Engineering Thermodynamics I

Bachelor of Engineering

BME I/II and BAS I/II

2. Energy and Energy Transfer

1
Energy
Energy can be defined as the capacity of a system to exert (provide)
force for a certain interval.

Energy is the capacity to do work.

Different forms of energies are classified into two groups / types in

thermodynamics: stored energy and transient energy.

Stored Energy Transient Energy

The stored energy is the energy Energy which can cross the
possessed by a system within its boundary of the system
boundaries. during a thermodynamic
Energy which remains within the process is called transient
system boundary as inherent energy.
property of the system is called
stored energy.
Engineering Thermodynamics I 2
 Stored Energy Transient Energy
Internal energy, potential Work transfer, heat
energy and kinetic energy transfer, electrical energy
are examples of stored are examples of transient
energy. energy.

Stored energies have unique Transient energy are path

value for each equilibrium function and are not
state (i.e., they are state thermodynamic properties.
function) and independent of
path and hence are
thermodynamic properties.

Engineering Thermodynamics I 3
Stored Energy
Internal Energy (U)
Internal energy is the energy of the system due to its
molecular arrangement and motion of the molecules.
It can also be defined as the summation of molecular
potential energy and molecular kinetic energy.
It is represented by U and its unit is J.
It is due to the microscopic phenomena, so is function of
temperature only.
Internal energy of ideal gas depends on temperature of the
gas only.
It is given by the relation;

𝑑𝑈 = 𝑚𝑐𝑣 𝑑𝑇

Engineering Thermodynamics I 4
Stored Energy
Potential Energy (PE)
It is the energy contained by the system by virtue of its
position with respect to certain reference level.
PE = 𝑚gz

Kinetic Energy (KE)

It is the energy of the system due to its motion.

1
𝐾𝐸 = 𝑚𝑉ത 2
2

Engineering Thermodynamics I 5
Total Energy
Total energy of a system is defined as the summation of its internal
energy, potential energy and kinetic energy.

1 2
𝑒 = 𝑢 + 𝑔𝑧 + 𝑉ത
2
Enthalpy
The expression U+PV occurs so frequently in thermodynamics that it
has been given a special name and symbol; enthalpy and H.

Hence, enthalpy is defined as the summation of internal energy and

the product of pressure and volume.

Engineering Thermodynamics I 6
Heat Transfer
Transfer of energy, without transfer of mass, because of temperature
difference between the system and the surroundings is called heat
transfer.
Heat transfer is denoted by Q and expressed in J.
❖ Heat is transient energy.
❖ Heat is boundary phenomena.
❖ Heat is path function and hence inexact differentials.
❖ Heat is not the property of the system.
In thermodynamics, heat transferred (supplied) to the system is taken
as positive heat transfer and heat transferred (lost) from the system is
taken as negative heat transfer.
Sign Convention
Heat flow into a system is taken as positive.
Heat flow out of a system is taken as negative.

Engineering Thermodynamics I 7
Work Transfer
According to mechanics; work is defined as the product of a force
and the distance travelled in the direction of force.
Work = Force x distance travelled
= F x d [1 Nm = 1 J)
In thermodynamics;
Work is the interaction between system and surrounding.
Work transfer is the transfer of energy, without transfer of mass,
because of any property difference other than temperature that exists
between system and surroundings.
Work transfer is denoted by W and expressed in J.
Common property differences that can produce work transfer are
pressure, gravitational potential, electrical potential etc.

In thermodynamics, work done by the system is taken as positive

work transfer and work done on the system is taken as negative work
transfer.
Engineering Thermodynamics I 8
 Comparison Between Heat and Work
Similarities
i. Heat and work are both transient energy. The system
never posses heat or work.

ii. Heat and work are boundary phenomena.

iii. Heat and work both are path functions and hence
inexact differentials.

iv. Heat and work are not the thermodynamic properties of

the system.

Engineering Thermodynamics I 9
 Comparison Between Heat and Work
Differences
i. Heat is energy exchange between system and
surroundings due to temperature difference whereas work
is energy exchange between system and surroundings due
to intensive property difference other than temperature.

ii. Work is high grade form of energy, but heat is low grade
form of energy.

iii. Heat can be transferred or exchanged with or without

displacement of boundary but displacement work cannot be
transferred without displacement of boundary.

Engineering Thermodynamics I 10
 Comparison Between Heat and Work
Differences
iv. Heat flow into the system is taken as positive but work
done on the system is taken as negative and heat flow out
of the system is taken as negative but work done by the
system is taken as positive.

v. Work always produces some heat itself without any

device but the self conversion of heat to work (without any
device) cannot occur.

Engineering Thermodynamics I 11
Expression for Displacement Work Transfer
Consider a piston cylinder device containing a gas. During process 1-
2, piston is displaced by 𝑑𝑠ҧ from state 1 to state 2. Applying
mechanical definition, work transfer is evaluated as

Final position
ds
A Initial position
of piston
P
Boundary System
(Gas) Cylinder

Heat Input

𝛿𝑊 = 𝐹 𝑑𝑠ҧ
2
∴ W = ‫׬‬1 𝛿𝑊

where F is the force provided by the gas pressure, i.e., F = PA

Engineering Thermodynamics I 12
Expression for Displacement Work Transfer
Substituting F into above equation, we get
The above equation shows that the work
transferred during any process can be
determined by evaluating area covered by
the process on P- V diagram.

Engineering Thermodynamics I 13
Displacement Work Transfer for a Isochoric Process
A thermodynamic process during which the volume of a closed system
remains constant. E.g., heating of gas in a rigid container.
𝑉
Rigid Boundary
∴ W = ‫ 𝑉׬‬2 𝑃 𝑑𝑉 = 0, As, 𝑉1 = 𝑉2
1

System
(gas)

T
P
T2 2

Isochoric P2 2
Process

T1 1
P1 1

V1 = V2 V
T
T1 T2

Engineering Thermodynamics I 14
Displacement Work Transfer for a Isobaric Process
A thermodynamic process in which the pressure remains constant.
E.g., expansion or compression of a gas inside a cylinder with freely
moving frictionless piston. P
W1−2
Piston Isobaric
Process
P1 = P2 1 2

Cylinder
System W1−2
(gas)

V
V1 V2
Q P

Isobaric
Process
P1 = P2 1 2

T
T1 T2

Engineering Thermodynamics I 15
Displacement Work Transfer for a Isothermal Process
➢A process during which the W1−2
Piston
temperature remains constant. Weight
➢ It can be realized in a piston
cylinder device which is surrounded Cylinder
System
by a constant temperature reservoir (gas)
or constant temperature bath having Constant temperature
same temperature. Q
reservoir

❖ Pressure volume relationship for an ideal gas

undergoing a constant temperature process
(Boyle’s law) is given as;

Applying the Equation for initial, final and any intermediate states,

Pressure at any intermediate state is given as;

Engineering Thermodynamics I 16
Displacement Work Transfer for a Isothermal Process
Then work transfer is given as; P
1
P1
Isothermal
Process

P2 2
W1−2
W1− 2 = mRT1 ln (V2 V1 ) V
V1 V2
T Isothermal
Process
P
1 2
T1 = T2 1
P1
Isothermal
Process

P2 2

V
V1 V2 T
T1 = T2
Engineering Thermodynamics I 17
Displacement Work Transfer for a Polytropic Process
Thermodynamic process which follows the relation PVn = constant
is called a polytropic process and the index n is a polytropic index.

It is a generalized equation for thermodynamic processes and

represents different processes for different values of n.
Value of index n Equation Process

0 P = Constant Constant pressure or

Isobaric
1 PV = Constant Constant temperature or
Isothermal
γ PVγ = Constant Adiabatic
Constant volume or
∝ V = Constant Isochoric

Engineering Thermodynamics I 18
Pressure-volume relationship for initial, final and any intermediate
state during a polytropic process is given as P
n=  n=
n=1
Pressure at any intermediate state is given as Initial state
Compression
n=0 n=0
Expansion
n=1

Then work transfer is given as n=

n =

mR (T2 − T1 )
W1−2 =
1− n
Engineering Thermodynamics I 19
 Power
Power is defined as a rate of energy transfer. In
thermodynamics, we deal with two modes of energy transfer:
work transfer and heat transfer.
Power due to work transfer also called mechanical power is
defined as the rate of work transfer. Mathematically,

Power due to heat transfer also called thermal power is defined

as the rate of heat transfer. Mathematically,

Power is expressed in J/s or Watt (W).

Engineering Thermodynamics I 20
Modes of Heat Transfer
According to the physical mechanism and the governing law
associated with them, heat transfer is classified into three modes:
conduction, convection and radiation.
Conduction
Heat conduction is the transfer of heat due to the property of matter
which allows the passage for heat energy even its parts are not in
motion relative to one another.
Magnitude of conduction heat transfer is given by Fourier Equation,

Engineering Thermodynamics I 21
Convection
Convection is the transfer of heat in fluid medium and heat is
transferred by the actual movement of the molecules.
Magnitude of convection heat transfer is given by Newton's
law of cooling,

The heat transfer coefficient h depends upon the

thermodynamic and transport properties (e.g. density,
viscosity, specific heat and thermal conductivity of the fluid),
the geometry of the surface, the nature of fluid flow, and the
prevailing thermal conditions. 22
Engineering Thermodynamics I
Nature of Heat Convection
According to the mechanism of fluid flow, convection heat transfer
is classified into two types: free convection and forced convection.
Free convection
Convection heat transfer process in which flow of fluid is caused by
density gradient is called free convection or natural convection.
Example: cooling of a room without a fan by natural circulation of air.
During Natural convection, flow rate of fluid is usually low, so heat
transfer rate is also very low and heat transfer rate cannot be
controlled.
Forced Convection
Convection heat transfer process in which flow of fluid is caused by
some external devices such as pump, fan, blower, etc. is known as
forced convection. Example: cooling of a room by a fan.
Heat transfer rate is relatively higher in forced convection due to
increased mass flow rate of fluid and heat transfer rate can be
controlled.
Engineering Thermodynamics I 23
 Free Convection Forced Convection
1. Flow of fluid is caused by 1. Flow of fluid is caused by
density gradient. some external devices such as
pump, fan, blower etc.
2. Example: Cooling of a 2. Example: Cooling of a room
room without a fan by natural by fan
circulation of air (ventilation)

3. Mass flow rate of fluid is 3. Mass Flow rate of fluid is

usually low. relatively high.
4. Heat transfer takes place at 4. Heat transfer takes place at a
a very low rate. relatively faster rate.

Engineering Thermodynamics I 24
Radiation
Radiation is the heat transfer without any medium in the form of
electromagnetic wave (EMW).
Stefan’s Boltzmann law states the total emissive power (intensity
of radiation) of the perfect black body is directly proportional to the
fourth power of its absolute temperature.
Mathematically,
qb  T 4 where, qb is intensity of radiation heat transfer of black body
T is absolute temperature of black body
qb =  T 4 where,  is Stefan Boltzmann Constant
 = 5.67 10−8W / m 2 K 4

For normal object or body,

q =  T 4 where,  is the emissivity of the object or body

Engineering Thermodynamics I 25
Radiation
From above expressions, we can write;
q (at T, K)
=
qb (at T, K)

Emissivity (ε)
It is the ratio of heat emitted by a surface as compared to that of a
perfect surface under same condition. Its varies with the temperature
of the emitting surface.
Emissivity is the ratio of intensity of radiation of normal object to the
black body at the same temperature.
Its value is same with absorptivity for the same wavelength of
radiation, but may differ for different wavelengths.
The wavelength of the emitted radiation depends on the temperature of
the emitter surface.
For perfect black body, ε = 1
0   1 For perfect white body, ε = 0
Engineering Thermodynamics I 26
Radiation
Magnitude of radiation heat exchange between two practical bodies
at temperatures T1 and T2 is given by Stefan-Boltzmann law,

The amount of heat transferred by conduction and convection largely

depends upon temperature difference rather than temperature level.

But in radiation it is the temperature of the emitting surface that

controls the quality of the energy transmitted.
Radiation is very much a surface phenomenon and will leave the
transmitting surface through a wide wavelength band.
A surface will emit or absorb radiant energy without a temperature
difference, but in order for the energy transfer to occur there must be a
temperature difference between the exchanging surfaces.
Engineering Thermodynamics I 27
Radiation Surface Properties
Surfaces are capable of emitting, absorbing, reflecting or transmitting
radiant energy.
The radiation incident to any surface must be equal to the radiation
reflected, absorbed or transmitted through the surface of the material.

Engineering Thermodynamics I 28
Radiation Surface Properties
If Qi = Total incident radiation to the surface
QR = reflected radiation from the surface
QA = Absorbed radiation by the material
Qτ = transmitted radiation through the material
Then, Absorptivity (α)
QA + QR + Q = Qi It is the ratio of absorbed radiation to the
total incident radiation.
QA QR Q
+ + =1
Qi Qi Qi It is the factor indicating the relative
 +  + = 1 amount of radiation absorbed by a
Where,  - Absorptivity surface compared to an absorbing perfect
black body under same conditions.
 - Reflectivity
 - Transmissivity Its value is dependent upon the
temperature of the source as also that of
receiving surface.
Engineering Thermodynamics I 29
Radiation Surface Properties
Reflectivity (ρ)
It is the ratio of reflected radiation to the total incident radiation.
It is the ratio of the reflected heat to that of the total heat incident on a
surface at a certain mean temperature range.

Transmissivity (τ)
It is the ratio of transmitted radiation to the total incident radiation.
QA + QR + Q = Qi
QA QR Q
+ + =1
Qi Qi Qi
 +  + = 1
Where,  - Absorptivity
 - Reflectivity
 - Transmissivity
Engineering Thermodynamics I 30
Radiation
Black Body
Such body which absorbs all the incident radiation to its surface is
known as black body. Black body is the perfect absorber and perfect
emitter. For black body, α = 1, ρ = τ = 0, ε =1.

White Body
Such body which reflects all the incident radiation to its surface is
known as white body. For white body, ρ = 1, α = τ = 0, ε =0 .

Grey Body
If the radiative properties (α, ρ, τ, ε) of the body are uniform through
out the entire wavelength spectrum of radiation then such body is
known as grey body.
For grey body, 0    1
 +  + = 1
Opaque Body
Engineering Thermodynamics I 31