The coefficient of linear expansion of a metal rod is `12 xx 10^(-6//0)C`, its value in per ``^(0)F`

Options

A. `(20)/(3) xx 10^(-6//0)F`
B. `(15)/(4) xx 10^(-6//0)F`
C. `21.6 xx 10^(-6//0)F`
D. `12 xx 10^(-6//0)F`

Answer

To convert the coefficient of linear expansion from degrees Celsius to degrees Fahrenheit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Value**:
The coefficient of linear expansion of the metal rod is given as:
\[ \alpha = 12 \times 10^{-6} \, \text{per degree Celsius} \]

2. **Understand the Relationship Between Celsius and Fahrenheit**:
The relationship between the temperature change in Celsius (\(\Delta T_C\)) and Fahrenheit (\(\Delta T_F\)) is given by:
\[ \Delta T_C = \frac{5}{9} \Delta T_F \]
This means that a change of 1 degree Fahrenheit corresponds to a change of \(\frac{5}{9}\) degrees Celsius.

3. **Convert the Coefficient of Linear Expansion**:
To convert the coefficient of linear expansion from per degree Celsius to per degree Fahrenheit, we can use the following relationship:
\[ \alpha_F = \alpha_C \times \frac{9}{5} \]
where \(\alpha_F\) is the coefficient in per degree Fahrenheit and \(\alpha_C\) is the coefficient in per degree Celsius.

4. **Substitute the Given Value**:
Now, substituting the value of \(\alpha_C\):
\[ \alpha_F = 12 \times 10^{-6} \times \frac{9}{5} \]

5. **Calculate the Value**:
First, calculate \(12 \times 9 = 108\), and then divide by 5:
\[ \alpha_F = \frac{108}{5} \times 10^{-6} = 21.6 \times 10^{-6} \, \text{per degree Fahrenheit} \]

6. **Final Answer**:
Therefore, the coefficient of linear expansion in per degree Fahrenheit is:
\[ \alpha_F = 21.6 \times 10^{-6} \, \text{per degree Fahrenheit} \]