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QPage 11: Q13: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Page 11: Q13 Solution: A spherical shell is heated. The volume changes according to…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently apply the volumetric expansion law $V=V_0(1+\gamma\theta)$ to the empty space inside a hollow sphere, assuming the interior volume expands directly. In reality $V$ refers to the volume of the shell material itself; the cavity’s volume changes only as a geometric consequence of the shell’s thickness expanding, not because the interior obeys the same thermal‑expansion coefficient.

A spherical shell is heated. The volume changes according to the equation Vθ=V01+γθ)V_\theta = V_0 1 + \gamma\theta). Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell?

Step-by-Step Verified Solution

**Answer:** The volume refers to the volume of the material making up the shell, not the enclosed volume. **Step-by-Step Explanation:** When a spherical shell is heated, the material of the shell expands. Vθ=V0(1+γθ)V_\theta = V_0(1+\gamma\theta) describes the volume of the shell material. The hollow space inside also expands geometrically, but this is a consequence of the material expansion, not a separate thermal expansion of the enclosed volume.

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