Taking on Gibbs Entropy and Defining Temperature

Last time we derived the Boltzmann entropy equation. Today we use that equation to derive the Gibbs entropy equation using the canonical ensemble. We also define temperature from first principles and use it to connect entropy to experiments. Very few students of physics or chemistry get to see these derivations, and typically both of these equations are simply given as fact. -- Previous Video: The Origins and Maths of Entropy Explained -    • The Origin and Maths of Entropy Explained   Supplemental Videos: Energy -    • Supplemental: What Exactly is Energy?   Logarithms -    • Supplemental: The Rules for Using Logarithms   Derivatives -    • Supplemental: Derivatives and Statistical ...   -- Please support me by subscribing, liking, and sharing this video. If you would like to support me directly, please consider donating to my Patreon to help encourage these types of videos and more in depth teaching of advanced science concepts that I attempt to explain such that any student of the field can understand them. Thank you! https://www.patreon.com/thebeardedche...