Question

For a class demonstration, your physics instructor uniformly heats a bimetallic strip that is held in a horizontal orientation. As a result, the bimetallic strip bends upward. This tells you that the coefficient of linear thermal expansion for metal T, on the top is _____ that of metal B, on the bottom. a) smaller than b) larger than c) equal to

Short answer

a) Smaller than b) Larger than c) Equal to Answer: b) Larger than

Step-by-step solution

Understanding the concept of a bimetallic strip

A bimetallic strip is made up of two different metals with different coefficients of linear thermal expansion, joined together. As the temperature of the strip changes, both metals expand or contract, but one does so more than the other, causing the strip to bend.

Coefficient of linear thermal expansion and bending

The coefficient of linear thermal expansion, often represented as α, is a measure of how much a material expands for a given change in temperature. The relationship between the expansion of a material and its coefficient of linear thermal expansion can be represented as ΔL = α * L₀ * ΔT, where ΔL is the change in length, L₀ is the original length, and ΔT is the change in temperature.

Analyzing the bending of the bimetallic strip

When the bimetallic strip is uniformly heated, both the top and the bottom layers will expand. As the strip bends upward, this implies that the bottom layer (metal B) is expanding more than the top layer (metal T).

Comparing the coefficients of linear thermal expansion

Since metal B is expanding more than metal T, we can say that the coefficient of linear thermal expansion for metal B is larger than that of metal T. Therefore, the correct answer is: b) Larger than

Key concepts

Bimetallic Strip

A bimetallic strip is an intriguing device that is ingeniously simplistic yet demonstrative of the fundamental principle of thermal expansion in solids. It consists of two metals with distinct coefficients of linear thermal expansion that have been bonded together. These coefficients reflect how much a material will expand or contract when subjected to temperature changes. When heated or cooled, each metal in the strip will react differently, either expanding or contracting at its unique rate. This discrepancy in reaction rates causes the bimetallic strip to bend, curl, or twist, which is a compelling manifestation of the differing expansion rates at play.

Bimetallic strips have practical applications, including use in thermostats, where they can trigger a mechanical response to temperature changes, such as turning a heater or an air conditioner on or off. The bending of the bimetallic strip can also be harnessed to actuate switches or move pointers on temperature gauges, thereby converting thermal activity into mechanical movements.

Thermal Expansion

Thermal expansion is a concept central to understanding behavior of materials when subjected to changes in temperature. When an object is heated, its particles begin to move more vigorously, requiring more space to move around. This increase in particle movement results in the expansion of the material. Conversely, as an object cools down, particle movement decreases, and the material contracts. This behavior can be quantified by a property known as the coefficient of linear thermal expansion, denoted by alpha (\( \text{α} \)).

The coefficient of linear thermal expansion is defined for a unit of length. The relationship that describes how much a linear dimension changes with temperature is given by the equation \[ \text{ΔL} = \text{α} \times \text{L}_0 \times \text{ΔT} \],where \( \text{ΔL} \) is the change in length, \( \text{L}_0 \) is the original length, and \( \text{ΔT} \) is the change in temperature. Materials with a larger coefficient will experience a greater change in length for the same temperature change than those with a smaller coefficient.

Physics Demonstration

Physics demonstrations are powerful tools for visualizing and understanding abstract concepts. In the case of thermal expansion and bimetallic strips, a classroom demonstration provides a clear and dramatic illustration of how different materials react to heat. By uniformly heating a bimetallic strip, students can directly observe the bending behavior that results from the uneven expansion of the two metals. Such demonstrations enhance comprehension by bridging the gap between theoretical concepts and real-world phenomena.

Experimentation, such as observing a bimetallic strip, encourages hands-on learning and can spark curiosity. By connecting theory with physical observation, instructors can probe students' critical thinking and encourage questions like 'Why does the strip bend in a certain direction when heated?' This question leads to discussions about the coefficients of thermal expansion, solidifying students' grasp of the topic through tangible experiences.