Question

Two metal strips that constitute a thermostat must necessarily in their (A) Mass (B) Length (C) Resistivity (D) Coefficient of liner expansion

Short answer

The two metal strips in a thermostat must necessarily have different coefficients of linear expansion (D) to function properly. This property allows the strips to expand or contract at different rates due to temperature changes, enabling the thermostat to regulate temperature effectively.

Step-by-step solution

Understand the role of each option

Let's first look at the role that each of the properties plays in the functioning of a thermostat: (A) Mass - This refers to the amount of matter in the metal strips. It does not have a direct role in the functioning of a thermostat. (B) Length - The initial length of each strip may vary but it is not a necessary condition for the thermostat to work. (C) Resistivity - This refers to the electrical resistance of the metal strips. Although a thermostat can use changes in resistance due to temperature changes, it is not required that both strips have equal resistivity. (D) Coefficient of linear expansion - This is the property that causes metal strips to expand or contract differently due to temperature changes, making them ideal for usage in a thermostat.

Choose the correct option

Based on our understanding of the role of each property in the functioning of a thermostat, it is clear that the two metal strips must have different coefficients of linear expansion to ensure proper functioning. Therefore, the correct answer is: (D) Coefficient of linear expansion

Key concepts

Coefficient of Linear Expansion

When it comes to understanding thermostats, one of the most crucial properties is the Coefficient of Linear Expansion. This coefficient defines how much a material's length changes in response to temperature variations. It is usually represented by the Greek letter \( \alpha \).

• For most materials, as temperature increases, molecules move more vigorously and the material expands.
• The coefficient measures expansion per degree increase in temperature.

For example, if a metal strip has a high coefficient, it will expand significantly with heat. Conversely, a low coefficient means less change in length. This property is vital in thermostats because it causes the bimetallic strip—composed of two metals with differing coefficients—to bend. This bending triggers the switch mechanism in the thermostat, allowing it to regulate temperature effectively.
In equation form, the linear expansion can be expressed as:\[ \Delta L = \alpha \cdot L_0 \cdot \Delta T \]where:

• \( \Delta L \) is the change in length,
• \( \alpha \) is the coefficient of linear expansion,
• \( L_0 \) is the original length of the material, and
• \( \Delta T \) is the change in temperature.

Thermal Expansion

Thermal Expansion describes the tendency of matter to change in shape, area, and volume in response to a change in temperature. This phenomenon is observed in solids, liquids, and gases, but is most commonly associated with solids in thermostat applications. There are several key points to note about thermal expansion:

• In solids, thermal expansion is predominantly linear; for a given increase in temperature, the length can change predictably.
• The rate of expansion depends on the material's properties, specifically what's known as its Coefficient of Linear Expansion.
• In thermostats, thermal expansion is harnessed to move mechanical parts without needing external power sources.

This principle is essential in mechanisms that need to respond to temperature changes autonomously. As temperature rises, the material expands and can perform specific functions, such as opening a contact in an electrical circuit. This expansion and resulting movement are what make bimetallic strips in thermostats so effective at regulating temperature environments.

Bimetallic Strip

A bimetallic strip is a simple yet ingenious device that is central to many thermostats. It consists of two strips of different metals bonded together. Each metal has its own Coefficient of Linear Expansion, meaning they expand at different rates when exposed to temperature changes.

• As the temperature rises, the metal with the higher expansion coefficient lengthens more.
• This causes the strip to bend towards the side of the metal with the lower coefficient.

The bending action is the key functional mechanism in devices like thermostats. When the bimetallic strip bends, it can open or close a circuit, which stops or starts heating to maintain an optimal environment.
This simple physical principle is at the heart of many temperature-regulating devices. The design of bimetallic strips takes advantage of the predictable nature of thermal expansion to automate functions without complex electronics. It's an excellent example of how foundational physics principles can lead to practical, everyday technology applications.