https://gdpark.blog/tags/ideal-gas/Recent content in Ideal Gas on gdpark.blogHugoenThu, 07 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-10-expected-speed-expected-energy-and-statistical-analysis-of-i/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-10-expected-speed-expected-energy-and-statistical-analysis-of-i/We ditch talking distributions and actually calculate averages — finding the expected speed and energy of an ideal gas molecule using integrals and odd-function tricks.https://gdpark.blog/posts/thermal-statistical-11-ideal-gas-equation-of-state-and-pressure/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-11-ideal-gas-equation-of-state-and-pressure/Diving into Chapter 6 to microscopically derive PV=nRT, kicking things off with the definition of pressure and then wrestling with the surprisingly weird world of solid angles.https://gdpark.blog/posts/thermal-statistical-12-chapter-6-practice-problems/Fri, 01 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-12-chapter-6-practice-problems/Working through Chapter 6 practice problems on ideal gas volume at STP, kinetic energy density, and what happens to the air in your room when you turn up the heat.https://gdpark.blog/posts/thermal-statistical-17-chapter-11-practice-problems/Sun, 03 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-17-chapter-11-practice-problems/Working through Chapter 11 thermo problems — isothermal expansion of a monatomic ideal gas and showing those Cv/Cp identities with γ, step by step.https://gdpark.blog/posts/thermal-statistical-18-isothermal-expansion-and-contraction-adiabatic-expansion-and/Sun, 03 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-18-isothermal-expansion-and-contraction-adiabatic-expansion-and/We revisit isothermal and adiabatic processes under the reversible + ideal gas assumptions, and get clear on what ‘reversible’ actually means before the real fun begins!https://gdpark.blog/posts/thermal-statistical-19-chapter-12-practice-problems/Mon, 04 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-19-chapter-12-practice-problems/Chapter 12 practice problems working through adiabatic expansion, ideal gas state equations, and partial derivative relations for heat capacity — some surprisingly simple!https://gdpark.blog/posts/thermal-statistical-24-free-expansion-joule-expansion-and-entropy-of-mixing/Wed, 06 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-24-free-expansion-joule-expansion-and-entropy-of-mixing/A casual walkthrough of Joule (free) expansion and entropy of mixing, showing why both processes increase entropy even when internal energy stays zero.https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/Mon, 25 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/We finally tackle the ideal gas and why we can actually compute Z for it — turns out independent subsystems make partition functions way more manageable lol.https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/Tue, 26 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/We grind through the ideal gas partition function integral step by step, then dig into what the result actually tells us about quantum concentration and the thermal de Broglie wavelength.https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Wed, 27 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Turns out Z_sys = (Z_1)^n only works for distinguishable particles — we break down why indistinguishable ones mess up the math using a simple two-level system.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-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-54-van-der-waals-gas-equation-of-state/Wed, 29 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-54-van-der-waals-gas-equation-of-state/We crack open two ideal gas assumptions — molecular size and intermolecular forces — to build the Van der Waals equation of state from intuition up.https://gdpark.blog/posts/thermal-statistical-55-critical-temperature-volume-and-pressure-of-the-van-der-waal/Thu, 30 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-55-critical-temperature-volume-and-pressure-of-the-van-der-waal/We figure out exactly when a van der Waals gas stops acting like an ideal gas and hunt down the critical temperature where that wild dented p-V curve first appears!https://gdpark.blog/posts/thermal-statistical-58-joule-coefficient-and-joule-expansion-of-an-ideal-gas/Sun, 03 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-58-joule-coefficient-and-joule-expansion-of-an-ideal-gas/Starting from the age-old puzzle of how to make things cold, we dig into Joule expansion to see why ideal gases don’t cool down — but real gases do!https://gdpark.blog/posts/thermal-statistical-62-temperature-dependence-of-latent-heat-for-an-ideal-gas/Thu, 07 Jul 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-62-temperature-dependence-of-latent-heat-for-an-ideal-gas/We derive the liquid-gas phase boundary with the Clausius-Clapeyron equation, then dig into why latent heat L actually depends on temperature.