1. Atkins’ Physical Chemistry Eighth Edition Chapter 2 – Lecture 5 The First Law Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

2. Changes in Internal Energy at Constant Pressure May also express the difference in heat capacities with observables: C p – C v = nR Since H = U + PV = U + nRT And:

3. The Joule-Thomson Effect Consider H = U + PV and H(P,T) then the full differential of H: Which by rearrangement and substitution becomes: where μ ≡ the Joule-Thompson coefficient isenthalpic

4. Fig 2.27 Apparatus for measuring Joule-Thomson effect Process is adiabatic Gas expands through a porous barrier which acts as a throttle Temperature monitored to obtain ΔT Observed that dT ∝ dP i.e.: P low P high

5. Fig 2.28 Thermo basis measuring Joule-Thomson expansion Process is adiabatic: q = 0, so ΔU = w w 1 = − P i ΔV = − P i (0 – V i ) = P i V i w 2 = − P f ΔV = − P f (V f - 0) = − P f V f So: w = w 1 + w 2 = P i V i − P f V f ΔU = U f – U i = w = P i V i − P f V f U f + P f V f = U i + P i V i or: H f = H i ∴ isenthalpic

6. Fig 2.30 Modern apparatus for measuring the isothermal Joule-Thompson coefficient Measures Isothermal Joule-Thompson coefficient Gas is pumped through a porous plug (throttle) Steep pressure drop is monitored on right side Drop in T is offset by heater Electrical energy ∝ ΔH T High T Low P High P Low

7. Fig 2.29 The isothermal Joule-Thompson coefficient

8. The Joule-Thomson Effect Isothermal J-T coefficient important in liquification of gases For real gases: μ T ≠ 0 If μ T > 0, then gas cools on expansion If μ T its inversion temperature Gases typically have two inversion temperatures One T I at high T, the other at low T

9. Fig 2.31 The isothermal Joule-Thompson coefficient Sign of μ T depends on conditions TI TI

11. Fig 2.32 The inversion temperatures for three real gases

12. Fig 2.33 Principle of the Linde refridgerator Gas is recirculated As long as its below its T I, it will cool upon expansion through the throttle Liquified gas drips from the throttle TITI