Carnot cycle is based on 4 reversible process.
(1) Reversible isothermal expansion from A to B.
ΔEAB = 0 ,
(2) Reversible adiabatic expansion from B to C
ΔEBC = nCV(T2 -T1)
WBC = ΔEBC
(3) Isothermal compression from C to D
ΔECD = 0,
(4) Adiabatic compression from D to A.
ΔEDA = nCV(T1 - T2)
WDA = ΔEDA
ΔECycle = 0
Wcycle = -nR(T1 - T2)ln V2/V1
Efficiency of any engine may be given as
ΔEcycle = qcyc wcycle
This means ΔS is a state function
Gibb's Free Energy (G)
Gsystem = Hsystem - TSsystem
W = Wexpansion +Wnon-expansion
Wnon - expansion = wuseful (useful work)
ΔG = Wnon expansion = Wuseful
All those energy which is available with the system which is utilized in doing useful work is called Gibb's free energy :
1. ΔGsystem = ΔHsystem - TΔSsystem = - TΔSuniverse = Wnon expansion = Wuseful
2. ΔGsystem = - TΔSuniverse
(a) ΔSuniverse > 0 or ΔGsystem < 0 ⇒ Spontaneous
(b) ΔSuniverse = 0 or ΔGsystem = 0 ⇒ Equilibrium
(c) ΔSuniverse < 0 or ΔGsystem > 0 ⇒ Non-Spontaneous
APPLICATION OF ( ΔG )
(1) aA + bB ⇌ cC + dD
ΔG° = Standard Gibb's free energy change (P = 1 atm, 298 K)
ΔG = Gibb's free energy change at any condition.
ΔG = ΔG° + 2.303 RT log Q ; Q = Reaction Quotient
At equilibrium, ΔG = 0 and Q = Keq.
0 = ΔG° 2.303 RT log keq
ΔG° = -2.303 RT log keq
å G°(product) - å G° (Reactant) = - 2.303 RT log keq
ΔH° - T ΔS° = -2.303 RT log keq
(2) Wcell = q × E
ΔG = - Wcell
ΔG = - q × Ecell
Now, one mole e- have charge 96500 coulomb = 1 Faraday (F)
n mole of e- will have charge = n × F or q = n × F
ΔG = - nFEcell
ΔG° = -nFE°cell
THIRD LAW OF THERMODYNAMICS
limitT→0 S = 0
Third law of thermodynamics states that as the temperature approaches absolute zero, the entropy of perfectly crystalline substance also approaches zero.
APPLICATION OF THIRD LAW OF THERMODYNAMICS
Taking T2 = T and T1 = 0°k.
For perfectly crystalline substance. The entropy of perfectly crystalline substance can be determined using third law of thermodynamics.
With the help of third law of thermodynamics we can calculate the exact value of entropy.
ΔG AND NON PV WORK (NON EXPANSION/COMPRESSION)
(ΔG)T,P is a measure of useful work a non PV work (non expansion work) that can be produced by a chemical transformation.e.g.electrical work .
For reversible reaction at constant T & P
dU = dq + dWtotal
dU = dq + dWP, V + dWnon P,V
dU = T.dS - P. dV + dWnon P,V
dU + P.dV = T. dS + dWnon P,V
dH = T.dS + dWnon P,V
(dGsys)T,P = dWnon P,V
Useful work done on the system = increase in Gibb's energy of system at constant T & P.
- (ΔGsys)T,P= - Wnon P,V
- (ΔGsys)T,P= - Wby, non P,V
Useful work done by the system = decrease in Gibb's energy of system at constant T & P.
If (ΔGsys)T,P = 0, then system is unable to deliver useful work.
For reversible process in which non-expansion work is not possible
dU = dq + dW
H = U + PV
dH = dU + P.dV + VdP
dH = T.dS - PdV + PdV + V.dP
dH = T.dS + V.dP
G = H -TS
dG = dH - T.dS -S.dT
dG = T.dS + V.dP - T.dS - S.dT
For a particular system (s/ℓ/g)
(1) At constant temperature dG = V.dP
(A) For a system is s/ ℓ phase
(B) For an ideal gas, expansion/compression:-
(2) At constant pressure : dG =-S.dT
For phase transformation/chemical reaction
d(ΔG) = ΔV.dP - ΔS dT
H2O(s) → H2O(l)
ΔV = VM(H2O,l) - Vm(H2O,s)
ΔS = SM(H2O,l) - Sm(H2O,s)
A(s) → B(g) + 2C(g)
ΔrS = SM(B,g ) 2Sm(C,g) - Sm(A,s)
C (s, graphite) → C(s, diamond)
ΔV = Vm(C, diamond) - Vm(C-graphite)
At constant temperature:-
d(ΔG) = ΔV. dP
At constant pressure
ΔrGT2 - ΔrGT1 = - ΔrS(T2 - T1)