Td pctf july_28_2018

Teaching & Learning in the New
era of CBCS
Exploring through Thermodynamics
PCTF Interactive Discussion Meeting
July 28, 2018

CORE COURSES FOR B. SC. HONOURS (CHEMISTRY)
SEM CODE* PAPER Credit Classes
1 CEMA CC-1-2-TH PHYS CHEM-1 4 40/60
ORG -1B
CEMA-CC-1-2-P PRAC 2 30/45
2 ---------------- ----------
3 CEMA-CC-3-5-TH PHYS CHEM-2 4
CEMA-CC-3-5-P PRAC 2
4. CEMA-CC-4-9-TH PHYS CHEM-3 4
5. CEMA-CC-5-11-TH PHYS CHEM-4 4
6 CEMA-CC-6-14-TH PHYS CHEM-5 4
CEMA-CC-6-14-P PRAC 2 .
Total 28/(56+28=84) 490
CEMA-CC1-1-TH/P : Chemistry Honours- Core Course- First Semester- Paper 1- Th /P]
** Practicals are based on the corresponding theoretical papers.
Course Phys/Total [credit]
CORE 28 / 84 Th + P
DSE 4 / 16 Th*
2 / 8 P*
SEC 2 / 4
Total 36 / 112*[nearly 1/3rd]
Gen Elec 16+8= 24 [Th + P]
(AECC) 4 .
Total Credit 140
DSE: Discipline Specific Elective
SEC: Skill Enhancement Elective
AECC: Ability Enhancement
Compulsory Course

P-2/S-1 P-14/S-6
Spectroscopy,
Photochemistry
Surface
Phenomena
Physical Chemistry Courses
PIN: 2591114
P-11/S-5
Kinetic
theory,
Transport
Chemical
kinetics
P-5/S-3 P-9/S-4
Physical Chemistry-
(Th + P)
1 2 3 4 5
Chem Thermo-I,II
TD Appln-I
Electrochemistry
TD Appln-II
Quantum-I
Crystal
Quantum-II
Statistical TD
Numerical Analysis
SEC 1 – MATHEMATICS AND STATISTICS FOR CHEMISTS Sem-3
DSE-A2: APPLICATIONS OF COMPUTERS IN CHEMISTRY (Th+P) Sem-5
DSE-B4: DISSERTATION Sem-6

6 new courses
Core Course :
1.Quantum Chemistry-II [CC-5-11-TH ; PHYS CHEM-4 , Sem-5]
2.Numerical Analysis [CC-5-11-TH ; PHYS CHEM-4 , Sem-5]
3.Practical : Based on Numerical Analysis [CC-5-11-P, Sem-5]
4. SEC 1 – MATHEMATICS AND STATISTICS FOR CHEMISTS; Sem-3
5. DSE-A2: APPLICATIONS OF COMPUTERS IN CHEMISTRY; Sem-5
6. DSE-A2-Practical: APPLICATIONS OF COMPUTERS IN CHEMISTRY; Sem-5
Expectation from PCTF: On
Introduction: What/why/how?
Outline (brief)
Detailed Content (with handouts?)
Exercises/Problems (with Hints/solutions?)
Q-A [Objective (SCQ, MCQ) + others
Emphasis/effective delivery
Effective References
Anything Else…?
You all are welcome
to
contribute
From either side…

Workshop [24/05/2018, Gokhale College]
Debasish, Kingshuk, Chaitali, Sukanya, …On
From Teacher Centric  Student Centric. ?. !. …
Or, a deep rooted one!!!
Syllabus: content &
its distribution
Assessment /
ExamTeaching/covering the syllabus
CBCS and PCTF
New Topics ?
Objectives?
Objective?
“the goals of teaching and learning science include
knowledge (cognition), emotion and motivation.”

Objective Soft Skills Values/
Ethics
Teaching
Team work
Communication
Leadership
Time Management
Human Values
Professional Ethics
< 10% of sanctioned posts
Innovation/
Entrepreneurship
Display Skills/Talents
Employment/ self
Employment
Higher Studies
Link with society &
Industry
To The VC of all Universities
24/05/2018; Target Year: 2022
UGC Quality Mandate
Believe: Only Degrees do not make us qualified to be Teachers.

Induction
Program
ICT based Exam
Reforms
RC/OP
Concept/
Application
On Duty
To The VC of all Universities
24/05/2018; Target Year: 2022
UGC Quality Mandate [Initiative]
Research
Power point
On-Line (Net)
Critical
Thinking
100 % of them are Oriented about
the latest and emerging trends
The Pedagogies that translate their knowledge to he students.
Don’t believe: “Great teachers are Born, not made”

Teaching: The Middle Way
Formal lecture  facilitation
“Inspiration >> information.”
Education= Teaching +Fostering
Mutual Growth,
Fostering Each Other
Shared Commitment
Classroom Level:
Originality, Creativity, Awareness
Human Education:
Capable of
Value CreatingBenefit
Co-living toward Personally and Socially beneficial Ends.
Oneness with the Teacher
Dialogic Process
Two components of Education
And Learning
Happy?relative Relative
Outward/
Material
QuestMiddle way/
combined
BeautyGood

Eugene Wigner’s two minutes Nobel speech
1963, (Nobel in Physics): Theory of atomic nucleus and elementary particles; through
the discovery and application of fundamental symmetry principles. [Google search]
He taught me…
Science begins with and consists in assimilating the coherence in a body
of phenomena and creating concepts to express these regularities in a
natural way. It is this method of science rather than the concepts
themselves (such as energy) which should be applied to (other fields of)
learning.
A student remembers his Teacher: Michael Polanyi-Wigner
How to Learn rather than learning the Topics only
“Education is what remains long after the lesson-content we were
taught has been forgotten”
Daisaku Ikeda, Educator

CBCS and PCTF
More syllabus-Load in Lesser Time
OSAG in stead of spoon feeding/ rote learning
 Be Smart along with Chalk & Talk
 Trust and Rely on, have confidence in your students
Thermodynamics
as a Model
Open
Show
Awaken
Guide

A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
 A few fundamentals
 First and second law on the same footings
 Joule and Joule-Thomson: On the same footings
Show
2. Be picturesque, be Graphical
 statements of second law;
 Third law: dS versus S
3. Revisit the concepts
 Ek Dozen Satyi-Mithye (T/F) Gappo
Awaken
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
 Understanding conventions, assumptions and
approximations
 One single problem is enough!
6. Fun in finding/discovering Pattern
 P Club vs. V Club:
 Thermodynamics is reduced by 50%
 Fun with Transformation: The Maths behind the P-
V rivalry!
7. Learning: An Interactive, Joyful
experience
 Playing through Quiz, SCQ, and MCQ.
Postscript
Assessment, Timeline, What Next, References
Open Guide

 First and second law on the same
footings
 Joule and Joule-Thomson: On the
same footings
4. Effective Learning: Concept map rather than
concepts only
 Understanding conventions, assumptions and approximations
 Fun with Transformation: The Maths behind the P-V rivalry!
7. Learning: An Interactive, Joyful experience

Physical &
Chemical
Processes
developing models to describe physical and
chemical processes;
David Ball in his textbook Physical Chemistry
Success= thinking about a system macroscopically, at the
molecular level, and mathematically.
The First Day in a CBCS-Physical Chemistry Class
Its Relevance,
Its uniqueness,
Its Beauty/attraction
Challenge:
how to engage students in Learning endeavors?
What do they need to be successful?
Macroscopic Molecular-Level Mathematical
Pressure Point mass, PV=RT
volume less
Liquification inter mol Lennard-Jones
of gas, TC etc forces van der Waals
Preparation Attractive/repulsive μJT = (∂T/∂P)H
of liq Nitrogen intermolecular forces

Subscripts are important
(∂z/∂x) = (∂z/∂y) .(∂y/∂x)
(∂z/∂x)= [1/(∂y/∂z)] [1/(∂x/∂y)
(∂z/∂x) (∂y/∂z) (∂x/∂y) = 1  (∂x/∂y) (∂y/∂z) (∂z/∂x) = 1 ;
but Euler cyclic/chain relation is (∂x/∂y) (∂y/∂z) (∂z/∂x) = −1
In fact. for, z = f (x,y),
The relation is (∂x/∂y)z (∂y/∂z)x(∂z/∂x)y = -1
R R R
For ideal gas
(∂U/∂V)T = (∂H/∂P)T = 0
(∂U/∂P)T = (∂U/∂V)T (∂V/∂P)T
(∂H/∂V)T = (∂H/∂P)T (∂P/∂V)T
 (∂U/∂P)T = (∂H/∂V)T = 0
1 = -1
2 = 0 ?

More fundamentally,
Mala Badal…
z = f (x,y): Is dz exact differential? Is Z state function?
Prescription: (∂2z/∂y∂x) = (∂2z/∂x∂y) … (A)
Fundamentally: dz = M(x,y) dx + N(x,y) dy
If (∂M/∂y)x = (∂N/∂x)y Then dz is exact. Is it equivalent to (A)?
dz = M(x,y) dx + N(x,y) dy
dz = (∂z/∂x)y dx + (∂z/∂y)T dy
(∂M/∂y)x = (∂N/∂x)y (∂2z/∂y∂x) = (∂2z/∂x∂y) …(A)
 For Volume, V: (∂2V/∂P∂T) = (∂2V/∂T∂P);
 What about Work= -pdV?
dV = (∂V/∂P)T dP + (∂V/∂T)P dT
(∂2V/∂P∂T) = (∂2V/∂T∂P)= -R/P2
dV = (-RT/P2) dP + (R/P) dT
-pdV = (RT/P) dP + (-R) dT
(∂M/∂y)x = R/P but
(∂N/∂x)y = 0
So, w=-pdV is not exact.

Joule coefficient (μJ)
Extensive or Intensive?
μJ = (-1/CV) (∂U/∂V)T
 (∂U/∂V)T  ratio of two extensive  intensive;
 CV not independent of size μJ is not intensive;
 CV  2CV, μJ  (1/2) μJ ;
 μJ is not additive;
 so not extensive either.
 So, μJ is neither intensive, nor extensive.
Mass dependent? P = n R T /V; P =f(m) or P = (1/3)m n c2, P=f(m) ?
Additivity or size-dependence:
Z = Zi, for all i (intensive); or Z = ∑i Zi (extensive). Size Dependent?
YESNO
Intensive
Keq , ∏
YESNO
Additive
Neither/Nor
μJ
Extensive
V U H

Entropy
Definition, origin, significance
• dS =qrev/T why rev? what for irreversible?
 S is not defined but dS
• Carnot cycle; §q/T =0
• dU = dq – PdV
 CVdT = dq – RT dV/V [rev., trouble in integration]
 CVdT/T = dq/T - RdV/V [No trouble]
• S Randomness or disorder-ness? Subjective!
 How comes from qrev/T?
• qrev /T justifies Clausius statement.
• S= kB ln W

On the same footing
Joule experiment
The Cause: ∆V
The Effect: ∆T
The Constant: U
Effect/Cause : ΔT/ ΔV
The coefficient: μJ = (∂T/∂V)U
Expression: =-(1/CV) (∂U/∂V)T
For ideal gas: μJ =0; ΔT = 0
Observation
Status: Wrong
Joule-Thomson
∆ P
∆T
H
ΔT/ΔP
μJT =(∂T/∂P)H
=-(1/CP) (∂H/∂P)T
μJT =0; ΔT = 0
Right
μJT = - (V/CP)[ CV μJ к - P к + 1]
Levine, Prob. 2.35, Page-75

Each of q, w, ΔU and ΔH is positive, zero or
negative?
Joule experiment
 q = 0 ; adiabatic
 w = 0; Pex =0, w=-P dV
 ΔU = q + w = 0
 ΔH = ΔU + Δ(PV)
 = nR ΔT
 =0 [ΔT = 0 as μJ =0]
Joule-Thomson experiment
 q = 0 ; adiabatic
 ΔH = 0
 as μJT =0 for a perfect gas,
 So, ΔT = 0 ,
 hence ΔU = CV ΔT = 0
 w = ΔU – q = 0 – 0
 w = 0

1st and 2nd Law on same footings
1st law [Phalo kaRi makho tel]
• Conservation
• possibility
• Introduces U
• dU = q + w
• ∆U =0, isolated system
• PMM-I not possible.
• PMM-I: keeps on doing work
without any supply of energy.
2nd law [a natural Tax]
• Spontaneity/direction
• Feasibility
• Introduces S
• ds=qrev /T
• ∆S ≥ 0, isolated system.
• PMM-II not possible
• PMM-II: Which can draw energy
and do work but does not
require a sink.

1st and 2nd Law on same footings
1st law [Phalo kaRi makho tel]
• Carnot engine, ∆U =0
-w= qnet = qh – qc ;
Silence: qc =0?, -w = qh
Silence broken: 2nd law
-w ≠ qh ; complete
conversion of heat into
work is not possible.
2nd law [a natural Tax]
• Carnot engine:
-w/qh = (Th – Tc)/Th ; Th > Tc
Silence: Tc =0? –w=qh
Silence broken: Third Law
Tc ≠ 0; Absolute zero is not
possible.

than concepts only
approximations
 Fun with Transformation: The Maths behind the P-V
rivalry!
experience

No Sink: qC = 0 or TH = TC
Kelvin statement
qC=0
-w=qH
qH
-w/qH = (TH – TC)/TH ; for TC=TH , -w = 0, No work.
Kelvin: No cyclic process is possible in which heat is taken
from a hot source and converted completely into work”.

Let us keep a sink at TC < TH but effectively qC =0
Th
Tc
qC
qC qH
qC
-w=qH – qC
-w= qH – qC
Unfortunately, C is not possible: The Clausius statement.
“ heat does not pass from a body at low temperature
to one at high temperature without any change elsewhere”.
qH – qC

C N P
If Kelvin= 2nd Law then is Clausius=third Law?
No! They are Equivalent.

Why an anti-Clausius device does not exist?
Equivalence with Entropy statement
Th
Tc
q
ΔSc = - q/Tc
ΔSh = + q/Th
ΔSdevice = 0 [cyclic]
ΔSsurr = ΔSc + ΔSh
ΔSuniv = - q/Tc + q/Th
= q(Tc – Th)/(TcTh)
< 0 [Th > Tc]
But, ΔSuniv ≥ 0 [2nd law]
So the device violates the 2nd law.

The Third Law?
S is defined!
• No new state function like U (1st) and S (2nd), or exact differential
like dU and dS
• No new PMM-impossibility ; Only refers to T(0th)and S (2nd )
Unattainability of T=0
 LtT0 S = 0 [only after statistical interpretation].
• dS = kB dln W  S = kB ln W? by integration?
• S = kB ln W + S0 S0 = 0? Third Law is there.
• LtT0 ΔS =0; LtT0 S=0,;
LtT0 S = LtT0 (kB ln W) + S0
0 (3rd law) = kB ln 1 + S0 = 0 + S0
or, S0 = 0; therefore S = kB lnW

 Ek Dozen Satyi-Mithye (T/F)
Gappo
than concepts only
approximations
rivalry!
experience

Ek Dozen Satyi-Mithye Gappo
1. Isothermal  ΔT = Tf – Ti = 0? 
 ΔT = 0  isothermal? 
2. U remains constant in every isothermal process in a
closed system. T/F?
 False. Only for perfect gas U=f(T, only).
Isothermal pressure change, average intermolecular
distance and hence its contribution to U through
intermolecular interaction will change.
True
False

3. 1∫2 (1/V)dV = ln(V2 – V1 ) or (lnV2)/(lnV1)?
 Both False. Its ln(V2/V1)
4. 1∫2 T dT = (1/2)(T2 – T1)2
 False. Its (1/2)(T2
2 – T1
2 )
5. ΔU is a state function.
 False. ΔU is the change in a state function.
6. For a closed system at rest in the absence of external fields, U
= q + w.
 Its ΔU = q + w

7. PV = k1 and V/T = k2
So, PV . V/T = k1 k2 = k
Or, PV2 /T = k; is it not PV/T = k?
8. A perfect gas [Cv,m ≠f(T) & = 3 R] expands adiabatically into vacuum
to double its initial volume.
Banga: T2/T1 = (V/2V)ϒ-1 = (V/2V)R/3R or T2 = T1/21/3 .
Bangla: ΔU =q+w =0+0 =0 and ΔU= Cv ΔT=0, so, T2 =T1
Who is correct?
 T2 = T1 is correct. [since irreversible].
PV=c and PVγ =c
How both refer to
Ideal Gas?
Reversible
in which
step?

9. Enthalpy (H) is called Heat Content. Why? Why
misleading?
 ΔH = qp
 Mislead to think that q is a state function.
10. Δq or Δw; should we write?
 q and w are not state functions.
 Not change of heat of a system but heat transfer in a
process?
 Not work of a system but work involved in a process.

11. ΔH = qp for a constant-pressure process. if P is not
constant throughout but Pinitial = Pfinal. Is ΔH=q here?
 No. For example, in a cyclic process, ΔH = 0 but q
need not be zero, since q is not a state function.
12. ΔS > 0 [2nd law] and (dU)S,V > 0 or (dH)S,P > 0
[Clausius inequality]; both are criteria for
spontaneity. Don’t they contradict each other?
 No. S of what? Of universe [2nd law] and of system in
Clausius inequality.

 Joule and Joule-Thomson: On the same
footings
4. Effective Learning:
Concept map rather than
concepts only
 Understanding conventions, assumptions
and approximations
6. Fun in finding/discovering
Pattern
 Fun with Transformation: The Maths behind
the P-V rivalry!
experience

Thermodynamic
Equation of State
What is
it?
Derivation Applying Reverse Journey
Joules Law
Ideal gas
Exact
Differential
State function
1st/2nd
Laws
Maxwell
Relations
Three Gases
PV=RT
P(V-b)=RT
V d W gas
Ideal Gas Real Gas
U &H= f(T,only)
Ideal=Perfect?
(∂CV /∂V)T
(∂CP /∂P)T
(∂H/∂P)T is better
internal pressure:a/V2
Molecular insight, IMF
Atomicity & CV
CUQ-2018: other properties
Pattern
Entropy Meter?
WHY?
Equation of state
Thermodynamic
CONCEPT MAP: An Example,
Integrated & coherent cognition, interconnected, deeper insight,
Making sense, Learning how to learn
Statistical
Partition function

S p
TV
(+)
U=f(S,V)
dU=TdS-PdV
(∂P/∂S)V
= - (∂T/∂V)S
H=f(S,P)
dH=TdS + VdP
(∂S/∂V)T = (∂P/∂T)V
G=f(P,T)
dG=VdP-SdT
(∂S/∂P)T = - (∂V/∂T)P
A=f(V,T)
dA=-PdV – SdT
(∂S/∂V)T = (∂P/∂T)V
(−)
dz = M(x,y) dx + N(x,y) dy
Samrajnee from some
answerscript

Relation between μJT and μJ
A Good Exercise on mathematical relations
Levine, unsolved Prob. 2.35, Page-75
μJT = - (V/CP)[ CV μJ к - P к + 1]
μJ = (∂T/∂V)U = -(1/CV) (∂U/∂V)T ; (∂U/∂V)T = -CV μJ
μJT = (∂T/∂P)H = -(1/CP) (∂H/∂P)T ; (∂H/∂P)T = -CP μJT
H = U + PV
(∂H/∂P)T = (∂U/∂P)T + P(∂V/∂P)T + V
= (∂U/∂V)T (∂V/∂P)T – PV к + V
-CP μJT = [-CV μJ] [-V к ] – PV к + V
= V [CV μJ к – P к + 1]
μJT = - (V/CP)[ CV μJ к - P к + 1]

than concepts only
 Understanding conventions,
assumptions and
approximations
rivalry!
experience

Understanding Physical Chemistry = understanding
conventions, assumptions and approximations
A problem on liquid water: as simple as water:
 Water (liq) is vaporized at 1000 C and 1.013 bar. The heat of
vaporization is 40.69 kJ mol-1 . Find the values in kJ mol-1 of (a)
w, (b) q, (c) ΔU, and (d) ΔH.
Assumption
 water vapor is ideal,
 Volume of liq water is negligible.
 W=-PΔV ̴ -P(Vvap) = RT -3.10
 q= heat of vaporization 40.69
 ΔU= q+w 37.59
 ΔH= ΔU + Δ(PV) = ΔU+ P ΔV = ΔU +RT 40.69 = ΔHvap

Understanding Physical Chemistry =
understanding
conventions, assumptions and approximations
Consider a n-particle, 2-level system. Evaluate W1:1 and
Wtotal. Compare the results. Comment.
 W= n!/Пi ni!  W1:1 = (n/2)! / (n/2)!2
 ln W1:1 = n ln2 = ln Wtotal
 Its good! But too good to be true!
 Why?
N w
1 2 (H T)
2 4 (HH, HT, TH, TT)
3 8 ( HHH
HHT HTH THH
TTH THT HTT
TTT)
N ?

So much from a single equation
 RT ln KP = - ΔG0 (T) or, KP = Exp[- ΔG0 /RT]
 ΔG0 mol-1 ? per mole of equation/reaction
KP is
 Dimensionless
 ≠ f(P)
 = f(stoichiometry)
 = f(standard state)
Dimensional Analysis
[any coefficient= effect/cause
CP – CV = T V αm / βn
α = (1/V) (∂V/∂T)P
; β = (-1/V) (∂V/∂P)T

One single problem is enough!
[four in one, in fact]
1 mole ideal gas at T1 and P1 expands (or compresses) to P2 . Calculate q, w, ∆U,
∆H, ∆S.
To start with: w=-pexdV; ∆U = CV ∆T; ∆H=CP ∆T (ideal); ∆U=q+w ∆S=qrev /T
. Process? .
Iso, rev. Iso, irrev. Adia, rev. Adia, irrev.
T2 =T1 ; ∆T =0= ∆U= ∆H q=0, w= ∆U;
∆U=q+w; q=-w, only w! w or ∆U, hence T2 needed.
rev w= irrev rev T2= irrev
-RTln(P1/P2) -P2 (V2–V1) TPR/Cp=c w= ∆U
= -RT(1-P2/P1) gives T2 -P2(V2– V1)=CV∆T
T2=[CV +(P2/P1)R](T1/CP )
∆S=qrev /T ∆S≠qirrev /T but final
states are same; (T1,P2) ∆S=qrev /T , which T? T1 or T2?
So, ∆S=qrev /T= Rln(P1/P2) in both the cases. = 0 ∆S=CV ln(T2/T1)+Rln(P1/P2)

All four problems in a single frame
• Isothermal  (a) reversible, (b) irreversible
• Adiabatic  (c) reversible, (d) irreversible
• One mole of a perfect gas at 300 K and 106 Pa expands to 105 Pa.
Calculate w, q, ΔU, and ΔH for each process. [cV = 1.5R]
V2 T2 -W q ΔU ΔH
(a) 10V1 T1 RT ln(P1/P2) -w 0 0
(b) 10V1 T1 P2(V2-V1) -w 0 0
=RT[1-P2/P1]
(c) 3.98V1 T1(P2/P1)R/Cp -ΔU 0 CVΔT CPΔT
(d) 6.40V1 T1[CV+(P2/P1)R]/Cp - ΔU 0 CVΔT CPΔT

All four problems in a single frame
• Isothermal  (a) reversible, (b) irreversible
• Adiabatic  (c) reversible, (d) irreversible
• One mole of a perfect gas at 300 K and 106 Pa expands to 105 Pa.
Calculate w, q, ΔU, and ΔH for each process. [cV = 1.5R]
• T1 =300K, P1=106 Pa, V1,
V2 T2 -W q ΔU ΔH
(a) 10V1 T1 5744.0 5744.0 0 0
(b) 10V1 T1 2245.0 2245.0 0 0
(c) 3.98V1 119.4 2252.0 0 -2252 -3753
(d) 6.40V1 192.0 1347.0 0 -1347 -2245
T in K; energy in J

than concepts only
approximations
Pattern
 Thermodynamics is reduced by
50%
 Fun with Transformation: The
Maths behind the P-V rivalry!
experience

Your Club vs. Our Club: P vs. V
Thermodynamics is reduced to/by 50%
• dU = q – PdV (first law)
• dUV = qV
• q behaves like a state function,
at V.
• What about q at P?
• P and V rivalry starts!
• qP = d(?)
• Let, X= U+ PV
• dX = dU+ PdV + VdP
• = q + VdP
X = H = U + PV (enthalpy)
[energy, state fun, extensive]
dH= dU + PdV + V dP
= q + V dP
q = dH - VdP, and
q = dU + PdV
Both are first law?
dXP = qP

P-V rivalry continues …
• qV = ΔU
• U=H-PV
• dU=TdS+PdV
• q = dU + PdV
• CV = (∂U/∂T)V
• Joule, ΔU=0
• μJ = (∂T/∂V)U
• =(-1/CV) (∂U/∂V)T
• (∂U/∂V)T =T(∂P/∂T)V - P
• (∂U/∂V)T =0; (∂U/∂P)T=?
• (∂T/∂V)S = - (∂P/∂S)V
• qP = ΔH
• H=U+PV
• dH=TdS-VdP
• q = dH – VdP
• CP = (∂H/∂T)P
• Joule-Thomson, ΔH=0
• μJ-T = (∂T/∂P)H
• =(-1/CP) (∂H/∂P)T
• (∂H/∂P)T =-T(∂V/∂T)P + V
• (∂H/∂P)T =0; (∂H/∂V)T=?
• (∂T/∂P)S = + (∂V/∂S)P

P-V rivalry continues …
• A = U – T S
• dA = -PdV - SdT
• dAV,T ≤ 0
• dUS,V ≥ 0
• μj = (∂A/∂ni)V,T,nj
• = (∂U/∂ni)V,S,nj
• Helmholtz
• Van’t Hoff isochore
• KC
• (∂S/∂V)T = (∂P/∂T)V
• G = H – T S
• dG = VdP – S dT
• dGP,T ≤ 0 [most useful]
• dHS,P ≥ 0
• μj = (∂G/∂ni)P,T,nj
• = (∂H/∂ni)P,S,nj
• Gibbs
• Van’t Hoff isobar
• KP
• (∂S/∂P)T = - (∂V/∂T)P

Fun with Transformation:
The Maths behind the P-V rivalry!
• f= f(x,y)  df = p dx + q dy
Lets play: Evaluate df – d(qy)
 df–d(qy) = pdx +qdy –qdy –ydq
 d(f – qy) = p dx – y dq
 dX = p dx – y dq;
where, X = f – qy and X= f(x,q);
So, we got
f(x,y)  X(x,q) and df  dX
Similarly
• f= f(x,y)  df = p dx + q dy
Lets play: Evaluate df – d(px)
 df–d(px)= pdx +qdy–pdx– xdp
 d(f – px) = q dy – x dp
 dY = q dy – x dp;
where, Y = f – px and Y = (p,y);
So, we got
f(x,y)  Y(p,y) and df  dY
Can we think of yet another
transformation
f(x,y)  Z(p,q) and df  dZ?

Fun with Transformation:
The Maths behind the P-V rivalry!
• f = f(x,y) df = p dx + q dy
• X = f(x,q) = f – qy ;
• Y = f(p,y) = f – px;
• Z = f(p,q) = f – px –qy
• df = p dx + q dy
• dX = p dx – y dq
• dY = – x dp + q dy ;
• dZ = -x dp- y dq
• From 1st & 2nd laws
• dU = T dS – P dV
• d f = p dx + q dy
f = U; x=S, y=V, p=T, q=-P
therefore
f = U(S,V); dU = T dS – P dV
• X = U – (-P)V
• = U + PV
• Y = U – TS
• Z = U-TS-(-P)V = H – TS;
dH = T dS –Vd(-P)
=TdS+VdP
dA = -SdT – PdV
dG = VdP - SdT

 Joule and Joule-Thomson: On the same
footings
4. Effective Learning: Concept map
rather than concepts only
 Understanding conventions, assumptions
and approximations
Pattern
 Fun with Transformation: The Maths behind
the P-V rivalry!
7. Learning: An Interactive,
Joyful experience
 Playing through Quiz, SCQ,
and MCQ.
Please participate

A few Interesting References
The Journal of Chemical Education (JCE) Articles
1. Teaching and Learning Problem Solving in Science, 58,51-55, 1981
2. Teaching Thermodynamics of Ideal Solutions: An Entropy Based Approach,
91, 74-83, 2014
3. Two Kinds of Conceptual Problems in Chemistry Teaching, 84, 172-174,
2007
4. The Chemical Adventures of Sherlock Holmes, 77, 471-474, 2000
5. Making Chemistry Learning More Meaningful, 69, 464-467, 1992
6. Introductory Students, Conceptual Understanding, and Algorithmic
Success, 75, 809-810, 1998
7. Logic, History, and the Chemistry Textbook, 75, 679-687, 1998
8. Conceptual Questions and Challenge Problems, 75, 1502-1503, 1998
9. Conceiving of Concept Maps to Foster Meaningful Learning, 81, 1303-
1308, 2004
10. Teaching Thermodynamics and Kinetics Using P-V Diagrams, 91, 74-83,
2014

A few more …
1. What The Best College Teachers Do, Ken Bain, Hervard University Press.
2. 53 Interesting Things To Do In Your Lectures, A. Haynes, K. Haynes, P&H,
UK.
3. Learning How to Learn, Joseph D. Novak, Cambridge University Press.
1. From Learning To Understanding: A Journey Explored Through Dialogues:
Conversation with Sanjib Bagchi, Subir Bhattacharyya and Rana Sen;
Communique, 6, No.1, 29-36, 2012
2. Value Creating Education: A Philosophical Inspiration, Communique, 10,
No.1, 35-42, 2017
3. Meaningful Learning in Science Classes: A Value Creating Inspiration,
International Conference on Soka Education, August 9-11, 2018, DePaul
University, Chicago, USA.

SKILL ENHANCEMENT COURSES SEC-A [SEMESTER 3]
SEC 1 – Mathematics and Statistics for Chemists (Credits: 2 Lectures: 30)
1.Functions, limits, derivative, physical significance, basic rules of differentiation,
maxima and minima, applications in chemistry, Error function, Gamma function, exact
and inexact differential, Taylor and McLaurin series, Fourier series and Fourier
Transform, Laplace transform, partial differentiation, rules of integration, definite and
indefinite integrals. (08 Lectures)
2.Differential equations: Separation of variables, homogeneous, exact, linear equations,
equations of second order, series solution method. (04 Lectures)
3. Probability : Permutations, combinations and theory of probability (03 Lectures)
4.Vectors, matrices and determinants: Vectors, dot, cross and triple products,
introduction to matrix algebra, addition and multiplication of matrices, inverse, adjoint
and transpose of matrices, unit and diagonal matrices. (04 Lectures )
5. Qualitative and quantitative aspects of analysis: Sampling, evaluation of analytical data,
errors, accuracy and precision, methods of their expression, normal law of distribution if
indeterminate errors, statistical test of data; F, Q and t test, rejection of data, and confidence
intervals. (03 Lectures)
6. Analysis and Presentation of Data: Descriptive statistics. Choosing and using
statistical tests. Chemometrics. Analysis of variance (ANOVA), Correlation and
regression, fitting of linear equations, simple linear cases, weighted linear case, analysis
of residuals, general polynomial fitting, linearizing transformations, exponential
function fit. Basic aspects of multiple linear regression analysis. (08 Lectures)

CEMA-CC-5-11-TH : (Credits: Theory-04, Practicals-02) PHYS CHEM – 4; Sem-5
Quantum Chemistri-II
Setting up of Schrödinger equation for many-electron atoms (He, Li)Need for
approximation methods. Statement of variation theorem and application to simple
systems(particle-ina-box, harmonic oscillator, hydrogen atom).
LCAO :Born-Oppenheimer approximation. Covalent bonding, valence bond and
molecular orbital approaches, LCAO-MO treatment of H2+; Bonding and antibonding
orbitals; Qualitative extension to H2; Comparison of LCAO-MO and VB treatments of
H2 and their limitations.( only wavefunctions, detailed solutionnot required) and their
limitations.
Numerical Analysis (10 Lectures)
Roots of Equation:Numerical methods for finding the roots of equations: Quadratic
Formula, Iterative Methods (e.g., Newton Raphson Method).
Least-Squares Fitting.Numerical Differentiation.Numerical Integration( Trapezoidal
and Simpson's Rule)
CEMA-CC-5-11-P
Computer programs(Using FORTRAN or C or C ++) based on numerical methods :
Programming 1: Roots of equations: (e.g. volume of van der Waals gas and
comparison with ideal gas, pH of a weak acid)
Programming 2: Numerical differentiation (e.g., change in pressure for small change
in volume of a van der Waals gas, Potentiometric titrations)
Programming 3: Numerical integration (e.g. entropy/ enthalpy change from heat
capacity data), probability distributions (gas kinetic theory) and mean values

DSE-A-2: APPLICATIONS OF COMPUTERS IN CHEMISTRY (Credits: Theory-04, Practicals-02)
Theory: 60 Lectures
• Computer Programming Basics (FORTRAN): (Lectures: 20)
Elements of FORTRAN Language. FORTRAN Keywords and commands, Logical and
Relational Operators, iteration, Array variables, Matrix addition and multiplication. Function and
Subroutine.
• Introduction to Spreadsheet Software(MS Excel): (Lectures 25)
Creating a Spreadsheet, entering and formatting information, basic functions and
formulae, creating charts, tables and graphs. Incorporating tables and graphs into word
processing documents, simple calculations.
Solution of simultaneous equations(for eg: in chemical Equilibrium problems) using Excel
SOLVER Functions. Use of Excel Goal Seek function.
Numerical Modelling : Simulation of pH metric titration curves, Excel functions
LINEST and Least Squares. Numerical Curve Fitting, Regression, Numerical Differentiation and
Integration
 Statistical Analysis: (Lectures: 15)
Gaussian Distribution and Errors in Measurement and their effect on data sets.
Descriptive Statistics using Excel, Statistical Significance Testing, the T test and the F
test.

PRACTICALS DSE-A-2: APPLICATIONS OF COMPUTERS IN CHEMISTRY (45 Lectures)
( At least 10 experiments are to be performed.)
1. Plotting of Graphs using a spreadsheet. ( Planck's Distribution Law, Maxwell
Boltzmann Distribution Curves as a function of temperature and molecular weight)
2. Determination of vapour pressure from Van der Waals Equation of State.
3. Determination of rate constant from Concentration-time data using LINEST function.
4. Determination of Molar Extinction Coefficient from Absorbent's data using
LINEST function.
5. Determination of concentration simultaneously using Excel SOLVER Function.(For
eg: Determination of [OH-], [Mg2+] and [H3O+] from Ksp and Kw data of Mg(OH)2.)
6. Simultaneous Solution of Chemical Equilibrium Problems to determine the
equilibrium compositions from the Equilibrium Constant data at a given Pressure and
Temperature.
7. Determination of Molar Enthalpy of Vaporization using Linear and Non Linear Least
squares fit.
8. Calculation and Plotting of a Precipitation Titration Curve with MS Excel.
9. Acid-Base Titration Curve using Excel Goal Seek Function.
10. Plotting of First and Second Derivative Curve for pH metric and Potentiometric
titrations .
11. Use of spreadsheet to solve the 1D Schrodinger Equation(Numerov Method).
12. Michaelis-Menten Kinetics for Enzyme Catalysis using Linear and Non - Linear
Regression

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