FYKOS Year 30 Series 2 Problem 2 — ultra high temperature superconducticvity · FYKOS 30 #30.2.2
Physics · electromagnetism · thermodynamics
Problem
Many types of materials, mostly metals, have increasing dependence of resistivity on temperature. However, there are semiconductors or graphite which show a decreasing dependence. And you have also probably heard about superconductivity, the natural phenomenon when a cooled material shows almost no electrical resistance and becomes a perfect conductor. Our current state of knowledge says that the temperature of a superconductor must be well below room temperature, but let's assume that the equation defining the resistance is R_{0} (1 + αΔt)$R_{0}isαisΔtα_{C}=-0.5\cdot 10^{-3}K^{−1}α_{Si}=-75\cdot 10^{-3}K^{−1}$ for silicon, we obtain zero resistance for high temperatures. Determine these two temperatures and explain why the superconducting phenomenon does not work this way, i.e. neither carbon nor silicon are superconductors at high temperatures.Intuitive explanation
The core concept here is using a linear resistance-temperature model to find where mathematically reaches zero, then recognizing why this prediction fails physically. For each material, you'll set in the given equation and solve for —but the real insight is that this linear approximation breaks down at extreme temperatures; materials don't actually maintain constant as temperature climbs, and long before reaching that calculated point, other physical effects (like thermal ionization, material breakdown, or phase changes) dominate and invalidate the simple model. Understanding the limits of a formula is as important as using it correctly.
Intuitive explanation
The core concept here is using a linear resistance-temperature model to find where mathematically reaches zero, then recognizing why this prediction fails physically. For each material, you'll set in the given equation and solve for —but the real insight is that this linear approximation breaks down at extreme temperatures; materials don't actually maintain constant as temperature climbs, and long before reaching that calculated point, other physical effects (like thermal ionization, material breakdown, or phase changes) dominate and invalidate the simple model. Understanding the limits of a formula is as important as using it correctly.