The coefficient of linear expansion of a certain of a certain solid is `9xx10^(-6)//""^@C` Assuming this solid behaves like most solids , what is its coefficient of volume expansion ?

Options

A. `9.1 xx10^(-6) //""^@C`
B. `2.7 xx10^(-6) //""^@C`
C. `27 xx10^(-6) //""^@C`
D. `729 xx10^(-6) //""^@C`

Answer

To find the coefficient of volume expansion (denoted as γ) of a solid given its coefficient of linear expansion (denoted as α), we can use the relationship between the two. The formula that relates the coefficient of volume expansion to the coefficient of linear expansion is:

\[ \gamma = 3\alpha \]

### Step-by-Step Solution:

1. **Identify the given data**:
- The coefficient of linear expansion (α) is given as \(9 \times 10^{-6} \, \text{°C}^{-1}\).

2. **Use the formula for volume expansion**:
- We know that the coefficient of volume expansion (γ) is related to the coefficient of linear expansion (α) by the equation:
\[ \gamma = 3\alpha \]

3. **Substitute the value of α into the equation**:
- Substitute \(α = 9 \times 10^{-6} \, \text{°C}^{-1}\) into the equation:
\[ \gamma = 3 \times (9 \times 10^{-6} \, \text{°C}^{-1}) \]

4. **Calculate γ**:
- Perform the multiplication:
\[ \gamma = 27 \times 10^{-6} \, \text{°C}^{-1} \]

5. **Final result**:
- Therefore, the coefficient of volume expansion (γ) is:
\[ \gamma = 27 \times 10^{-6} \, \text{°C}^{-1} \]