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The second law, Entropy, Entropy changes
1.
Second law of Thermodynamics
•A gas expands to fill the available volume.
•A hot body cools to the temperature of its
•A chemical reaction runs in one direction rather
than another.
The direction of change that does not require work
to be done to bring the change about is called
spontaneous direction of change.
Internal energy lets us access whether a change is
permissible. Only those changes occurs for which the
internal enegy of an isolated system remains constant.
2.
Is it perhaps the internal energy that tends toward
minimum for a spontaneous process?
System
dU<0
dU>0
Surroundings
Perfect gas expands spontaneously into vaccum. dU=0
3.
No process is possible in which the sole
result is the absorption of heat from a
reservoir and its complete conversion into
4.
A ball bouncing on the floor
A ball resting on the warm surface.
5.
Entropy is measure of randomness/ chaosness.
Total entropy of the system and its surroundings
increases in the course of a spontaneous change.
6.
Thermodynamic definition of entropy.
dqrev
dS
T
For a spontaneous change,
dSTotal 0
dS sys dS surr 0
dqsys ,rev
dS sys
Tsys
dqsurr ,rev
dS surr
Tsurr
7.
dq surr , rev
dS surr
Tsurr
Since Surroundin g consists of reservoir
of constant volume.
dq surr dU surr
Since U is a state function.
dU surr , rev dU surr ,irr
dq surr , rev dq surr ,irr dq surr
dq surr , rev dq surr
dS surr
Tsurr Tsurr
8.
T1,V1,p1 T1,V2,p2
A
T B
C
T2,V2,p3
V
(A) Isothermal process :
dV
dq A dw A pdV RT
V
dq A V2
T R ln
V1
(B) Isochoric (Const. V) process
w 0, dq dU CV dT
dq B dT T2
T CV CV ln
T T1
(C)Adiabatic process
dq
dqC 0; T C 0
R
T1 V2 CV T1 V2
Also,
V CV ln R ln
T2 1 T2 V1
dq dq dq V T
T A T B T C R ln V12 CV ln T12 0
9.
T2,V2,p1
B
T C
A
T1,V1,p1 T1,V2,p2
(A) Isothermal process : V
dV
dq A dwA pdV RT
V
dq A V2
T R ln
V1
(B) Isochoric (Const. V) process
w 0, dq dU CV dT
dq B dT T2
T CV CV ln
T T1
(C)Isobaric process
dqC dH T1
T T C P ln
T2
V2 T
Also, 2
V1 T1
dq A dq B dqC V2 T2 T1
T T T R ln CV ln C P ln
V1 T1 T2
dq T2 T1
T R ln (C p CV ) ln 0
T1 T2
10.
dqrev VA VC
nR ln nR ln
T VB VD
For Process 2
VC TcC VBThC (i)
For process 4
V AThC VDTcC (ii)
Multiplication of (i) and (ii) gives
V AVC ThC TcC VBVDThC TcC
VA V
D
VB VC
dqrev VA VC
nR ln nR ln 0
T VB VD
11.
A Isothermal
nt V
Consta
B
P Adiabatic
C
D Constant P
V
12.
Clausius inequality theorm
dS sys dS surr 0
dS sys dS surr
dq
dS sys
T
If the system is isolated,
dq 0
dS sys 0
The entropy of an isolated system
increases in the course of a spontaneous
Entropy change for a reversible process
dqsys dqsurr
dS sys dS surr
dS sys dS surr 0
13.
From first law of thermodynamics,
dq dU dw
d ( H pV ) dw
dH pdV Vdp pdV
dH Vdp
H H
dq dT
p dp Vdp
T P T
H H
dq dT
V dp
T P p T
dq 1 H 1 H
dT
V dp
T T T P T p T
From thermodynamic equation of state
H V
p
T V
T T P
1 H V
dS dT dp
T T P T P
Cp V
dT dp
T T P
14.
From first law of thermodynamics,
dq dU dw
U U
dq dT dV pdV
T V V T
U U
dq dT
p dV
T V V T
dq 1 U 1 U
dT
p dV
T T T V T V T
From thermodynamic equation of state
p U
T p
T V V T
1 U p
dS dT dV
T T V T V
C dT p
V dV
T T V
15.
Entropy changes in a Reversible process
(a) Phase change :
Phase change is always a reversible process.
liquid (T, P) vapour (T, P)
dq rev , sys dq p dH
dS sys
T T T
H
S sys
T
dq surr dq rev , sys dH
dS surr
T T T
H
S surr
T
STotal S sys S surr 0
Trouton' s Rule :
vap H
Tb 85 JK 1mol 1
16.
Heating or Cooling process
Heating and cooling can be carried
out reversibly.
CV dT p
dS sys dV
T T V
At constant volume,
C dT
dS sys V
T
Tf
S sys CV ln
Ti
Cp V
Also, dS sys dT dp
T T P
At const. Pressure,
Cp
dS sys dT
T
Tf
S sys C p ln
Ti
17.
CV dT
dS sys
T
Tf
S sys CV ln
Ti
19.
Isothermal process for an ideal gas
Reversible process :
CV dT p
dS sys dV
T T V
At constant Temperatur e,
p
dS sys dV
T V
nR
dS sys dV
V
V2
S sys nR ln
V1
V2
S surr nR ln
V1
For an irreversible process,
dqrev V2 wrev
dS sys nR ln
T V1 T
dq surr dq sys w p (V2 V1 )
dS surr ext
T T T T
20.
Adiabatic Processes for an ideal gas
dq sys
dS surr
T
Since, in an adiabatic process,
dq sys 0
S surr 0
(a) Reversible process :
dq sys , rev dq sys
dS sys 0
T T
(b) Irreversible process :
dq sys , rev dq sys
dS sys
T T
For an ideal gas,
Vf Tf ,irrev
S sys R ln CV , m ln
Vi Ti
Tf , rev Tf , irrev
S sys CV , m ln CV , m ln
Ti Ti
Tf ,irrev
S sys CV , m ln
Tf , rev
21.
Entropy changes in irreversible Processes
To obtain the change in entropy in an irreversible
process we have to calculate S along a reversible
path between the initial state and the final state.
Freezing of water below its freezing point
Irrev
H2O( l , -10 °C) H2O( s , -10 °C)
H2O( l , 0°C) H2O( s , 0 °C)
273 H crys 263
S Cliq ln Cice
263 T 273
22.
Absolute entropy of a substance
Tf C p ( s ) dT f H
S (T ) S (0)
0 T Tf
Tb C p (l ) dT v H
Tf T Tb
T C p ( g ) dT
Tb T
Third law of thermodynamics:
The entropy of each pure element or substance in a
perfectly crystalline form is zero at absolute zero.
23.
Spontaneous process
dS sys dS surr 0
dS sys dS surr
dq
dS sys
T
dq TdS 0
At constant volume, no additional work
dqv TdS 0
dU TdS 0
dSU ,V 0 or
dU S ,V 0
At constant V and T
dU TdS dU d (TS )
d (U TS )V ,T 0
d ( A)V ,T 0
A is called helmholtz free energy.
24.
dS sys dS surr 0
dS sys dS surr
dq
dS sys
T
dq TdS 0
At constant pressure, no additional work
dq p TdS 0
dH TdS 0
dS H , p 0 or
dH S , p 0
At constant P and T
dH TdS dH d (TS )
d ( H TS ) P ,T 0
d (G )V ,T 0
G is called Gibb' s free energy.
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