Chapter 1 Review of Laws of Thermodynamics

AE 2031 APPLIED THERMODYNAMICS S. Y. B. Tech.
REVIEW OF LAWS OF
THERMODYNAMICS
Prof. Aniket Suryawanshi
Asst. Prof. Automobile Engg. Dept.
R. I. T. Rajaramnagar

OUTLINE OF CHAPTER
Basic concepts of thermodynamics
Laws of thermodynamics
Equation of state for ideal gases and real gases
Thermodynamic relations (Gibbs function and Helmholtz
function)
Thermodynamic relations (Maxwell’s relations)
First law applied to non flow process or closed systems.
Application of first law to steady flow processes.

Thermodynamics = Therme + Dynamics
(Heat energy) (Power or Motion)
WHAT IS THERMODYNAMICS?
 It is a science of energy that concerned with the ways in which energy is
stored within a body.
 Energy transformations – mostly involve heat and work movements.
 Interaction between energy and matter. e.g. Gas stove, Electric iron,
Fans, Cooler, Refrigerator, Pressure cooker and T.V.
 Thermodynamics plays important role in design of automobile engines,
Compressors, Turbines, Refrigerators, Rockets, Solar collectors, Nuclear
power plants and Energy- Efficient Home.

TEMPERATURE :-
- No EXACT Definition.
- Broad Definition : “Degree of Hotness / Cold”
- This definition is based on our physiological sensation.
- Hence, may be misleading.
- e.g. Metallic chair may feel cold than Wooden chair; even at SAME temperature.
- Properties of materials change with temperature.
- We can make use of this phenomenon to deduce EXACT level of temperature.
TEMPERATURE

1. Celsius Scale ( ºC ) – SI System
2. Fahrenheit Scale ( ºF ) – English System
3. Kelvin Scale ( K ) – SI System
4. Rankine Scale ( R ) – English System
Celsius Scale and Fahrenheit Scale – Based on 2 easily reproducible fixed states,
viz. Freezing and Boiling points of water.
i.e. Ice Point and Steam Point
Thermodynamic Temperature Scale – Independent of properties of any substance.
- In conjunction with Second Law of Thermodynamics
Thermodynamic Temperature Scale – Kelvin Scale and Rankine Scale.
TEMPERATURE

Hot End
Regenerator
Pulse Tube
T ( K ) = T ( ºC ) + 273.15
T ( R ) = T ( ºF ) + 459.67
T ( ºF ) = 1.8 T ( ºC ) + 32
T ( R ) = 1.8 T ( K )
-273.15 0
273.160.01
0-459.67
491.6932.02
ºC K ºF R
Conversion Factors :
TEMPERATURE

Definition : Normal Force exerted by a fluid per unit Area.
SI Units :
1 Pa = 1 N/m2
1 kPa = 103 Pa
1 MPa = 106 Pa = 103 kPa
1 bar = 105 Pa = 0.1 MPa = 100 kPa
1 atm = 101325 Pa = 101.325 kPa = 1.01325 bar
1 kgf/cm2 = 9.81 N/m2 = 9.81 X 104 N/m2 = 0.981 bar = 0.9679 atm
English Units :
psi = Pound per square inch ( lbf/in2)
1 atm = 14.696 psi
1 kgf/cm2 = 14.223 psi
PRESSURE

Absolute Pressure : Actual Pressure at a given position.
Measured relative to absolute vacuum i.e. absolute zero pressure.
Pressure Gauges are generally designed to indicate ZERO at local atmospheric pressure.
Hence, the difference is known as Gauge Pressure.
i.e. P (gauge) = P (abs) – P (atm)
Pressure less than local atmospheric pressure is known
as Vacuum Pressure.
i.e. P (vacuum) = P (atm) – P (abs)
PRESSURE

Local Atmospheric Pressure
( 1.01325 bar @ Sea Level )
Absolute Zero Pressure
P (gauge)
P (abs) P (atm)P (vacuum)
P (gauge) P1 = P (abs) – P (atm)
P (vacuum) P2 = P (atm) – P (abs)
PRESSURE
P (Absolute) above atmosphere
P 1
P (Absolute) below atmosphere
P 2

SYSTEM
SURROUNDINGS
BOUNDARY
SYSTEM :
Quantity of matter or region in space,
chosen for study.
SURROUNDINGS :
Mass or region outside the SYSTEM.
BOUNDARY :
Real / Imaginary surface that separates the
SYSTEM from SURROUNDINGS.
BOUNDARY :
Fixed / Movable
Shared by both,
SYSTEM and SURROUNDINGS
No Thickness
No Mass / Volume
SYSTEM, SURROUNDINGS AND BOUNDARY

TYPE OF SYSTEM (BASED ON MASS & ENERGY)
OPEN
System
Mass YES
Energy YES
Also known as CONTROL VOLUME
e.g. Water Heater, Car Radiator, Turbine, Compressor, Boiler and Nozzle
BOUNDARY of OPEN System is known as
CONTROL SURFACE
In Out
Imaginary Boundary
Real Boundary
OPEN SYSTEM:-
m = const.
E = const.

CLOSED SYSTEM:-
CLOSED
System
m = const.
Mass NO
Energy YES
GAS
2 kg
1 m3
GAS
2 kg
3 m3
CLOSED System
with Moving Boundary
Also known as CONTROL MASS
e.g. Pressure cooker, Refrigerator and Ice Cream-Freezer, Steam Power Plant and
Electrolytic Battery
E = const.

ISOLATED SYSTEM:-
ISOLATED
System
m = const.
E = const.
Mass NO
Energy NO
e.g. Thermos flask and Ice box.

ADIABATIC SYSTEM:-
ADIABATIC
System
m = const.
Q = const.
E = const.
Mass YES
Energy YES
e.g. Insulated turbines, Insulated heat exchangers.
Heat NO

TYPE OF SYSTEM (BASED ON PHASES)
 Homogeneous system consist of a single physical phase.
 It is treated as one constituent for its analysis (solid, liquid or gas).
 e.g. Ice, Water and steam, Sugar or salt dissolved in water, Air, Oxygen
gas and Nitrogen gas.
HOMOGENEOUS SYSTEM:-
HETEROGENEOUS SYSTEM:-
 Heterogeneous system is mixture of two or more than two phases of
matter.
 Each constituent present in the system has its own properties. System
cannot be analysed as a single constituent.
 e.g. Mixture of Ice and Water, Mixture of Water and steam, Rice and
water in pressure cooker (after cooked).

Any relevant characteristic of a System ≡ PROPERTY.
Intensive : Independent on mass of system.
- e.g. Pressure (p), Temperature (T), Density (), Velocity (v).
Extensive : Dependent on mass of system.
- e.g. Mass (m), Area (A), Volume (V), Internal Energy (U),
Enthalpy (H), etc.
System
φ, any Property
φ1 φ2
≡
PROPERTIES OF A SYSTEM
If φ = φ1 + φ2
→ Extensive
e.g. MASS
If φ = φ1 = φ2
→ Intensive
e.g. TEMPERATURE

TYPES OF PROPERTIES OF A SYSTEM
SPECIFIC PROPERTIES:-
The ratio of any extensive property of a system to that
of the mass of the system is called an average specific value of that property
(also known as intensives property)
Specific : Extensive properties per unit mass.
- e.g. Sp. Vol (v=V/m), Sp. Enthalpy (h=H/m), etc.

STATE OF A SYSTEM
→ “Situation the system exists in”.
Operational Definition :
1. Make list of all relevant characteristics of the SYSTEM.
e.g. Vol., m, Pr, Temp, …..
2. Quantify each characteristic.
e.g. Gas in the LPG cylinder in kitchen.
→ m
Vol
Pr
Temp
(14.6 kg)
(50 m3)
(18 bar)
(27 ºC)
Set of properties to completely describe the condition of the system ≡ STATE.
m = 2 kg
T1 = 25 ºC
V1 = 3 m3
STATE A
STATE:-

Series of intermediate STATES through which SYSTEM passes during the PROCESS ≡
PATH.
STATE, PATH AND PROCESS
PATH:-
Property A
State 1
State 2
PropertyB
Path State 1State 2

Property A
State 1
State 2
PropertyB
PROCESS A
PROCESS B
Since, All Intermediate Points
have Thermodynamic Equillibrium.
PROCESS A and PROCESS B
are DISTINCT processes.
STATE, PATH AND PROCESS
Transformation of thermodynamics system from one state to another state ≡ PROCESS.
PROCESS:-

t=0t=t1
t=0t=t2
t2 < t1
Quasi-Static
Non-Quasi-Static
Process proceeds in such a manner that
system remains infinitesimally close to
equilibrium conditions at all times.
It is known as QUASI-STATIC or
QUASI-EQUILIBRIUM Process.
PATH AND PROCESS
A QUASI-STATIC process is one that occurs slowly enough that a uniform
temperature and pressure exist throughout all regions of the system at all
times.

All Intermediate STATES
are in Thermodynamic Equilibrium.
→ QUASI – STATIC PROCESS.
→ Shown with CONTINUOUS LOCUS.
Property A
State 1
State 2
PropertyB
PROCESS A
PROCESS B
QUASI- STATIC PROCESS
State 1 State 2
Pressure
Quasi-Static
Process Path
Volume

All Intermediate STATES
not in Thermodynamic Equilibrium.
→ NON QUASI – STATIC PROCESS.
→ Shown with DASHED LOCUS.
Property A
State 1
State 2
PropertyB
Path
NON QUASI- STATIC PROCESS
State 1 State 2
Pressure
Volume
Non-Quasi-Static
Process Path

Property A
State 1
State 2
PropertyB
PROCESS A
PROCESS B
Characteristics:-
1) Must passes through same states on the
reversed path.
2) This process when undone will leave no
history of events in the surroundings.
3) Must pass through a continuous series of
equilibrium states.
REVERSIBLE PROCESS
One which can be stopped at any stage and reversed so that system and
surroundings are exactly restored to its initial state.
REVERSIBLE PROCESS (IDEAL):-
NOTE ≡ No real process is truly reversible but some processes may approach
reversibility, to close approximation.

REVERSIBLE PROCESS (IDEAL):-
Nearly close to reversible processes are:
1) Expansion and Compression of spring.
2) Frictionless adiabatic expansion or compression of fluid.
3) Polytropic expansion or compression of fluid.
4) Isothermal expansion or compression
5) Electrolysis.
REVERSIBLE PROCESS
Process that can be reversed without leaving any trace on the Surroundings.
i.e. Both, System and Surroundings are returned to their initial states at the end of the
Process.
This is only possible when net Heat and net Work Exchange between the system and the
surroundings is ZERO for the Process.

IRREVERSIBLE PROCESS (NATURAL):-
Irreversible processes are:
1) Relative motion with friction.
2) Combustion.
3) Diffusion.
4) Free expansion.
5) Throttling.
6) Electricity flow through a resistance.
7) Heat transfer
8) Plastic deformation.
Property A
State 1
State 2
PropertyB
Path
One in which heat is transferred through a finite temperature.
IRREVERSIBLE PROCESS

Most of the Processes in nature are IRREVERSIBLE.
i.e. Having taken place, they can not reverse themselves spontaneously and restore the
System to its original State.
e.g. Hot cup of coffee Cools down when exposed to
Surroundings.
But, Warm up by gaining heat from Surroundings.
i.e. w/o external Heat supply.
IRREVERSIBLE PROCESS (NATURAL):-
IRREVERSIBLE PROCESS

Why REVERSIBLE Process ?
1. Easy to analyze, as System passes through series of Equilibriums.
2. Serve as Idealized Model for actual Processes to be compared for analysis.
3. Viewed as Theoretical Limit for corresponding irreversible one.
Reversible Process leads to the definition of Second Law Efficiency; which is Degree
of Approximation (Closeness) to the corresponding Reversible Process.
( )Better the Design, ( )Lower the Irreversibilities; ( ) Second Law Efficiency.
REVERSIBLE PROCESS

A system is said to have undergone a cycle if it returns to its ORIGINAL
state at the end of the process.
Property A
State 1 = State 2
PropertyB
Hence, for a CYCLE, the
INITIAL and the FINAL states
are identical.
In other words, it should form a
“LOOP” in STATE SPACE.
CYCLE
CYCLE:-

Thermal Equilibrium: - The temperature of the system does not change with time and has
same value at all points of the system.
Mechanical Equilibrium: - There are no unbalanced forces within the system or between
the surroundings. The pressure in the system is same at all points and does not change
with respect to time.
Chemical Equilibrium:- No chemical reaction takes place in the system and the chemical
composition which is same throughout the system does not vary with time.
NOTE: The above three types of equilibrium states must be achieved is called
thermodynamics equilibrium.
THERMODYNAMIC EQUILIBRIUM

Thermal Equilibrium :
- NO Temperature Gradient throughout the system. (T=Uniform)
Mechanical Equilibrium :
- NO Pressure Gradient throughout the system. (ΣF = 0)
Phase Equilibrium :
- System having more than 1 phase.
- Mass of each phase is in equilibrium.
Chemical Equilibrium :
- Chemical composition is constant
- NO reaction occurs.
STATE in EQUILIBRIUM
≡ Can be represented by a point in Thermodynamic State Space.
Unique values of Properties.
THERMODYNAMIC EQUILIBRIUM

STATEMENT :
If two bodies are in Thermal Equilibrium with the third body, then they are also in
Thermal Equilibrium with each other.
This statement seems to be very simple.
However, this can not be directly concluded from the other Laws of Thermodynamics.
It serves as the basis of validity of TEMPERATURE measurement.
A
25 ºC 25 ºC 25 ºC
B
C
ZEROTH LAW OF THERMODYNAMICS

By replacing the Third Body with a Thermometer; the Zeroth Law can be stated as :
Two bodies are in Thermal Equilibrium, if both have same TEMPERATURE,
regarding even if they are not in contact with each other.
A
25 ºC 25 ºC
25 ºC
B
i.e. Temp (A) measured by Thermometer and is known.
(A) is in Thermal Equilibrium with (B).
Then, Temp (B) is also known, even not in contact with Thermometer.

Thermal Equilibrium : NO change w.r.t. Temperature
NO Temperature Gradient.
HOT cup of tea / coffee cools off w.r.t. time.
COLD Drink warms up w.r.t. time.
When a body is brought in contact with another body at different temperature, heat
is transferred from the body at higher temperature to that with lower one; till both
attain a THERMAL EQUILIBRIUM.
THERMAL EQUILIBRIUM

- Formulated and labeled by R.H. Fowler in 1931.
- However, its significance is realized after half a century after formation of First and
Second Laws of Thermodynamics.
- Hence named as Zeroth Law of Thermodynamics.

ENERGY
Types of energy in thermodynamics analysis:
1) Stored Energy:
A. Macroscopic forms of energy (K.E. & P.E.)
B. Microscopic forms of energy (I.E.)
2) Transit Energy
A. Heat Energy
B. Work transfer

Thermodynamic Interactions ≡ Energy in TRANSIT.
≡ Between 2 SYSTEMS.
Energy Transfer / Exchange : SYSTEM A & SYSTEM B
May be SURROUNDING …!!
≡ Change of STATE of System A : Change of STATE of System B.
≡ Interaction → Change of STATE
Q – W = ∆E ≡ Ist Law of Thermodynamics
(dQ / T) ≤ ∆s ≡ IInd Law of Thermodynamics
ENERGY

CLOSED
System
Heat
Work
Energy can cross the Boundary of the System in 2 forms : 1. Heat
2. Work
Heat is a form of Energy transferred between 2 Systems
( or a System and the surroundings ) by virtue of
Temperature Difference (∆T).
i.e. Heat is Energy in TRANSITION.
Process involving no Heat Exchange is known as
ADIABATIC Process.
Atmosphere 25ºC
25 ºC
15 ºC
Heat, QQ=0
Adiabatic
HEAT AND WORK

Possibilities of Adiabatic Process :
1. Perfect Insulation : Negligible Energy transfer through Boundary.
2. Both System and Surrounding at same temperature.
No Energy transfer due to absence of driving force (∆T).
NOTE : Adiabatic Process ≠ Isothermal Process
No Heat Transfer Energy content & temperature of the system can
be changed with help of Work.
HEAT AND WORK

Sign Convention :
Heat Transfer TO a System : + ve
Heat Transfer FROM a System : - ve
Work done BY a System : + ve
Work done ON a System : - ve
SYSTEM
SURROUNDINGS
QoutW
QinW
NOTE : In Chemical Engineering,
EAXCTLY Reverse Convention
is followed….!!
SIGN CONVENTION FOR HEAT AND WORK

dLFdW 
dVP
dxAPdW


 ddW 
dq
dtidW




of the form :
dYXdW  + Sign Convention
X and Y may / may NOT be PROPERTIES of the SYSTEM.
X and Y may be INTENSIVE / EXTENSIVE Properties .
Sometimes, BOTH Properties, sometimes BOTH NOT…!!!
Generally,
X ≡ INTENSIVE Property
Y ≡ EXTENSIVE Property
FORMS OF WORK TRANSFER
DIFFERENT MODES OF WORK TRANSFER

L
dL
dLFdW 
P
State 1State 2
dx
dVP
dxAPdW


MECHANCAL WORK:- MOVING BOUNDARY WORK:-

dθ
τ
 ddW 
Plane Stirrer ≡ NO WORK done
NOTE : τ and θ are NOT
Properties of System.
dq
dtidW




NOTE : ε and q are NOT
Properties of System.
PADDLE WHEEL WORK
OR STIRRING WORK:- ELECTRIC WORK:-

Sp. Work = Work per unit Mass
w = W/m ( J/kg )
Power = Work per unit Time
P = W/time ( J/sec OR W )
Sign Convention :
Heat Transfer TO a System : + ve
Heat Transfer FROM a System : - ve
Work done BY a System : + ve
Work done ON a System : - ve
SYSTEM
SURROUNDINGS
Qin
Qout
Win
Win
SIGN CONVENTION FOR HEAT AND WORK

Similarities between HEAT & WORK :
1. Both are recognized at the Boundary of the System, as they cross the
Boundary. Hence both are Boundary Phenomena.
2. System possesses Energy, but neither Heat nor Work. Hence both are
transient Phenomena.
3. Both are associated with Process, not State. Heat and Work have NO meaning
at a State.
4. Both are Path Functions and inexact differentials. It is denoted by Q and W.
HEAT AND WORK

Dissimilarities between HEAT & WORK :
1. Heat is low grade energy, whereas Work is high grade energy.
2. Heat transfer takes place due to temperature difference only, while work
transfer may takes place due to potential difference in pressure, voltage,
height, temperature etc.
3. In a stationary system there cannot be work transfer, however there is no
restrictions for the heat transfer.
4. Entire quantity of work can be converted into heat or any form of energy
(with single process), while conversion of entire quantity of heat into work is
not possible (without cyclic processes).
HEAT AND WORK

Let the Piston be moving from
Thermodynamic Equilibrium State 1 (P1, V1)
to State 2 (P2, V2).
Let the values at any intermediate
Equilibrium State is given by P and V.
State 2State 1
P1 V1
P2 V2
Area A
For an Infinitesimal displacement, dL, the Infinitesimal Work done is;
Similarly, for Process 1 – 2; we can say that;

2
1
21
V
V
PdVW
Volume
Pressure
Quasi-Static
Process Path
P1
P2
V1 V2
dW = F * dL = P*A*dL = PdV
PdV WORK

Path Functions have Inexact Differentials, designated by symbol δ.
Thus, a differential amount of Heat or Work is represented as δQ or δW; in stead of
dQ or dW.
Properties, on the other hand, are Point Functions, and have Exact Differentials,
designated by symbol d.
PATH FUNCTION AND POINT FUNCTION
Path Function : Magnitude depends on the Path followed during the Process, as
well as the End States.
Point Function : Magnitude depends on State only, and not on how the System
approaches that State.

e.g. Small change in Volume, is represented as dV, and is given by;
VVVdV  12
2
1
Thus, Volume change during Process 1 – 2 is always =
(Volume at State 2) minus (Volume at State 1).
Regardless of path followed.
Volume
State 1
State 2
Pressure
V1 V2
HOWEVER, total Work done during Process 1 – 2 is;
)(12
2
1
WNOTWdW 
i.e. Total Work is obtained by following the Process
Path and adding the differential amounts of Wok (δW)
done along it.
Integral of δW is ≠ ( W2 – W1 ).
PATH FUNCTION AND POINT FUNCTION

Also known as Law of Conservation of Energy
Important due to its ability to provide a sound basis to study between different
forms of Energy and their interactions.
STATEMENT :
Energy can neither be created nor
destroyed during a process; but can be only
converted from one form to another.
m g Δz = ½ m ( v1
2 - v2
2 )
PE = 7 kJ
KE = 3 kJ
m = 2 kg PE = 10 kJ
KE = 0
Δz
FIRST LAW OF THERMODYNAMICS

This forms the basis for Heat Balance / Energy Balance.
Net change ( increase / decrease ) in the total Energy of the System during a Process
= Difference between Total Energy entering and Total Energy leaving the System
during that Process.
Total Energy
entering the System
Total Energy
leaving the System
= Change in Total Energy
of the System
( EIN ) ( EOUT ) ( ΔE )
_
FIRST LAW OF THERMODYNAMICS

Different materials require different amount of Energy for their temperatures to
increase thought unit quantity ( i.e. 1 ºC) for identical mass.
1 kg
Fe
20 – 30 ºC
4.5 kJ
1 kg
H2O
20 – 30 ºC
41.8 kJ
Hence, it is required to define a
Property to compare the ENERGY
STORAGE CAPACITY of different
substances.
This Property is known as SPECIFIC
HEAT.
SPECIFIC HEAT

Specific Heat at Constant Pressure (CP) :
The Energy required to raise the temperature of a unit mass of a substance by 1 degree,
as the Pressure is maintained CONSTANT.
Specific Heat at Constant Volume (CV) :
The Energy required to raise the temperature of a unit mass of a substance by 1 degree,
as the Volume is maintained CONSTANT.
m = 1 kg
∆T = 1 ºC
Sp. Heat = 5 kJ/kg ºC
5 kJ
DEFINITION :
The Energy required to raise the temperature of a
unit mass of a substance by 1 degree.
SPECIFIC HEAT

V = Const
m = 1 kg
∆T = 1 ºC
3.12 kJ
CV = 3.12 kJ/kg.ºC CV = 5.19 kJ/kg.ºC
P = Const
m = 1 kg
∆T = 1 ºC
5.19 kJ
He Gas
CP is always greater than CV; as the
System is allowed to expand in case of
Const. Pr. and the Energy for this
expansion Work is also need to be
supplied.
SPECIFIC HEAT

Hence, CV is change in Internal Energy of a
substance per unit change in temperature at
constant Volume.
Consider a System with fixed mass and undergoing Const. Vol. Process (expansion /
compression).
First Law of Thermodynamics → ein – eout = ∆esystem
Since it is a Const. mass System;
Net amount of Change of Energy = Change in Internal Energy (u).
i.e. δein – δeout = du
V
V
V
T
u
C
dTCdu









 …by Definition of CV
Hence, CP is change in Enthalpy of a
substance per unit change in temperature at
constant Pressure.
P
P
P
T
h
C
dTCdh









 …by Definition of CP
SPECIFIC HEAT

h = u + Pv ….by Definition of Enthalpy
But, Pv = RT ….by Ideal Gas Law
Thus, h = u + RT
dh = du + R dT
CP dT = CV dT + R dT ….by Definition of CP and CV
CP = CV + R (kJ/kg.K)
Specific Heat Ratio, k ( or γ ) is given by;
k ( or γ ) =
V
P
C
C
SPECIFIC HEATS AND IDEAL GASES

In a closed system energy may be transferred
across the boundary in the form of work
energy and heat energy but the working fluid
itself never crosses the boundary
Any process undergone by a closed system is
referred to as a non-flow process.
NON-FLOW PROCESSES AND CLOSED SYSTEM
CLOSED
SYSTEM
Heat
Work

When the fluid in a closed system is undergoing a non flow process from State 1 to
State 2, the internal energy of a fluid depends on pressure and temperature.
• U2 the internal energy of the fluid at State 2.
• U1 the internal energy of the fluid at State 1.
• Q12 the net heat energy transferred to the system from the surrounding.
• W12 the net work energy transferred from the system to the surrounding.
U2 - U1 = Q12 –W12
 
2
1
2
1
WQ12 UU
NON-FLOW ENERGY EQUATION
The non-flow energy equation:

ISOBARIC ISOMETRIC/ ISOCHORIC
ADIABATIC
ΔT ≠ 0 BUT Q = 0
ISOTHERMAL
ΔT = 0 BUT Q ≠ 0
CYCLIC
IF CLOCKWISE – HEAT ENGINE
IF COUNTERCLOCKWISE – HEAT PUMP
NON-FLOW PROCESSES

Some thermodynamic cycle composes of processes in which the working fluid
undergoes a series of state changes such that the final and initial states are identical.
For such system the change in internal energy of the working fluid is zero.
The first law for a closed system operating in a thermodynamic cycle becomes
CLOSED SYSTEM FIRST LAW OF A CYCLE
cyclenetnet UWQ 
netnet WQ 

PdV Work in Different Quasi-Static Processes (Isobaric) :
)( 1221
2
1
VVPPdVW
V
V
 
Pressure(P)
Volume (V)
P=Const
Isobaric
W1-2
State 1 State 2
V2V1
PdV WORK

Pressure(P)
V=Const
Isochoric
Volume (V)
State 1
State 2P2
P1
0
2
1
21  
V
V
PdVW
PdV Work in Different Quasi-Static Processes (Isochoric) :
PdV WORK

2
1
11
1
2
111121
11
11
21
lnln
2
1
2
1
P
P
VP
V
V
VP
V
dV
VPW
V
VP
PCVPPV
PdVW
V
V
V
V







PdV Work in Different Quasi-Static Processes (Isothermal) :
Pressure
PV= C
Isothermal
Volume
State 1
State 2
P2
P1
V1 V2
PdV WORK

 











































nn
nnnn
nn
n
V
V
n
n
V
V
n
n
V
V
n
n
nnn
P
P
n
VP
n
VPVP
n
VXVPVXVP
VV
n
VP
n
V
VP
V
dV
VPW
PdVW
V
VP
PCVPVPPV
/1
1
2112211
1
111
1
2221
1
1
2
11
1
111121
21
11
2211
1
11
11
1
2
1
2
1
2
1
PdV Work in Different Quasi-Static Processes (Polytropic) :
Pressure
PVn = C
Volume
1
2
P2
P1
n =1
n =3 n =2
n =∞
PdV WORK

Process Index Heat added
Change in
Internal energy
Change in
Enthalpy
Change in
Entropy
Constant
Pressure
n=0 = Cp(T2-T1) = P(V2-V1) = m Cv(T2-T1) = m Cp(T2-T1) = m Cp ln(T2/T1)
Constant
Volume
n=
= Cv(T2-T1) = 0 = m Cv(T2-T1) = m Cp(T2-T1) = m Cv ln(T2/T1)
Constant
Temperature n=1
= P1V1 ln(V2/V1)
= P1V1 ln(P1/P2)
= mRT ln(V2/V1)
= mRT ln(P1/P2)
= P1V1 ln(V2/V1)
= P1V1 ln(P1/P2)
= mRT ln(V2/V1)
= mRT ln(P1/P2)
= 0 = 0
= mR ln(V2/V1)
= mR ln(P1/P2)
Reversible
Adiabatic
n=γ = 0
= (P1V1-P2V2)/ γ-1
= (P2V2-P1V1)/ 1-γ
= mR (T2-T1)/ 1-γ
= m Cv(T2-T1) = m Cp(T2-T1)
Polytropic n=n
= Cn(T2-T1)
= (γ-n/γ-1)* Poly. W.T.
= (γ-n/n-1)*Adia. W.T.
= (P1V1-P2V2 )/ n-1
= (P2V2-P1V1)/ 1-n
= mR (T2-T1)/ 1-n
= m Cv(T2-T1) = m Cp(T2-T1) = m Cn ln(T2/T1)
NON-FLOW PROCESSES

2
1
V
V
21 PdVW

f
i T
dQ
S
Cn= Cv(γ-n/1-n) Cn=(Cp -nCv)/(1-n)

CONTROL
VOLUME
Heat
Work
Mass in
Mass out
P1, V1, A1, V1
P2, V2, A2, V2
In an open system, in addition to energy transfers taking place across the
boundary, the fluid may also cross the boundary.
Any process undergone by an open system is called a flow process.
FLOW PROCESS AND CONTROL VOLUME
Ein – Eout = ∆Esystem

In steady flow, the mass flow rate of fluid is the same across any section in
the system
Consider m1 kg/s of fluid flowing through a system in which all conditions
are steady (i.e. under steady flow conditions)
system
Q W
m1
m1
system
Q W
m1
m1
Instant: t0 Instant: t0+dt
CONTINUITY OF MASS EQUATION
  outin mm

TOTAL ENERGY OF FLOWING FLUID
The total energy carried by a unit of mass as it crosses the control surface is the sum of
the internal energy + flow work + potential energy + kinetic energy
















gz
v
henergy
gz
v
PVuenergy
2
2
2
2
The first law for a control volume can be written as
















  in
in
in
in
inout
out
out
out
outnetnet gz
v
hmgz
v
hmWQ
22
22

TOTAL ENERGY OF FLOWING FLUID
The steady state, steady flow conservation of mass and first law of thermodynamics
can be expressed in the following forms







 



1000
)(
2000
12
2
1
2
2
12
zzgvv
uuwq netnet







 



1000
)(
2000
12
2
1
2
2
12
zzgvv
uumWQ netnet







 



1000
)(
2000
12
2
1
2
2
12
... zzgvv
uumWQ netnet
(kJ/kg)
(kJ)
(kW)

STEADY FLOW PROCESS ENGINEERING DEVICES

FLOW THROUGH NOZZLE AND DIFFUSER
Commonly utilized in jet engines, rockets, space-craft and even garden hoses.
Q = 0 (heat transfer from the fluid to surroundings very small
W = 0 and ΔPE = 0
Nozzle: - device that increases the velocity fluid at the
expense of pressure.
Diffuser: - device that increases pressure of a fluid by
slowing it down.

Energy balance (Nozzle & Diffuser):-
FLOW THROUGH NOZZLE AND DIFFUSER
















  out
out
out
out
outoutoutin
in
in
in
ininin gz
v
hmWQgz
v
hmWQ
22
22

















22
22
out
outout
in
inin
v
hm
v
hm

















22
22
out
out
in
in
v
h
v
h

FLOW THROUGH TURBINE AND COMPRESSOR
Turbine:– a work producing device through the
expansion of a fluid.
Q = 0 (well insulated), ΔPE = 0, ΔKE = 0
(very small compare to ΔH).
   outoutoutinin hmWhm
...

















  out
out
out
out
outoutoutin
in
in
in
ininin gz
v
hmWQgz
v
hmWQ
22
22
 outinout hhmW 
..
Energy balance (Turbine):-

Compressor (as well as pump and fan): - device
used to increase pressure of a fluid and involves
work input.
FLOW THROUGH TURBINE AND COMPRESSOR
Q = 0 (well insulated), ΔPE = 0, ΔKE = 0
(very small compare to ΔH).
















  out
out
out
out
outoutoutin
in
in
in
ininin gz
v
hmWQgz
v
hmWQ
22
22
 inoutin hhmW 
..
   outoutininin hmhmW
...

Energy balance (Compressor, Pump & Fan):-

FLOW THROUGH THROTTLING VALVE
Throttling valve:-Flow-restricting devices
that cause a significant pressure drop in the
fluid.
Some familiar examples are ordinary
adjustable valves and capillary tubes.

FLOW THROUGH MIXING CHAMBER
Mixing Chamber:-The section where the mixing
process takes place.
An ordinary T-elbow or a Y-elbow in a shower,
for example, serves as the mixing chamber for
the cold- and hot-water streams.

     3
.
32
.
21
.
1 hmhmhm 
FLOW THROUGH MIXING CHAMBER
     3
.
32
.
1
.
31
.
1 hmhmmhm 






   23
.
321
.
1 hhmhhm 
 
 21
23
.
3
.
1
hh
hh
mm



Energy Balance (Mixing Chamber) :-

FLOW THROUGH HEAT EXCHANGER
Heat Exchanger:- Devices where two moving
fluid streams exchange heat without mixing.
Heat exchangers typically involve no work
interactions (w = 0) and negligible kinetic
and potential energy changes for each fluid
stream.

Heating of a room by Electric heater; by passing Electric
Current through the Resistor.
Electric Energy supplied to the heater =
Energy transferred to the Surroundings ( room air ).
Here, First Law of Thermodynamics is satisfied.
HOWEVER, converse is NOT true.
Transferring Heat to the wire ≠
Equivalent amount of Electric Energy generated in wire.
Still, First Law of Thermodynamics is satisfied !
Heat
I
LIMITATIONS OF FIRST LAW OF THERMODYNAMICS

Paddle Wheel mechanism operated by falling mass.
Paddle wheel rotates as mass falls down and stirs the
fluid inside the container.
Decrease in Potential Energy of the mass =
Increase in Internal Energy of the fluid.
Here, First Law of Thermodynamics is satisfied.
HOWEVER, converse is NOT true.
Transferring Heat to the Paddle Wheel ≠
Raising the mass.
Still, First Law of Thermodynamics is satisfied !
Heat
LIMITATIONS OF FIRST LAW OF THERMODYNAMICS

From these day – to – day life examples, it can be clearly seen that;
Satisfying the First Law of Thermodynamics does not ensure for a Process to occur
actually.
Processes proceed in certain direction; but may not in Reverse direction.
First Law of Thermodynamics has no restriction on the DIRECTION of a Process to
occur.
This inadequacy of the First Law of Thermodynamics; to predict whether the Process
can occur is solved by introduction of the Second Law of Thermodynamics.
SECOND LAW OF THERMODYNAMICS

SIGNIFICANCE :
1. Second Law of Thermodynamics is not just limited to identify the direction of
the Process.
2. It also asserts that Energy has quantity as well as Quality.
3. It helps to determine the Degree of Degradation of Energy during the Process.
4. It is also used to determine the Theoretical Limits for the performance of the
commonly used engineering systems, such as Heat Engines and Refrigerators.

Thermal Energy Reservoir :
Hypothetical body with relatively very large Thermal Energy Capacity
( mass x Sp. Heat ) that can supply or absorb finite amount of Heat
without undergoing change in Temperature.
e.g. ocean, lake, atmosphere, two-phase system, industrial furnace, etc.
Reservoir that supplies Energy in form of Heat is known as SOURCE.
Source
Heat
Reservoir that absorbs Energy in form of Heat is known as SINK.
Sink
Heat

Water
Work
Heat
Water
No Work
Heat
From such examples, it can be concluded that,
1. Work can be converted to Heat.
2. BUT, Converting Heat to Work requires special devices.
These devices are known as Heat Engines.

Characteristics of Heat Engines :
1. They receive the Heat from High-Temp Reservoir ( i.e. Source )
(e.g. Solar Energy, Oil Furnace, Nuclear Reactor, etc.).
2. They convert part of this Heat to Work
( Usually in form of rotating shaft ).
3. They reject the remaining Heat to Low-Temp Reservoir ( i.e. Sink )
(e.g. Atmosphere, River, etc.)
4. They operate on a CYCLE.
Heat Engines are generally Work – Producing devices,
e.g. Gas Turbines, I.C. Engines, Steam Power Plants, etc.

HEAT ENGINE :
High Temp
Source
Low Temp
Sink
Qin
Qout
Heat Engine Wnet

Turbine
Boiler
Condenser
Pump
Win Wout
SOURCE
(Furnace)
SINK
(Atm. Air)
Qin
Qout
STEAM POWER PLANT :
Can Qout be eliminated ?
ANS : NO.
Without a Heat Rejection
Process, the Cycle can not
be completed.

Turbine
Boiler
Condenser
Pump
Win Wout
SOURCE
(Furnace)
SINK
(Atm. Air)
Qin
Qout
Net Work Output =
Worknet,out = Wout - Win
Each component is an OPEN SYSTEM
However, as a complete set of
components, no mass flows in / out of
the system
Hence, it can be treated as a
CLOSED SYSTEM ∆U = 0
Thus,
Worknet,out = Qout - Qin

Turbine
Boiler
Condenser
Pump
Win Wout
SOURCE
(Furnace)
SINK
(Atm. Air)
Qin
Qout
Part of Heat output that is
converted to net Work output, is
a measure of performance of the
Heat Engine; and is known as
the THERMAL EFFICIENCY
of the Heat Engine.
Thermal Efficiency =
Net Work Output
Total Heat Input
in
out
in
outnet
th
Q
Q
Q
W
 1,


Turbine
Boiler
Condenser
Pump
Win Wout
SOURCE
(Furnace)
SINK
(Atm. Air)
Qin
Qout
QH = Magnitude of Heat Transfer
between cyclic device and
Source at temperature TH
QL = Magnitude of Heat Transfer
between cyclic device and
Sink at temperature TL
Worknet,out = QH - QL
H
L
H
outnet
th
Q
Q
Q
W
 1,


Heat Engine must give away some heat to the Low Temperature Reservoir
( i.e. Sink ) to complete the Cycle.
Thus, a Heat Engine must exchange Heat with at least TWO Reservoirs for
continuous operation.
This forms the basis for the Kelvin – Planck expression of the Second Law of
Thermodynamics.

Kelvin – Planck Statement :
It is impossible for any device that operates on a Cycle to receive Heat
from a single Reservoir and produce net amount of Work.
Alternatively;
No Heat Engine can have a thermal
efficiency of 100 per cent.
Thermal Energy
Reservoir
Wnet =
100 kW
QH =
100 kW
QL = 0
Heat
Engine

REFRIGERATOR / HEAT PUMP :
Compressor
Condenser
Evaporator
Expansion
Valve
Wnet, in
Surrounding Air
Refrigerated Space
QH
QL
Heat is always transferred from High
Temperature to Low Temperature region.
The reverse Process can not
occur on itself.
Transfer of Heat from
Low Temperature region to High
Temperature one requires special devices,
known as REFRIGERATORS.

REFRIGERATOR / HEAT PUMP :
High Temp
Source
Low Temp
Sink
QH
QL
Refrigerator
Wnet, in

Compressor
Condenser
Evaporator
Expansion
Valve
Wnet, in
Surrounding Air
Refrigerated Space
QH
QL
Efficiency of a Refrigerator is expressed in
terms of Coefficient of Performance (COP)R.
innet
L
R
W
Q
Inputquired
OutputDesired
COP
,Re

First Law of Thermodynamics gives;
Worknet,in = QH - QL
1
1









L
HLH
L
R
Q
QQQ
Q
COP
Thus, COPR can be > 1

Compressor
Condenser
Evaporator
Expansion
Valve
Wnet, in
Surrounding Air
Refrigerated Space
QH
QL
innet
H
HP
W
Q
Inputquired
OutputDesired
COP
,Re










H
LLH
H
HP
Q
QQQ
Q
COP
1
1
For a Heat Pump, COP is expressed as
(COP)HP.
Thus;
COPHP = COPR + 1

Clausius Statement :
It is impossible to construct a device that
operates in a Cycle, and produces no effect
other than the transfer of Heat from a
Lower Temperature Body to a Higher
Temperature body.
Alternatively;
No Refrigerator can operate unless its
compressor is supplied with external
Power source.
Warm
Environment
Wnet = 0
QH =
5 kJ
QL = 5 kJ
Refrigerator
Refrigerated
Space

TH
Wnet =
QH
QH
QL = 0
Heat
Engine
Refrigerator
TL
QL
Q H + QL
=
TH
Wnet = 0
TL
DEVICE
QL
QL
This Proves that;
Violation of Kelvin – Planck Statement results in violation of Clausius Statement.
Converse is also True.
EQUIVALENCE OF CLAUSIUS AND KELVIN-PLANCK STATEMENTS

THIRD LAW OF THERMODYNAMICS
STATEMENT :
• As a system approaches absolute zero, all processes cease and the
entropy of the system approaches a minimum value. OR It is not
possible to lower the temperature of any system to absolute zero in
a finite number of steps.
– decreasing entropy of a system requires increasing the entropy of
surroundings
If the entropy of each element in some (perfect) crystalline state be taken as
zero at the absolute zero of temperature, every substance has a finite positive
entropy; but at the absolute zero of temperature the entropy may become
zero, and does so become in the case of perfect crystalline substances.

f
i T
dQ
S

THIRD LAW OF THERMODYNAMICS
• In simple terms, the Third Law states that the entropy of most pure substances approaches
zero as the absolute temperature approaches zero. This law provides an absolute reference
point for the determination of entropy. The entropy determined relative to this point is the
absolute entropy.
• Another application of the third law is with respect to the magnetic moments of a material.
Paramagnetic materials (moments random) will order as T approaches 0 K. They may order in
a ferromagnetic sense, with all moments parallel to each other, or they may order in an
antiferromagnetic sense, with all neighboring pairs of moments antiparallel to each other. (A
third possibility is spin glass, where there is residual entropy.)

Thank You !

Chapter 1 Review of Laws of Thermodynamics

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Chapter 1 Review of Laws of Thermodynamics