CY1001: Introduction to

Thermodynamics

Arti Dua
Department of Chemistry
IIT Madras
 Course material and general instructions
for this part…

• Reference Book: P. W Atkins

• Soft copies of my slides: will be uploaded in Moodle a day before my lecture.

• External Source: MIT lecture notes

https://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/lecture-
notes/
 Thermodynamics: Introduction

• The science of thermodynamics introduces a new

concept of temperature, which is absent from
classical mechanics and the theory of electricity and
magnetism.

• It describes macroscopic properties of

equilibrium system.
 What is a thermodynamic system?
• A thermodynamic system is a system of large number
A typical thermodynamic system of particles N at equilibrium. Typically,

N ⇡ 1023
• These particles can be atoms/molecules. However, their
identity, in terms of their microscopic properties
like position and velocity of individual particles, does not
matter in a thermodynamic description.

• A thermodynamic system is described in terms of

macroscopic variables like (N,V, E) or (N, p, E) or
(N,V, T) etc.

Surroundings • These macroscopic variables are called natural

variables of a thermodynamic system. The latter is
broadly classified as isolated, closed or open.

• The natural variables are independent of each other.

System + Surroundings = Universe The thermodynamic properties of a given system can,
thus, be described by changing one variable while
keeping other constant.
 Types of Thermodynamic Systems
Isolated System
System Natural Variables

Isolated System:
Energy
Insulted from the surroundings (N,V, E) or (N,p, E)
Or has no surroundings
Closed System (Universe is an isolated system)

Closed System:

Energy Exchanges energy E with the

surroundings until the temperature (N,V,T) or (N,p,T)
of the system and surroundings is
Surroundings the same temperature (thermal
equilibrium)
Open System

Open System:
Energy
Exchanges E and N with the (µ, V, T ) or (µ, p, T )
surroundings until the temperature
and chemical potential of the system
Surroundings and surroundings is the same

From the fundamental equation, we will find a thermodynamic function which

depends on these natural variables
 Thermodynamics: Introduction

• Thermodynamics provides relationship

between physical properties once certain
measurements are made.
dG = dH - TdS

• One can only know the change in the

thermodynamic quantities (dS, dU, dH, dA,dG)
and not their absolute value (S, U, H, A, G)

• Statistical thermodynamics enable us to

calculate the magnitudes of these properties.
 Thermodynamics: Introduction

Thermodynamics started as a result of attempts to improve the efficiencies of

steam engines.

Heat Work

The thermodynamic mode of reasoning is applicable to many

different systems from the production of low temperature devices
to information theory.
• Describing thermodynamic system requires:
• A few macroscopic properties: P, V, T, n...

• Knowledge if system is homogeneous or heterogeneous.

• Knowledge if system is in equilibrium state

• Knowledge of the number of components.

• Two classes of properties:

• Extensive: depends on the size/mass of the system (mass, no. of
moles, volume, entropy, energy, heat)

• Intensive: independent of the size/mass of the system

(temperature, pressure, chemical potential, density,…)
 Thermodynamics: Introduction

• It is based on four laws:

• Zeroth law defines temperature (T).
• First law defines energy (U).
• Second law defines entropy (S).
• Third Law gives numerical value to entropy.
Zeroth law of thermodynamics
 Zeroth law of thermodynamics

• It introduces a new property temperature,

which is a state function.

• State function is defined solely by

instantaneous state and is independent of
previous history (or path taken to reach that
state).
 State Function (mathematically)
If T(x, y) is a state function, which depends on two independent variables x and y, such
that the function and their derivatives are continuous and single valued then
✓ ◆ ✓ ◆
@T @T
dT (x, y) = dx + dy
@x y @y x

Total derivative
Partial derivatives

@ 2 T (x, y) @ 2 T (x, y) Follows from Green’s

= Theorem
@x@y @y@x
State functions are exact
differentials
Temperature, Pressure and Volume are state functions.
 State Function

Reversible path
For change in state from 1 2
Z T2
Irreversible path
dT = T = (T2 T1 )
T1

T1 T2 • Only depends on initial and final states.

• Is independent of which path is followed to reach these states

For cyclic change in state

I
dT = 0 Cyclic integral

For cyclic processes: T1 = T2

 Inexact differentials are path functions

@ 2 F (x, y) @ 2 F (x, y)
6=
@y@x @x@y

Work and heat are path functions. They depend on how the
thermodynamic system changes from the initial to final state
I Z
dw 6= 0 dw 6= w
I Z = w
dq 6= 0 dq 6= q
=q
Path Functions
 Work (mechanical)

Pex
force displacement

convention

work done on the system is positive and work done by the system is negative
 Reversible vs. Irreversible Processes

p
p

Irreversible Process: Reversible Process:

External pressure is applied fast such that External pressure is applied extremely slowly
such that

pext 6= p pext = p

p is the internal pressure of the gas

 Reversible Work
dw = Pext dV
Z Vf Z Vf
For a reversible
w= Pext dV process
Pext = p w= pdV
Vi Vi
For an ideal gas (n = 1 mole)

Z Vf
p is the internal pressure RT
For an ideal gas p = nRT/V w= dV
Vi V
Z Vf
w= RT d ln V
Vi

Vf
w= RT ln
Vi
 Reversible Work

Vf
w= RT ln
Vi

Work of Expansion
V f > Vi Done by the system (ideal
gas) (Negative)

V i > Vf Work of Compression

Done on the system (ideal
gas) (Positive)
 Compression
Irreversible Work
Pf > Pi dw = Pext dV
V f < Vi
p is the internal pressure

Expansion
Pext 6= p For an ideal gas p = nRT/V

Reduce pressure: work of expansion

Z Vi
Work of Expansion
w= Pi dV Done by the system (ideal
Vf gas) (Negative)
Pext = Pi
w= Pi (Vi Vf ) = Pi V

Apply pressure: work of compression

Z Vf
Work of Compression
w= Pf dV Done on the system (ideal
Pext = Pf Vi
gas) (Positive)

w= Pf (Vf Vi ) = Pf V
 % %
% =(1)M (x, y)dx + N (x, y)dy (1)
= M (x, y)dx + N (x, y)dy
!"#$%&'()*%&)+,&*-(&./#0*&1)2& !"#$%&'()*%&)+,&*-(&./#0*&1)2&
⇧ ⇧ ⇤
Compression ⌅ &
⇤M (x, y) Irreversible Expansion W
⇤N (x, y) work
=& F.l (2)
,&&&&&&
y)dy] =
2 # . "!& & W = F.l !&&!"#$3&
dxdy = 0 &&&&&& 2
(6) # . "
(2) ! &
S
⇥ ⇤y ⇥ ⇤x &
P > Pi & F⇤T= P A ⇥
45/(,&6"#7(&f & ⇤T,/0*)+7(
& &&&⇥
)445/(,&6"#7(& & F =,/0*)+7(
(3)
Pext A & (3)
ext ⇤T
dT = dx + ! dy & ⇤T !
Vf <
⇤M (x, ⇤x Vyi
y) ⇤N dT
(x, =
y)
⇤y x dx + dy
pext
% ⇤= ⇤x & ⇤y (7) pext
%
y
l = Pext ⇥V piston x W = (P A)l = Pext ⇥V (4)
&2"#$& = ⇤yM (x, y)dx
W =+⇤x
N
(P (x, y)dy
A)l 894)+0/"+&2"#$&(1) (4) ext
ext
= M (x,py)dx
ext
% %
+ &N (x, y)dy A (1) pext
% %

& ⇤ 2 FExpansion
(x, y) P ⇤=2PF (x, y) . # 4(9* : & Pext = Pf , Vf , T Pi , Vi , T (5)
⇤=
ext f , Vf , T Pi , Vi , T Expansion by (8) (5)
& ⇤y⇤xW = F.dl ⇤x⇤y &
reducing Pext(2)to Pi
& $ 4(9* : % ! # & 4(9* '; &
W =⇧ F.l 2 # & $ 4(9* : % ! # & 4⇧(9*⇧';⇤ & (2) ⌅
⇧ ⇧ ⇤ ⌅ ⇤M (x, y) ⇤N (x, y)
& ⇧ ⇤M (x, y) [M
⇤N (x,
(x, y)dx
y) + N& (x, y)dy] = dxdy = 0 (6)
[M (x, y)dx +F N (x, y)dy] = dxdy =(3) ⇤y
0 ')</+=&)&>?>&0/=+&-(#(&/@45/(0&
(6) ⇤x
7"+<(+*/"+3& 2 ( B&&/6&&'; ) B %&*-)*
C S
+3&
C W = = PextPA
')</+=&)&>?>&0/=+&-(#(&/@45/(0&
ext dV S 2 (
⇤yB&&/6&& '
F = Pext A; ) B
⇤x%&*-)*& (9) (3)
/0%&4"0/*/<(&2"#$&@()+0&*-)*&*-(&0A##"A+,/+=0&,"& /0%&4"0/*/<(&2"#$&@()+0&*-)*&*-(&0A##"A+,/+=0&,"&
Z Vi
⇧ ⇤M (x, y) ⇤N (x, y)
2"#$&*"&*-(&0C0*(@D&E6&*-(&0C0*(@&,"(0&2"#$&"+&*-(& 2"#$&*" &*-(&0C0*(@D&E6&*-(&0C0*(@&,"(0&2"#$&"+&*-(
P = nRT/V ⇤
= (7)
W = f dl⇤M (x, y) ⇤= ⇤N (x, y) (10) (7) ⇤y
0A##"A+,/+=0&
⇤x
$ '; ( w = 2 ) B D&&P dV
B % &&*-(+&&
0A##"A+,/+=0& $ '; ( B⇤y% &&*-(+&&
W = 2 )(P D&&
B⇤x A)l = P ⇥V (4)
Wexp = ⇧ Pext (Vi Vf ) ext &
ext (4) ⇤ 2 F (x, y) ⇤ 2 F (x, y) Vf
W = dA
⇤ 2 F (x, V
y) ) ⇤ 2 F (x, y) (11) ⇤= (8)
= P (V
+"*&7"+0*)+*%&*-(+&2(&-)<(&*"&5""$&)*&/+6/+/*(0/@)5&7-)+=(0&
i i f ⇤= E6& 4 (9* &/0&+"*&7"+0*)+*%&*-(+&2(&-)<(&*"&5""$&)*&/+6/+/*(0/@)5&7-)+=(0
(5) ⇤y⇤x
(8) ⇤x⇤y
⇧ ⇤y⇤x ⇤x⇤y
Pext = P & (5)
& ⇧
?& @()+0&*-/0&/0&+"*&)+&(9)7*&,/66(#(+*/)5& ?&
,&2 # & 4(9* ?&
,; & W & =,& @()+0&*-/0&/0&+"*&)+&(9)7*&,/66(#(+*/)5&
& 4 ,; W &
(9* & =,& ⇥dq ⇧ (12) P dV ext (9)
Area shown in blue color & ⇧ Area shown in blue & brown colors
W =
represents work of irreversible P ext dV (9) represents work of reversible
W F = P
=#)5& 2 # &*G 4(9*expansion
⇧ comp ext (V f ⇧ V ) ⇧ ⇧ ⇤
,; & ,(4(+,0&"+&*-(&4)*-HHH& ⇤M (x, y)
i (6)
E+*(=#)5& 2 # 4
W⌅&* F=(9* ,;f &
dl,(4(+,0&"+&*-(&4)*-HHH&
expansion
(10)
W = f=dl
⇤N (x, y) G
(10) dxdy⇧ = 0 (6)
& C
[M (x, y)dx
= +PNf
(x,
(V f
y)dy]
V ) & (7)
⇧i S ⇤x W 2=&&
⇤y!&&I)*-&,(4(+,(+7(&"6& dA (11)
4(+,(+7(&"6&2&& The magnitude of work of expansion in an irreversible
W =
0, the magnitude of work will
dA
have &
maximium value.
(11)
W =
⇧
⇥dq (12)
⇧
process is less than the reversible one
= ⇤M
)00A@(&)&#(<(#0/J5(&4#"7(00&0"&*-)*&
⇧ VW
(x, y)
4(9*&K&4&& ⇤=
⇥dq ⇤N89)@45(3
(x, y) &)00A@(&)&#(<(#0/J5(&4#"7(00&0"&*-)*&
(12) (7) 4(9*&K&4&&
i ⇤y &
⇤x
Wexp = P dV (8):#&L=%&4G%&;GM& K& :#&L=%&4F%&;FM& &
:#&L=%&4 %&; M&G K&
G :#&L=%&4 %&; M& &
F F
 Reversible and Irreversible transformation
l
Expansion A

Compression

Cyclic Transformation

Irreversible

Reversible
 Reversible processes

• Reversible processes are not real processes, but ideal ones.

• Reversible processes are important because the work

associated with them represent maximum or minimum
values.
done on the system
done by the system
(work of compression)
(work of expansion)

• In reality we always get less work than what we get in

reversible processes, but we must not expect to get
more...
I
dw 6= 0
I Path Functions

dq 6= 0

The sum is a State Function

Identify the sum of (infinitesimal change) in heat
and work as internal energy change dU (State
IFunction)
dU = 0

For infinitesimal change: 1

On integrating Eq. 1 on both sides:

For finite change:

On carrying out Cyclic Integration of Eq. 1 on both sides:

For cyclic process: