To determine the length of a steel railroad track on a hot day when the temperature increases, we can use the formula for linear expansion. The formula for linear expansion is given by: \[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \] Where: - \(\Delta L\) = change in length - \(L_0\) = original length of the object - \(\alpha\) = coefficient of linear expansion - \(\Delta T\) = change in temperature ### Step-by-Step Calculation 1. **Identify the given values:** - Original length of the track, \(L_0 = 20 \, \text{m}\) - Coefficient of linear expansion for steel, \(\alpha = 11 \times 10^{-6} \, \text{K}^{-1}\) - Initial temperature, \(T_1 = 20^\circ C\) - Final temperature, \(T_2 = 40^\circ C\) 2. **Calculate the change in temperature (\(\Delta T\)):** \[ \Delta T = T_2 - T_1 = 40^\circ C - 20^\circ C = 20 \, \text{K} \] 3. **Calculate the change in length (\(\Delta L\)):** \[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \] Substituting the values: \[ \Delta L = 20 \, \text{m} \cdot (11 \times 10^{-6} \, \text{K}^{-1}) \cdot 20 \, \text{K} \] \[ \Delta L = 20 \cdot 11 \cdot 20 \times 10^{-6} \, \text{m} \] \[ \Delta L = 4400 \times 10^{-6} \, \text{m} = 0.0044 \, \text{m} \] 4. **Calculate the new length of the track (\(L\)):** \[ L = L_0 + \Delta L \] \[ L = 20 \, \text{m} + 0.0044 \, \text{m} = 20.0044 \, \text{m} \] 5. **Round the answer to three decimal places:** \[ L \approx 20.004 \, \text{m} \] ### Conclusion The length of the steel railroad track on a hot dry day when the temperature is 40°C will be approximately **20.004 m**. Therefore, the correct option is **C. 20.004m**. ### Explanation of Other Options - **Option A (20.013m)**: This value is too high. It likely results from an incorrect calculation of the change in length or an incorrect assumption about the temperature change. - **Option B (20.009m)**: This value is also too high and does not accurately reflect the calculated change in length based on the given temperature increase. - **Option D (20.002m)**: This value is too low and does not account for the full change in length due to the temperature increase. ### Revision Summary - Use the linear expansion formula: \(\Delta L = L_0 \cdot \alpha \cdot \Delta T\). - Calculate the change in temperature accurately. - Substitute values carefully to find the change in length. - Add the change in length to the original length to find the new length.