A bimetallic strip is made of copper and steel. The linear expansivity of copper is $3.0 \times 10^{-5} /K$ and the linear expansivity of steel is $1.0 \times 10^{-5} /K$. What will happen when the strip is heated? We are given four options: (a) the strip will remain straight, (b) bend with copper on the convex side, (c) bend with steel on the convex side, and (d) get twisted.

1. Problem Description

A bimetallic strip is made of copper and steel. The linear expansivity of copper is $3.0 \times 10^{-5} /K$ and the linear expansivity of steel is $1.0 \times 10^{-5} /K$. What will happen when the strip is heated? We are given four options: (a) the strip will remain straight, (b) bend with copper on the convex side, (c) bend with steel on the convex side, and (d) get twisted.

2. Solution Steps

The linear thermal expansion coefficient $\alpha$ is a material property that describes how much a material's length changes per degree Celsius (or Kelvin) change in temperature.

$\Delta L = \alpha L_0 \Delta T$

where:

$\Delta L$ is the change in length

$\alpha$ is the coefficient of linear expansion

$L_0$ is the original length

$\Delta T$ is the change in temperature

Since the coefficient of linear expansion for copper ($3.0 \times 10^{-5} /K$) is greater than that of steel ($1.0 \times 10^{-5} /K$), copper will expand more than steel for the same temperature change. If the strip were to remain straight, it would require that the copper be compressed and the steel be stretched. Since the two materials are bonded together, the strip will bend. The material with the larger expansion will be on the outside of the curve (the convex side). Therefore, the strip will bend with the copper on the convex side.

3. Final Answer

Bend with Copper on Convex side