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 \(\Delta T\), what 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 of the bimetallic strip is decreased by \(\Delta T\), the strip will bend toward the side made of metal 1 (the metal with the higher linear expansion coefficient). When the temperature is increased by \(\Delta T\), the strip will bend away from the side made of metal 1.

Step-by-step solution

Understand what linear expansion coefficients represent

Linear expansion coefficients are measures of how much a material expands or contracts in response to a temperature change. A higher linear expansion coefficient means that the material will expand more when heated and contract more when cooled, as compared to a material with a lower expansion coefficient.

Determine the bending direction for a temperature decrease

Since \(\alpha_{1}>\alpha_{2}\), metal 1 will contract more than metal 2 when the bimetallic strip's temperature decreases. As a result, the strip will bend toward the side made of metal 1, as metal 1's greater contraction pulls the strip in that direction.

Determine the bending direction for a temperature increase

Like before, since \(\alpha_{1}>\alpha_{2}\), metal 1 will expand more than metal 2 when the bimetallic strip's temperature increases. As a result, the strip will bend away from the side made of metal 1, as metal 1's greater expansion pushes the strip in that direction.

Summarize the results

To summarize, when the temperature of the bimetallic strip is decreased by \(\Delta T\), it will bend toward the side made of metal 1 (with the higher linear expansion coefficient). Likewise, when the temperature is increased by \(\Delta T\), the strip will bend away from the side made of metal 1.

Key concepts

Linear Expansion Coefficient

The concept of the linear expansion coefficient is a key factor in understanding how materials respond to temperature changes. Every material has a unique linear expansion coefficient (\( \alpha \)), which quantifies how much it will expand or contract when exposed to temperature fluctuations. This coefficient is a crucial property for engineering and scientific applications because it helps predict the behavior of materials under different thermal conditions.

An important point to remember is that a material with a higher linear expansion coefficient will react more strongly to temperature changes. For example:

• When the temperature increases, the material expands more.
• When the temperature decreases, the material contracts more.

In the case of a bimetallic strip, if one metal has a higher linear expansion coefficient than the other, this difference will cause the strip to bend. Understanding this phenomenon is essential for correctly predicting the mechanical behavior of combined materials under thermal stress.

Thermal Expansion

Thermal expansion is a phenomenon observed in materials, where changes in temperature lead to changes in the size or volume of the material. This fundamental property means that as materials heat up, they usually expand; as they cool, they generally contract. Understanding thermal expansion is essential in a variety of engineering and design fields.

Thermal expansion is directly related to the linear expansion coefficient of a material. Materials with higher coefficients will experience more noticeable changes in their dimensions when subjected to the same temperature changes compared to those with lower coefficients.

When discussing a bimetallic strip, thermal expansion plays a pivotal role:

• If the temperature increases, and one metal expands more than the other due to a higher coefficient, the strip will bend in a predictable direction based on the differential expansion.
• Conversely, cooling the strip will result in bending in the opposite direction since the metal with the higher coefficient will contract more.

This knowledge helps us understand why the bimetallic strip bends towards or away from certain metals during temperature changes.

Temperature Change

Temperature change is a ubiquitous factor affecting almost every physical substance. It refers to any variation in the thermal state of a material—either heating up or cooling down. These changes are a significant cause of expansion or contraction in materials, demonstrated vividly in bimetallic strips.

In the context of a bimetallic strip, the effect of temperature change becomes evident in how the strip behaves under different thermal conditions.

When the temperature increases:

• The side made of metal with a higher linear expansion coefficient (\( \alpha_1 \)) expands more than the side made of metal with a lower coefficient (\( \alpha_2 \)).
• This results in the strip bending away from the side with the higher expansion coefficient, indicating the material's pronounced expansion.

Conversely, when the temperature decreases:

• The metal with the higher coefficient contracts more, causing the strip to bend towards this side.
• This showcases the stronger contraction of the material, pulling the strip in its direction.

Understanding these responses to temperature changes is vital for anticipating and controlling the performance of materials across varying thermal environments.