https://gdpark.blog/tags/chemical-potential/Recent content in Chemical Potential on gdpark.blogHugoenMon, 11 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Sun, 01 May 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Chapter 22 extends our model to allow particle exchange alongside energy flow, diving into the grand canonical ensemble where both energy and particle number can fluctuate.https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/Sat, 18 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/We let particles flow freely and ask what happens to the partition function — turns out there’s a grand version Z_G derived straight from entropy!https://gdpark.blog/posts/thermal-statistical-43-chemical-potential-of-an-ideal-gas/Mon, 20 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-43-chemical-potential-of-an-ideal-gas/We derive μ = k_BT ln(nλ_th³) for an ideal gas via the canonical ensemble and Helmholtz free energy — a relation we’ll keep pulling out freely from here on.https://gdpark.blog/posts/thermal-statistical-44-chemical-potential-as-gibbs-free-energy-per-particle/Tue, 21 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-44-chemical-potential-as-gibbs-free-energy-per-particle/We dig into what happens to Gibbs free energy and entropy once we let particles flow in and out, and see why chemical potential turns out to be G per particle!https://gdpark.blog/posts/thermal-statistical-45-chemical-potential-of-photons/Tue, 21 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-45-chemical-potential-of-photons/Turns out when a system doesn’t conserve particle number — like photons — the chemical potential just goes to zero at equilibrium, and that’s actually a huge deal!!https://gdpark.blog/posts/thermal-statistical-46-pressure-dependence-of-chemical-potential/Wed, 22 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-46-pressure-dependence-of-chemical-potential/Wrapping up chemical potential once and for all by rewriting μ in terms of pressure using the ideal-gas relation, and linking it to the Gibbs function per particle.https://gdpark.blog/posts/thermal-statistical-61-the-clausius-clapeyron-equation/Wed, 06 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-61-the-clausius-clapeyron-equation/We revisit phase transitions using Gibbs free energy and chemical potential to derive the phase coexistence condition and work toward the Clausius-Clapeyron equation hehehe.https://gdpark.blog/posts/thermal-statistical-64-kelvin-s-formula-and-why-water-boils/Sat, 09 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-64-kelvin-s-formula-and-why-water-boils/We dig into why water boils by layering surface tension on top of phase-transition theory, then crank through the math to land on Kelvin’s formula.https://gdpark.blog/posts/thermal-statistical-65-gibbs-free-energy-of-a-water-droplet-and-bubble-nucleation/Sun, 10 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-65-gibbs-free-energy-of-a-water-droplet-and-bubble-nucleation/Walk through calculating the Gibbs free energy of a liquid droplet in vapor equilibrium, factoring in surface tension to set up the physics behind bubble nucleation.https://gdpark.blog/posts/thermal-statistical-66-ebullioscopic-and-cryoscopic-constants/Mon, 11 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-66-ebullioscopic-and-cryoscopic-constants/Let’s derive the boiling point elevation and freezing point depression constants from scratch using chemical potential and Raoult’s law.