Parth G's video: The Forgotten Maxwell Equations

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/ParthG/. The first 200 of you will get 20% off Brilliant’s annual premium subscription. James Clerk Maxwell is most well know for his four equations that completely describe everything in Classical Electromagnetism - they're known as Maxwell Equations. However, did you know that he has yet more equations named after him in another field of physics that is thermodynamics? In this video we take a look at these "Maxwell Relations". We begin by looking at the First Law of Thermodynamics, which states that a system's internal energy, U, can change because of heat being transferred to the system or work being done by the system. These heat and work terms can also be described in terms of properties of the system such as temperature, entropy, pressure, and volume. When we find this expression in terms of the four properties of the system, we realize that it's made up of partial derivatives. Therefore, we can use the rules of partial derivatives generally and apply them to this specific thermodynamic scenario. Doing this, we find a relationship between partial derivatives of internal energy, and the properties we mentioned earlier (temperature, entropy, etc). Next, we can take second partial derivatives to find relationships between the properties themselves, that are not immediately obvious from just the physics of the situation. Instead, we've used math and physics together to come up with new, unintuitive relationships known as Maxwell Relations. In fact, these relations are better "Maxwell Equations" than the electromagnetic ones, as those four equations were actually devised by Oliver Heaviside after distilling many of Maxwell's actual equations down. Thanks for watching, please do check out my links: MERCH - https://parth-gs-merch-stand.creator-spring.com/ INSTAGRAM - @parthvlogs PATREON - patreon.com/parthg MUSIC CHANNEL - Parth G's Shenanigans Here are some affiliate links for things I use! Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL My Camera: https://amzn.to/2SjZzWq ND Filter: https://amzn.to/3qoGwHk Timestamps: 0:00 - Maxwell's Equations of Classical Electromagnetism 1:07 - The First Law of Thermodynamics 2:10 - Big Thanks to Brilliant for Sponsoring This Video! 3:22 - Heat and Work 4:52 - Partial Derivatives and Some Fun Math 7:06 - Second Derivatives and Maxwell Relations 9:35 - When Internal Energy Doesn't Work Useful Links to Understand This Video: 1) https://www.youtube.com/playlist?list=PLOlz9q28K2e6aNgl1zt1xccyy4Ofl3YAk 2) https://www.youtube.com/watch?v=bM4ykIumlss&t=4s 3) https://en.wikipedia.org/wiki/Heat 4) https://en.wikipedia.org/wiki/Partial_derivative This video was sponsored by Brilliant