Hot Molecules, Cold Electrons

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An entertaining mathematical exploration of the heat equation and its pivotal role in the development of the trans-Atlantic telegraph cable, this work reveals how heat influences various aspects of our world, from how milk dissolves in coffee to the cooling of molten planets. The heat equation, a cornerstone of modern physics, provides a mathematical framework for understanding heat diffusion through matter. The narrative recounts the historical journey of this foundational idea, beginning with Joseph Fourier, who discovered and solved the equation in the early nineteenth century. The story continues with William Thomson, whose analysis of Fourier's work led to the groundbreaking trans-Atlantic telegraph cable, drastically reducing message transmission time across the ocean from weeks to minutes. Additionally, readers learn that Thomson used Fourier's solutions to estimate the earth's age and that Charles Dickens relied on the cable to navigate a potential scandal. Accessible to those with basic high school calculus and physics knowledge, the book includes MATLAB code for readers interested in solving the heat equation themselves. It highlights the intricate connections between mathematics and physics and offers insight into the heat equation's impact on a significant advancement in human communication.