Chap. 3. The Second Law
Law of Spontaneity, world gets more random
Kelvin - No process can transform heat completely into work
Chap. 3. The Second Law
Law of Spontaneity, world gets more random
Kelvin - No process can transform heat completely into work
The entropy of an isolated system increases in the course of
a spontaneous change.
- Entropy, the degree of randomness
- State function, completely specified by thermodynamic variables
- Unit: Energy/temperature (K)
- Thermodynamic definition:
Chap. 3. The Second Law
Law of Spontaneity, world gets more random
Kelvin - No process can transform heat completely into work
The entropy of an isolated system increases in the course of
a spontaneous change.
- Entropy, the degree of randomness
- State function, completely specified by thermodynamic variables
- Unit: Energy/temperature (K)
- Thermodynamic definition:
For surroundings,
because
The above relation holds
even for finite amount of heat
For surroundings,
because
The above relation holds
even for finite amount of heat
For adiabatic process,
For surroundings,
because
The above relation holds
even for finite amount of heat
For adiabatic process,
Isothermal expansion of an ideal gas
Carnot Cycle (Ideal Gas)
1
I - (VI ,T1)
II - (VII ,T1)
4
IV - (VIV ,T2)
2
3
Fig. 3.6 (with
different notations)
III - (VIII ,T2)
1,3 - Reversible and isothermal processes
2,4 - Reversible and adiabatic processes
Carnot Cycle (Ideal Gas)
1
I - (VI ,T1)
II - (VII ,T1)
4
IV - (VIV ,T2)
Fig. 3.6 (with
different notations)
2
3
III - (VIII ,T2)
1,3 - Reversible and isothermal processes
2,4 - Reversible and adiabatic processes
and
Carnot Cycle (Ideal Gas)
1
I - (VI ,T1)
II - (VII ,T1)
4
IV - (VIV ,T2)
Fig. 3.6 (with
different notations)
2
3
III - (VIII ,T2)
1,3 - Reversible and isothermal processes
2,4 - Reversible and adiabatic processes
and
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
III - (VIII ,Tlo)
Fig. 3.6 (with
different notations)
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
Fig. 3.6 (with
different notations)
III - (VIII ,Tlo)
and
See further information 2.1 (page 69)
, where
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
Fig. 3.6 (with
different notations)
III - (VIII ,Tlo)
and
See further information 2.1 (page 69)
, where
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
III - (VIII ,Tlo)
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
III - (VIII ,Tlo)
Carnot Cycle (Ideal Gas)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
Efficiency:
2
3
III - (VIII ,Tlo)
Carnot Cycle (General)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
III - (VIII ,Tlo)
(First law)
Efficiency:
S is not a state function
Carnot cycle B with
Carnot cycle A with
I - (T
(Tup)
1
4
IV - (T
(Tlo)
II - (T
(Tup)
2
3
III - (T
(Tlo)
I’ - (T
(Tup)
1’
2’
4’
IV’
IV’ - (T
(Tlo)
II’
II’ - (T
(Tup)
3’
III’
III’ - (T
(Tlo)
Carnot cycle B with
Carnot cycle A with
1
I - (T
(Tup)
4
IV - (T
(Tlo)
2
3
I’ - (T
(Tup)
II - (T
(Tup)
III - (T
(Tlo)
+
1’
4’
IV’
IV’ - (T
(Tlo)
2’
3’
Combine A and reverse of B, and assume
Then,
This contradicts the second law by Kelvin!
II’
II’ - (T
(Tup)
III’
III’ - (T
(Tlo)
Carnot Cycle (General)
1
I - (VI ,Tup)
II - (VII ,Tup)
4
IV - (VIV ,Tlo)
2
3
III - (VIII ,Tlo)
Efficiency:
Any cycle can be considered as the sum
of infinitesimal Carnot cycles (Fig. 3.9)
Clausius Inequality:
Clausius Inequality:
(i)
System does maximum work
for reversible process.
(ii) Consider a change of system through a reversible process
(1)
The same change can happen through another process.
(2)
Clausius Inequality:
System does maximum work
for reversible process.
(i)
(ii) Consider a change of system through a reversible process
(1)
The same change can happen through another process.
(2)
(1)=(2)
For adiabatic process
(i)
Entropy change due to phase transition
Normal transition temperature: temperature at which
two phases are in equilibrium at 1 atm.
Heat transfer during phase
transition is reversible
Constant pressure
Entropy change due to heating
Constant pressure
If Cp is independent
of temperature
Entropy of a gas
(Debye extrapolation)
Nernst heat theorem
Third law of thermodynamics
Standard (third law) entropy
- the entropy in the standard state under the
assumption that S=0 at T=0.
Entropy of reaction for
Standard of entropies of ions are defined such that
Helmholtz free energy
Determines the spontaneous
(free) process at constant volume
(no non-expansion work)
Gibbs free energy
Determines the spontaneous
(free) process at constant process
(no non-expansion work)
Helmholtz free energy
Determines the spontaneous
(free) process at constant volume
(no non-expansion work)
Maximum work system can do in isothermal situation
Gibbs free energy
Determines the spontaneous
(free) process at constant process
(no non-expansion work)
Maximum non-expansion work system can do in
isothermal and isobaric situation
Standard Gibbs energy of reaction
Standard Gibbs energy of
formation
The standard Gibbs energy of formation for
ions are defined such that
zero standard Gibbs energy of
formation at all temperature
Fundamental equation
closed system, no non-expansion work, reversible change
valid even for irreversible change
Assume
and
Assume that
and
(2)
(3)
(4)
(2’
(2’)
(3’
(3’)
(4’
(4’)
(2)
(3)
(4)
(2’
(2’)
(3’
(3’)
(4’
(4’)
(2’
(2’)
(3’
(3’)
(4’
(4’)
Gibbs-Helmholtz equation
Important equation for
understanding phase transition
At constant temperature,
Molar Gibbs energy
Molar volume
For liquids or solids, Vm is insensitive to pressure change
For an ideal gas,
When