To calculate the strain in the steel railroad due to the increase in temperature, we can use the formula:

$\text{Strain} = \alpha \times \Delta T$

Where:

• $\alpha$ is the coefficient of thermal expansion (given as $11.7 \times 10^{-6}$ m/m°C),
• $\Delta T$ is the change in temperature in °C.

Step 1: Convert the temperature difference from Fahrenheit to Celsius

The temperature difference in Fahrenheit is:

$\Delta T_{F} = 95^\circ F - 70^\circ F = 25^\circ F$

To convert Fahrenheit to Celsius:

$\Delta T_{C} = \frac{5}{9} \times \Delta T_{F} = \frac{5}{9} \times 25 = 13.89^\circ C$

Step 2: Calculate the strain

Now, we can calculate the strain:

$\text{Strain} = 11.7 \times 10^{-6} \, \text{m/m}^\circ C \times 13.89^\circ C$

Let me calculate that.The calculated strain is $1.625 \times 10^{-4}$.

Therefore, the correct answer is: B. $1.625 \times 10^{-4}$.

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How does thermal expansion affect different materials like steel and aluminum?
2. What factors can influence the coefficient of thermal expansion?
3. How would the strain change if the temperature difference were larger?
4. Why do engineers need to account for thermal expansion in railroad tracks?
5. Can you derive the relationship between strain and stress due to thermal expansion?

Tip: Always ensure that the temperature units are consistent when calculating strain or thermal effects.