Chem 402 Lecture 12: L12 2:13:17

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University College - Chemistry
University College - Chemistry Chem 402
Barnes Alexander

13 February 2017 L12: The Joule-Thompson Coefficient and Heat Capacities I. Heat Capacities A. Joule Thompson Coefficient 1. Meaning πœ•π» πœ•π» a. 𝑑𝐻 = ( )πœ•π‘‡π‘‡π‘ƒ+ ( ) π‘‘πœ•π‘=𝑇𝐢 𝑑𝑇 + 𝑃𝐢 πœ‡ 𝑑𝑝 𝑃 𝐽𝑇 b. If πœ‡π½π‘‡= 0, an ideal gas or a real gas invT β€’ For an ideal gas, βˆ†H = nCpβˆ†T πœ•π‘‡ βˆ†π‘‡ c. πœ‡ 𝐽𝑇= ( πœ•π‘ƒ=𝐻( ) βˆ†π‘ƒx𝐻erimentally) d. For an expansion, πœ‡ > 0 𝐽𝑇 β€’ βˆ†T/βˆ†P = (-)/(-) β€’ Need βˆ†T to be negative (cool on expansion) for πœ‡ to be positive 𝐽𝑇 e. For an expansion, πœ‡π½π‘‡ < 0 β€’ βˆ†T/βˆ†P = (+)/(-) β€’ Need βˆ†T to be positive (heat on expansion) for𝐽𝑇 to be negative 2. For a van der Waals gas: π‘Ž a. πœ‡ π½π‘‡β‰ˆ π‘…π‘‡βˆ’ 𝑏 π‘Ž π‘Ž βˆ†π‘‡ b. If𝑅𝑇 < 𝑏, then T > 𝑅𝑏 = 𝑇 𝑖𝑛𝑣 thus (βˆ†π‘ƒ)𝐻< 0) β€’ If βˆ†P < 0, then βˆ†T > 0 and gas heats on expansion β€’ It takes energy to expand when 𝐽𝑇 > 0, such energy comes from the translational and rotational degrees of freedom (decreases energy level occupations to expand gas) – not from vibrational energy (ground state around room temp) c. If π‘Ž > 𝑏, then T< π‘Ž = 𝑇 , thus (( ) > 0) 𝑅𝑇 𝑅𝑏 𝑖𝑛𝑣 βˆ†π‘ƒ 𝐻 β€’ If βˆ†P < 0, then βˆ†T < 0 and gas cools on expansion d. Most real gases have Tinv>> 300K 3. JT Experiment + Barnes Lab a. NMR polarization with even populations for 300 MHz separation b. EPR polarization with even populations for 198 GHz separation c. At thermal eq’b, higher population in lower energy state (look 6 sig figs out for differences) d. For β€œspectral density junction”, a given point on the stretch tells us the frequency of changing flip spin state β€’ Graphs frequency (x axis) vs. degeneracy*energy (y-axis) β€’ Will get increased sensitivity by bringing down the temperature (from 298K
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