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

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:

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

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

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

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

Fig 2.29 The isothermal Joule-Thompson coefficient

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

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

Fig 2.32 The inversion temperatures for three real gases

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