Problem 28 - College Physics

Question

Sketch a qualitative (no numbers) graph of the resistance as a function of temperature for (a) an ordinary conductor, such as Cu, including temperatures approaching \(0 \mathrm { K } ;\) (b) a superconductor; include temperatures above and below the critical temperature, and let the temperature approach 0\(\mathrm { K }\) .

Step-by-Step Solution

Answer

For Cu, resistance rises with temperature; for a superconductor, it's zero below a critical temperature and rises above it.

Step 1: Familiarize with Conductor Properties

An ordinary conductor, like copper (Cu), typically has a resistance that increases with temperature. This is due to increased atomic vibrations as temperature rises, which leads to more collisions for moving electrons.

Step 2: Identify Superconductor Properties

A superconductor exhibits zero resistance below a certain critical temperature. Above this critical temperature, its resistance behaves like that of an ordinary conductor, increasing with temperature.

Step 3: Sketch Resistance vs Temperature for an Ordinary Conductor

Draw a graph with temperature on the x-axis and resistance on the y-axis. For an ordinary conductor, resistance starts low at 0 K and increases as the temperature rises. The curve is typically upward sloping from the origin.

Step 4: Sketch Resistance vs Temperature for a Superconductor

Draw another graph with the same axes. For a superconductor, resistance stays at zero as temperature rises up to its critical temperature. Beyond the critical temperature, resistance behaves like an ordinary conductor, increasing with temperature.

Step 5: Considerations Near Absolute Zero

In both graphs, note that near absolute zero (0 K), conductors and superconductors behave differently; conductors still have a small, non-zero resistance, while superconductors have exactly zero resistance below their critical temperature.

Key Concepts

Ordinary Conductors

Ordinary conductors like copper (Cu) play a major role in our daily lives, enabling the flow of electricity in wires and electronic devices. These materials have a particular behavior when it comes to temperature and resistance.

• As temperature increases, the resistance of an ordinary conductor increases. This is because higher temperatures cause atoms to vibrate more vigorously.
• The increased atomic vibrations interfere with the flow of electrons, causing more collisions and, thus, higher resistance.
• Even as the temperature approaches absolute zero, these materials do not reach zero resistance. There's always some resistance present due to minimal atomic motion.

Understanding this behavior is crucial for designing electronic components that can optimize performance by managing heat and energy loss.

Superconductors

Superconductors are fascinating materials that behave differently than ordinary conductors. Their unique properties give them profound applications in technology.

• Superconductors exhibit zero electrical resistance when cooled below a critical temperature. This allows for the unimpeded flow of electricity, which is ideal for efficient power transmission.
• When the temperature is above this critical point, superconductors behave like ordinary conductors, with resistance increasing as temperature increases.
• The ability to conduct electricity without resistance makes superconductors vital for advancements in magnetic levitation, MRI machines, and quantum computing.

The transition from zero to ordinary resistance as temperature crosses the critical point is a defining characteristic that sets superconductors apart in the world of physics.

Critical Temperature

The concept of critical temperature is central to understanding the behavior of superconductors. It is the threshold below which materials enter a superconducting state.

• The critical temperature is unique to each superconducting material. For some metals and alloys, it can be just a few degrees above absolute zero, while for others, it can be significantly higher.
• At temperatures below the critical value, superconductors lose all electrical resistance, making them extraordinarily efficient conductors.
• The exact determination of the critical temperature is crucial for utilizing superconductors effectively in technology and research.

This temperature-dependent transition is key to harnessing the potential of superconductors in various scientific and industrial applications.

Absolute Zero

Absolute zero is the lowest possible temperature where all atomic motion theoretically stops. However, in practice, it is unattainable, but understanding its implications is crucial.

• At temperatures close to absolute zero, ordinary conductors still exhibit some resistance due to residual atomic vibrations, though minimal.
• In contrast, superconductors at temperatures below their critical point show zero resistance, highlighting their distinction.
• The concept of absolute zero helps in understanding the limits of cooling and its impacts on material properties.

Knowing this extreme temperature guards our exploration of quantum phenomena and further pushes the boundaries of low-temperature physics.