Atkins & de Paula:
Atkins’ Physical Chemistry 8e
Checklist of key ideas
Chapter 3: The Second Law
Chapter 3: The Second Law
spontaneous process, a process that does not require work
to be done to bring it about.
Second Law of thermodynamics: (Kelvin statement) No
process is possible in which the sole result is the absorption
of heat from a reservoir and its complete conversion into
work.
THE DIRECTION OF SPONTANEOUS CHANGE
3.1 The dispersal of energy
Collapse into disorder as the driving force of change.
Chapter 3: The Second Law
3.2 Entropy
Second Law of thermodynamics (entropy statement): The
entropy of an isolated system increases in the course of a
spontaneous change: ∆S tot > 0.
thermodynamic definition of entropy, dS = dqrev/T.
entropy change in the surroundings, ∆Ssur = qsur/Tsur .
entropy change for an adiabatic process, ∆Ssur = 0.
Boltzmann formula for the entropy, S = k ln W.
statistical entropy, the entropy calculated by using the
Boltzmann formula.
Chapter 3: The Second Law
3.2 Entropy (cont..)
Carnot cycle, a cycle composed of alternating isothermal
and adiabatic reversible expansions and compressions.
efficiency of a heat engine, ε = |w|/qh.
Carnot efficiency, εrev = 1 – Tc/Th.
proof that entropy is a state function by showing
that Ñ
∫ (1/ T )dqrev = 0 .
thermodynamic temperature scale, T = (1 – ε)Th.
Clausius inequality, dS ≥ dq/T.
Chapter 3: The Second Law
3.3 Entropy changes accompanying specific processes
Entropy change accompanying isothermal expansion of a
perfect gas, ∆S = nR ln(Vf/Vi).
normal transition temperature, T trs, the temperature at which
two phases are in equilibrium at 1 atm.
Entropy of transition at the transition temperature,
∆trsS = ∆trsH/T trs.
Trouton’s rule: many normal liquids have approximately the
same standard entropy of vaporization (about 85 J K–1 mol–1).
variation of entropy with temperature,
S(Tf) = S(T i) +
∫
Tf
Ti
(C p / T )dT .
Chapter 3: The Second Law
3.3 Entropy changes accompanying specific processes (cont..)
measurement of entropy, from area under graph of Cp/T
against T.
Debye extrapolation, Cp = aT3 as T → 0.
3.4 The Third Law of thermodynamics
Nernst heat theorem: The entropy change accompanying
any physical or chemical transformation approaches zero as
the temperature approaches zero: ∆S → 0 as T → 0
provided all the substances involved are perfectly ordered.
Chapter 3: The Second Law
3.4 The Third Law of thermodynamics
Third Law of thermodynamics: The entropy of all perfect
crystalline substances is zero at T = 0.
Third-Law entropy, an entropy reported on the basis that
S(0) = 0 .
standard reaction entropy,
∆rSo = ΣProductsνSmo – ΣReactantsνSmo.
CONCENTRATING ON THE SYSTEM
3.5 The Helmholtz and Gibbs energies
criteria of spontaneity, dSU,V ≥ 0 and dUS,V ≤ 0.
Chapter 3: The Second Law
3.5 The Helmholtz and Gibbs energies (cont..)
Helmholtz energy, A = U – TS.
Gibbs energy, G = H – TS.
criteria of spontaneity, dAT,V ≤ 0 and dGT,p ≤ 0.
criterion of equilibrium at constant temperature and
volume, dAT,V = 0.
maximum work and the Helmholtz energy, wmax = ∆A.
criterion of equilibrium at constant temperature and
pressure, dGT,p = 0.
maximum additional (non-expansion) work and the
Gibbs energy, wadd,max = ∆G.
Chapter 3: The Second Law
3.6 Standard reaction Gibbs energies
standard Gibbs energy of reaction,
∆rGo = ∆ rHo - T∆rSo = Σ Products vGmo – ΣReactants vGmo .
standard Gibbs energy of formation, ∆ fGo , the standard
reaction Gibbs energy for the formation of a compound
from its elements in their reference states.
expressing ∆rGo in terms of ∆fGo ,
∆rGo = Σ Products v∆fGo – Σ Reactants v∆fGo .
Born equation for the Gibbs energy of solvation of an ion,
∆Gsolv = –(zi2e2NA/8πε0ri)(1 – 1/εr).
Chapter 3: The Second Law
COMBINING THE FIRST AND SECOND LAWS
3.7 The fundamental equation
fundamental equation, dU = TdS – pdV.
3.8 Properties of the internal energy
∂T
∂p
Maxwell relations:   = −  
 ∂ V S
 ∂ S V
 ∂T 
 ∂V 

 =

 ∂ p S  ∂ S  p
∂p
∂S 
=




 ∂ T V  ∂ V T
∂S
 ∂V 
=
−


 ∂T 

p
 ∂ p T
dU = TdS − pdV
(H ≡ U+pV)
dH = TdS + Vdp
(A ≡ U − TS)
dA = −SdT − pdV
(G ≡ H − TS)
dG = −SdT + Vdp
Chapter 3: The Second Law
3.8 Properties of the internal energy (cont..)
thermodynamic equation of state, an expression for pressure in
terms of thermodynamic quantities, πT = T(∂p/∂T)V – p.
3.9 Properties of the Gibbs energy
general change in Gibbs energy, dG = Vdp – SdT.
variation of Gibbs energy with temperature, (∂G/∂T)p = –S.
Gibbs–Helmholtz equation, (∂(G/T)/∂T)p = –H/T 2.
variation of Gibbs energy with pressure, (∂G/∂p)T = V.
for a condensed phase, G(pf) = G(pi) + Vm∆p.
for a perfect gas, G(p f) = G(p i) + nRT ln(pf/pi).
Chapter 3: The Second Law
3.9 Properties of the Gibbs energy
fugacity, the effective pressure of a gas, Gm = Gm°+ RT ln(f/po).
fugacity coefficient, φ = f/p, with ln φ =
∫ { (Z −1) / p} dp .
p
0