the outer sphere and the cavity. Step 6: Hence, the volume of the cavity increases when the sphere is heated.

Verification / Alternative check:
This result is consistent with mathematical treatments of thermal expansion, where overall linear scale is multiplied by a factor (1 + α ΔT). Applied uniformly, all radii, including the inner radius of the cavity, are increased by the same factor. Consequently, the inner radius grows, so the cavity becomes larger. Experiments with rings and rods, where metal rings expand and can no longer fit on rods when heated, follow the same logic: the hole in the ring also expands. This analogy reinforces the idea that cavities expand when the surrounding material undergoes uniform thermal expansion.

Why Other Options Are Wrong:
The volume of the cavity decreases: This reflects the incorrect intuition that the metal expands inward, squeezing the cavity, but uniform expansion actually increases all distances from the centre.
The volume of the cavity remains unchanged: This would mean no thermal expansion at the cavity boundary, which contradicts the material behaviour.
The shape changes but volume stays same: For uniform isotropic expansion, the spherical shape of the cavity is preserved and the volume increases, not stays constant.

Common Pitfalls:
The most common mistake is visualising expansion as pushing into the cavity rather than uniformly stretching the material. To avoid this, always imagine a cavity as space occupied by imaginary material that expands just like the rest of the solid. Once you adopt this picture, it becomes easy to see that the cavity must enlarge when the body is heated. Another pitfall is forgetting that expansion is three dimensional, so changes in radius produce even larger relative changes in volume.

Final Answer:
When the metal ball is heated uniformly, the volume of the cavity increases along with the rest of the sphere.