Two spheres of the same size are made of the same metal, but one is hollow and the other is solid. They are heated to the same temperature. Then,

Options

A. the hollow sphere will expand more
B. the solid sphere will expand more
C. both spheres will expand almost equally
D. only the solid sphere will expand

Answer

To solve the problem regarding the expansion of two spheres made of the same metal—one hollow and one solid—we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two spheres of the same size and made of the same metal: one is hollow, and the other is solid.
- Both spheres are heated to the same temperature.

2. **Thermal Expansion Basics**:
- When materials are heated, they expand. The degree of expansion depends on the material's properties.
- The coefficient of linear expansion (α) and the coefficient of volume expansion (γ) are key properties that describe how materials expand with temperature changes.

3. **Coefficients of Expansion**:
- Since both spheres are made of the same metal, they will have the same coefficient of volume expansion (γ). This means that both will expand in volume at the same rate when subjected to the same temperature increase.

4. **Volume Expansion Formula**:
- The formula for volume expansion is given by:
\[ \Delta V = \gamma \cdot V_0 \cdot \Delta T \]
- Where:
- \(\Delta V\) = change in volume
- \(V_0\) = original volume
- \(\Delta T\) = change in temperature
- \(\gamma\) = coefficient of volume expansion

5. **Applying the Formula**:
- For the solid sphere:
\[ \Delta V_{solid} = \gamma \cdot V_{solid} \cdot \Delta T \]
- For the hollow sphere:
\[ \Delta V_{hollow} = \gamma \cdot V_{hollow} \cdot \Delta T \]
- Since both spheres are of the same size and made of the same material, we can conclude that:
\[ \Delta V_{solid} = \Delta V_{hollow} \]

6. **Conclusion**:
- Both spheres will expand equally in volume when heated to the same temperature because they are made of the same material and have the same coefficient of volume expansion.

### Final Answer:
Both spheres will expand almost equally.