To calculate the linear expansion coefficient (α) of the wire, we can use the formula for linear expansion:
\[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \]
Where:
- \( \Delta L \) = change in length
- \( L_0 \) = original length
- \( \alpha \) = linear expansion coefficient
- \( \Delta T \) = change in temperature
Given:
- Original length (\( L_0 \)) = 120 mm
- Final length = 120.324 mm
- Initial temperature = 20 °C
- Final temperature = 95 °C
Step 1: Calculate the change in length (\( \Delta L \))
\[ \Delta L = \text{Final length} - L_0 = 120.324 , \text{mm} - 120 , \text{mm} = 0.324 , \text{mm} \]
Step 2: Calculate the change in temperature (\( \Delta T \))
\[ \Delta T = \text{Final temperature} - \text{Initial temperature} = 95 , \text{°C} - 20 , \text{°C} = 75 , \text{°C} \]
Step 3: Rearranging the linear expansion formula to find \( \alpha \)
We can rearrange the formula to solve for \( \alpha \):
\[ \alpha = \frac{\Delta L}{L_0 \cdot \Delta T} \]
Step 4: Substitute the values into the equation
\[ \alpha = \frac{0.324 , \text{mm}}{120 , \text{mm} \cdot 75 , \text{°C}} \]
Step 5: Calculate \( \alpha \)
\[ \alpha = \frac{0.324}{120 \cdot 75} = \frac{0.324}{9000} \approx 3.6 \times 10^{-5} , \text{°C}^{-1} \]
Conclusion
The linear expansion coefficient of the wire is approximately:
\[ \alpha \approx 3.6 \times 10^{-5} , \text{°C}^{-1} \]