## Superconductivity This section explores the phenomenon of superconductivity, defining the critical temperature ($T_c$) and outlining its discovery, characteristics, and practical applications. It details how certain materials exhibit zero electrical resistance below this critical temperature, linking it to Bose-Einstein condensation and the formation of Cooper pairs. **Superconductivity:** The property of certain materials to conduct electric current without any energy loss when they are cooled below a specific temperature. Below this temperature, the electrical resistance drops to zero. **Bose-Einstein Condensation and Cooper Pairs:** Superconductivity arises when two electrons form boson-like entities called *Cooper pairs*. These pairs behave as bosons and can occupy the same quantum state, forming a condensate. The condensate moves through the material without scattering, leading to zero electrical resistance. This phenomenon is related to . **Superconductors:** Substances whose resistivity becomes zero at very low, specific temperatures. **Critical Temperature ($T_c$):** The temperature at which, and below which, the electrical resistivity ($\rho$) of a substance becomes zero. This is the superconducting transition temperature. Figure 16.8 illustrates the relationship between resistivity and temperature for a superconducting material. **Discovery of Superconductivity:** First discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes, who observed the sudden disappearance of electrical resistance in mercury at 4.2 K. **Highest Confirmed $T_c$:** A lanthanum superhydride ($\mathrm{LaH}_{10}$) compound, under a pressure of approximately 170 gigapascals, exhibits superconductivity with a critical temperature of 250 kelvin. This is the highest confirmed $T_c$ to date. Materials that exhibit superconductivity at relatively higher temperatures are often referred to as High-Temperature Superconductors (HTS). **Applications of Superconductors:** - Powerful electromagnets (e.g., 32 Tesla) - Particle accelerators - Magnetic levitation (Maglev) trains - Small but powerful electric motors - Fast computer chips - Potentially more efficient power transmission lines - Magnetic Resonance Imaging (MRI) machines Ongoing research aims to achieve superconductivity at higher temperatures for broader practical use. **Critical Temperatures for Various Substances:** | Substance | $T_c$ | |-----------|-------| | Mercury ($\mathrm{Hg}$) | 4.2 K | | Aluminum ($\mathrm{Al}$) | 1.18 K | | Tin ($\mathrm{Sn}$) | 3.72 K | | Lead ($\mathrm{Pb}$) | 7.2 K |