The expansion of the length of an iron bridge, Δ*l*, during hot summers is directly proportional with the increase of temperature, Δ*T,* and the length, *l*0, of the bridge at 0 °C. Write a formula for the relationship between the change in length, Δ*l*, change in temperature, Δ*T,* and length at 0 °C.

The expansion of the length of an iron bridge, \(\Delta l\), during hot summers can be described using the linear thermal expansion formula. This relationship can be expressed as:

\[ \Delta l = \alpha l_0 \Delta T \]

where:
- \(\Delta l\) is the change in length of the bridge.
- \(\alpha\) is the coefficient of linear expansion for iron.
- \(l_0\) is the original length of the bridge at 0°C.
- \(\Delta T\) is the change in temperature.

This formula indicates that the change in length is directly proportional to both the original length and the change in temperature.

Would you like more details or have any questions?

Here are 5 related questions you can ask:
1. How do you calculate the coefficient of linear expansion?
2. What are typical values of the coefficient of linear expansion for common materials?
3. How does the expansion affect the structural integrity of bridges?
4. Can this formula be applied to other materials besides iron?
5. How do engineers mitigate the effects of thermal expansion in large structures?

Tip: When solving thermal expansion problems, always ensure the temperature change (\(\Delta T\)) is in the same units (usually °C or K) as the coefficient of linear expansion.

Understand how iron bridges expand with temperature changes using the linear thermal expansion formula Δl = α l₀ ΔT. Explore the relationship between temperature change, initial length, and bridge expansion. Ideal for high school students studying thermal expansion in materials.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation