Question

Suppose a bimetallic strip is constructed of two strips of metals with linear expansion coefficients \(\alpha_{1}\) and \(\alpha_{2},\) where \(\alpha_{1}>\alpha_{2}\) a) If the temperature of the bimetallic strip is reduced by \(\Delta T\), which way will the strip bend (toward the side made of metal 1 or the side made of metal 2)? Briefly explain. b) If the temperature is increased by \(\Delta T\), which way will the strip bend?

Short answer

Answer: When the temperature is reduced, the bimetallic strip will bend towards the side made of metal 1. When the temperature is increased, the bimetallic strip will bend towards the side made of metal 2.

Step-by-step solution

Understand the concept of linear expansion coefficients

Linear expansion coefficients represent the relative change in length of a material when its temperature is changed. A material with a larger linear expansion coefficient will expand more than a material with a smaller coefficient when subjected to the same temperature change. In our problem, metal 1 has a larger linear expansion coefficient than metal 2, which means it will expand more when heated and contract more when cooled.

Effect of temperature decrease on the bimetallic strip

When the temperature of the bimetallic strip is reduced by \(\Delta T\), both metals will contract. Since metal 1 has a higher linear expansion coefficient, it will contract more than metal 2. This difference in contraction will cause the strip to bend. To visualize which way it will bend, imagine fixing one end of the strip and letting the other end move. Metal 1 contracts more, pulling the free end towards itself, causing the strip to bend towards the side made of metal 1.

Determine the bending direction when the temperature is decreased

Since metal 1 contracts more than metal 2 when the temperature is reduced, the bimetallic strip will bend towards the side made of metal 1.

Effect of temperature increase on the bimetallic strip

When the temperature of the bimetallic strip is increased by \(\Delta T\), both metals will expand. Since metal 1 has a higher linear expansion coefficient, it will expand more than metal 2. This difference in expansion will again cause the strip to bend. With the same visualization as before, metal 1 expands more, pushing the free end away from itself, causing the strip to bend towards the side made of metal 2.

Determine the bending direction when the temperature is increased

Since metal 1 expands more than metal 2 when the temperature is increased, the bimetallic strip will bend towards the side made of metal 2. In conclusion: a) When the temperature is reduced by \(\Delta T\), the bimetallic strip will bend towards the side made of metal 1. b) When the temperature is increased by \(\Delta T\), the bimetallic strip will bend towards the side made of metal 2.