This Class
2nd & 3rd Law
of
Thermodynamics:
(Directionality
/Spontaneity, Scale)
Initialization
Q1=100
Non-EQ
Q2=50
T1=10
T2=1
Q1/T1=10 < Q2/T2=50
W=50
Q1=100
Non-EQ
Q2=20
T1=10
T2=1
Q1/T1=10 < Q2/T2=20
W=80
Q1=100
EQ
Q2=10
T1=10
T2=1
Q1/T1=10 = Q2/T2=10
W=90
Carnot Cycle
A
Temperature Scale
System
A at T
Q
System
B at T-1
Same Mechanical
Effect Irrespective of
Material Properties
Carnot Engine in Details (Assignment – Self Reading)
All steps are reversible, so maximum work is expected => Incorporation of Idealism
Continuing…..
As General Case
Here, 𝐶𝑉. ln
𝑡1
𝑡2
+ 𝑅. ln
𝑉3
𝑉2
= 0 & 𝐶𝑉. ln
𝑡2
𝑡1
+ 𝑅. ln
𝑉1
𝑉4
=0
In Carnot cycle T1 & T2 are fixed => V2/V1 =V3/V4
Entropy: One of Most Used Terms
Continuing with Entropy
Both Statements (Clausius & Kelvin) & More….
Clausius: It is not possible to draw a certain amount of heat, say Q, from a cold body and
transfer it all to a hot body.
Kelvin: It is not possible to convert heat entirely into work.
Hot
Q2
Hot
Hot
1
1
3
2
Q1-Q2
W=Q1-Q2
Q2
Q2
Q2
Cold
Q1-Q2
Q1
Q2
Cold
Cold
Better Than Reversible Efficiency: Possible or not?
Hot
Q=100
Q=10
W=90
Reversible Engine
Better Than
Reversible Engine
Q=9
Q=100
W1 – W = 1 => This way we can
generate work for ever =>
Impossible Demand (Reversible
path is already in maximum ordered
energy path out of total energy)
W1=91
Cold
W
Qs
From source
Qloss
To sink
Uncompensated Transformation
(Qs-Qloss)rev > (Qs-Qloss)irre
Qloss (heat loss) is min. for reversibility
dS is the difference between heats in
transit i.e. transfer and loss.
Entropy Change for an Isothermal Expansion of an Ideal Gas
Entropy: Extensive Property
Molar Entropy (Entropy per Mole): Intensive Property
Exothermic Reactions: Entropy Change for Surroundings
For an adiabatic reversible change: ∆Ssys = 0 and ∆Ssurr = 0
Some Essential Derivations
Entropy Balance
S
• Having directional property of a process
• Guided by a fundamental law (entropy can’t decrease: Which Law??)
• Definable non-zero generation term of a process
• Universally applicable state variable with physical significance
• Another balance equation (more access to a system)
Basic Ideas
Reversible Process
Irreversible Process
Basic Ideas
A
Matter Exchange in the system + Irreversibility
Cyclic Process
Systems in Non-equilibrium
Basic Ideas
Expression
Rate of Entropy Generation
=
Net change of entropy flow due to flows of mass in and out of the system
+
Net change of entropy flow due to flow of heat across the system boundary
+
Rate of internal generation of entropy within the system
Entropy Generation = 0
Entropy Generation > 0
=> at equilibrium
=> All non-equilibrium conditions
Entropy Balance Equation for Open System
Important Equation
Continuing
A
One Problem
Another Problem
Continuing with the Solution
Continuing with the Solution
Statements of Second Law
For Irreversible Process Overall Entropy Increases:
Prove Mathematically: Assignment
Few Important Points
A
Problem
Continuing…..
Problem (from different Universities)
Another Problem
Third Law: Relooking The Definition
1. If a single process of reversible extraction of heat results in the reduction of the
temp. for a crystal to the lowest measurable temp. near 0K, then zero entropy at
0K remains an obvious extrapolation from that measured point.
2. What the 3rd law tells us in real life is that curves of many reasonable physical
quantities plotted against T must come in flat as T approaches 0. Kittel-Kroemer
3. The entropy of a system at absolute 0 is a universal constant, which may be taken
to be 0. Huang
4. The entropy of a system approaches a constant value as the temperature
approaches zero.
Molten SiO2 to Glass
Different S0 for same matter: Not Permissible
Attaining T=0: Infinite Reversible Cycles
Third Law: Relooking The Definition
A
Third Law: Relooking The Definition
Third Law & Beginning of Statistical Journey
Continuing…..
Few Points
2nd law: The entropy of an isolated system never decreases.
liquid
S
supercooled
liquid
glass
residual
entropy
crystal
T
−1
  S (U ,V , N ,...) 

T  
U

V , N
Sample Problems (Assignments)
1. Derive the Relation
2. Drive the Relations
3.
Follow any standard text books (preferably references) to see the solved problems
related to 2nd as well as 3rd Laws of thermodynamics and practice the derivations
4.
Answer:
5.
Entropy & Information
Picking
Red Ball
Ball
Picking Red
with
=>
with Certainty
Certainty =>
Knowledge
=>
Precise
Information
toDecreasing
Definefrom left
the
to
right,
while
System
=>
entropy
is
Decreasing
from left
increasing
to
right,
while
entropy is increasing
https://www.youtube.com/watch?v=9r7FIXEAGvs
Entropy & Information-2
1
Entropy & Information-3
Picking
‘A’
with
Certainty => Precise
Information
to
Define the System
=> Decreasing from
left to right, while
entropy is increasing
Entropy & Information-4
A
Entropy & Information-5
A
Next Class
Quick Review – III
Some Concepts,
Definitions & Aspects