Atkins’ Physical Chemistry Eighth Edition Chapter 3 – Lecture 2 The Second Law Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Entropy Changes Accompanying Specific Processes (a)Expansion, isothermally from V i to V f : ΔS path-independent, so ΔS of the system is same for reversible and irreversible process Logarithmic dependence of ΔS shown in Fig 3.12

Fig 3.12 Logarithmic increase in entropy of a perfect gas expanding isothermally Reversible or irreversible

Entropy Changes Accompanying Specific Processes (b) Phase changes Entropy increases with the freedom of motion of molecules: S(g) >> S(l) > S(s) Recall that T does not change during a phase transition So:

Trouton’s rule – wide range of liquids have approximately the same ΔS vap q vap = ΔH vap = T b ∙ (85 J K -1 mol -1 )

Entropy Changes Accompanying Specific Processes (c) Heating From: At constant pressure: Gives:

Fig 3.13 Logarithmic increase in entropy of a substance heated at constant volume

Entropy Changes Accompanying Specific Processes (d)Measurement of entropy for phase changes Entropy of a system increases from S = 0 at T = 0 to some final S at T

Heating curve for water Indicates changes when 1.00 mol H 2 O is heated from 25°C to 125°C at constant P

Entropy Changes Accompanying Specific Processes (d)Measurement of entropy for phase changes Entropy of a system increases from S = 0 at T = 0 to some final S at T Evaluate integrals and include ΔH trs Integrals may be evaluate graphically

Fig 3.14(a) Variation of C p /T with temperature of a substance e.g., area under Solid region of the curve is: For S(0) use Debye approximation: C P ∝ T 3 at low temperatures Then C P = aT 3

Fig 3.14(b) Calculation of entropy from heat capacity data The entropy for each region = the area under each upper curve up to the corresponding temperature T trs plus the entropy of each phase transition passed

The Third Law of Thermodynamics At T = 0 all thermal motion has been quenched In a perfect crystal all particles are arranged uniformly This perfection suggests that S(0) = 0 Nernst heat theorem: ΔS → 0 as T → 0 provided that the substance is perfectly crystalline 3 rd Law: The entropy of all perfectly crystalline substances is zero at T = 0

The Third Law Entropies Third law definition is a matter of convenience Sets a standard for relative entropies at other T Standard reaction enthalpies used analogously to ΔH f may be found in Table 3.3