Physical equilibria: pure substances 자자자자자자 자자자 자자자 자자
Physical equilibria: pure sub-stances
5.1 The thermodynamics of transition 5.1.1 The condition of stability 5.1.2 The variation of Gibbs energy with pressure 5.1.3 The variation of Gibbs energy with temperature
5.2 Phase diagrams 5.2.4 Phase boundaries 5.2.5 The location of phase boundaries 5.2.6 Characteristic points 5.2.7 The phase rule 5.2.8 Phase diagrams of typical materials 5.2.9 The molecular structure of liquids
The condition of stabilityWhen an amount dn of the substance changes from phase 1 with Gm(1) to phase 2 with Gm(2),
Gi = n1Gm(1) +n2Gm(2)
Gf = (n1 - dn)Gm(1) +(n2+dn) Gm(2)
ΔG < 0 to be sponta-neous
if Gm(2) > Gm(1), dn < 0; 2→1
if Gm(2) < Gm(1), dn > 0; 1→2
if Gm(2) = Gm(1), at equilib-rium
n1
n2
phase 1
phase 2
n1 - dn
n2 + dn
phase 1
phase 2
ΔG = {Gm(2) − Gm(1)}dn
Pressure dependence of G
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G = H – TSdG = dH – TdS – SdT = Vdp - SdT
= V
For liquid or solid, ΔG = VΔp
For vapor, ΔG = ∫Vdp = nRT ∫(1/p)dp=nRT ln(pf/pi)
ΔGm = RT ln(pf/pi)
Calculate the Vapor pressure increase of water, when the pressure is increased by 10 bar (Δp = 1.0 × 10 6 Pa) at 25°C.
water: density 0.997 g cm-3 at 25°C , molar volume 18.1 cm3 mol-1.
Gm,i(l)
Gm,i(g)
water, p1 = 1 bar
vapor, pi
Gm,f(l)
Gm,f(g)
water, p2= 11 bar
vapor, pf
Temperature dependence of G
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G = H – TSdG = dH – TdS – SdT = Vdp - SdT
= -S
ΔGm = -Sm ΔT
For liquid or solid,
1. Sm > 0, so G will decrease as T increases.
2. Sm(s) < Sm(l) <<Sm(g)
The location of phase boundaries and Clapeyron equation
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dGm(1) = Vm(1)dp − Sm(1)dT
dGm(2) = Vm(2)dp − Sm(2)dT
dGm(1) = dGm(2),
(a) Use the Clapeyron equation to estimate the slope of the solid–liquid phase boundary of water given the enthalpy of fusion is 6.008 kJ mol−1 and the densities of ice and water at 0°C are 0.916 71 and 0.999 84 g cm−3, respectively. Hint: Express the entropy of fusion in terms of the enthalpy of fusion and the melting point of ice.
(b) Estimate the pressure required to lower the melting point of ice by 1°C.
열역학 제 1 법칙은 많은 사실에 적용된다 . 전압이 1.2V 인 어떤 건전지가 있다 . 이 전지가 1A 의 전류로 1 시간 동안 소형 모터를 작동하는데 사용되었다 .
a. 이 건전지의 일을 계산해 보시오 .b. 이 건전지의 내부에너지 변화를 계산해 보시오 .