Addis Ababa University

Faculty of Technology and Built Environment

School of Mechanical and Industrial Engineering

Chapter Two
Lecture 4
Energy Transport By Heat, Work, and Mass

Prepared By:- Desta Lemma

Thermal & Energy
Conversion Stream

Engineering Thermodynamics -I SMiE, AAiT-AAU 1

 Energy of a System
▪ Energy can be viewed as the ability to cause change.

▪ Energy can exist in numerous forms, such as

✓ Thermal, ✓ Electric,

✓ Mechanical, ✓ Magnetic,

✓ Chemical, and
✓ Kinetic,
✓ Nuclear
✓ Potential,

▪ Their sum constitutes the total energy E of a system

▪ In thermodynamic analysis, energy can be grouped into two forms:

1. Microscopic forms of energy

2. Macroscopic forms of energy

Engineering Thermodynamics -I SMiE, AAiT-AAU 2

 Energy of a System
▪ Microscopic forms of energy are those related to the molecular
structure of a system and the degree of molecular activity, and
they are independent of outside reference frames.

Engineering Thermodynamics -I SMiE, AAiT-AAU 3

 Energy of a System
▪ The sum of all the microscopic forms of energy is called the
internal energy of a system and is denoted by U.
Example:
✓ Latent energy – related to the phase change of a substance.
✓ Chemical energy – related to chemical bond b/w atoms or molecules.
✓ Nuclear energy – related to nuclei of the atoms (protons and neutrons).
✓ Sensible energy - related to the temperature change of a substance without
phase change.

Engineering Thermodynamics -I SMiE, AAiT-AAU 4

 Energy of a System
▪ Macroscopic forms of energy are those that a system possesses as a
whole with respect to some outside reference frame, such as kinetic
and potential energies.

Engineering Thermodynamics -I SMiE, AAiT-AAU 5

 Energy of a System
▪ The energy that a system possesses as a result of its motion relative to some
reference frame is called kinetic energy (KE) and is expressed as

V2 V2
KE = m (kJ ) ke = (kJ / kg )
2 2

▪ The energy that a system possesses as a result of its elevation in a gravitational

field is called potential energy (PE) and is expressed as

PE = mgz (kJ ) pe = gz (kJ / kg )

▪ The total energy of a system consists of the kinetic, potential, and internal
energies and is expressed as

Engineering Thermodynamics -I SMiE, AAiT-AAU 6

 Energy of a System
V2
E = U + KE + PE E =U + m + mgz
2

e = u + ke + pe V2
e=u+ + gz
2
▪ Most closed systems remain stationary during a process and thus experience no
change in their kinetic and potential energies.
▪ Closed systems whose velocity and elevation of the center of gravity remain
constant during a process are frequently referred to as stationary systems.
▪ The change in the total energy E of a stationary system is identical to the
change in its internal energy U.
∆𝐸 = ∆𝑈

Engineering Thermodynamics -I SMiE, AAiT-AAU 7

 Energy transport by heat and work
▪ Energy can cross the boundary of a closed system in two distinct forms: heat and work.

Engineering Thermodynamics -I SMiE, AAiT-AAU 8

 Energy transport by heat
▪ Heat is defined as the form of energy that is transferred between two systems (or a
system and its surroundings) by virtue of a temperature difference.

▪ A process during which there is no heat transfer is called an adiabatic process.

▪ There are two ways a process can be adiabatic:

1. Well insulated

2. Both the system and the surroundings are at the same temperature

Engineering Thermodynamics -I SMiE, AAiT-AAU 9

 Energy transport by heat
▪ As a form of energy, heat has energy units, kJ

▪ The amount of heat transferred during the process between two states (states 1 and 2)
is denoted by Q12, or just Q

▪ Sometimes it is desirable to know the rate of heat transfer (the amount of heat
transferred per unit time) 𝑄ሶ

▪ Heat is transferred by three mechanisms:

1. Conduction – needs physical contact and a solid medium.

2. Convection – needs a fluid medium for heat transfer.

3. Radiation – requires no medium, occurs through electromagnetic waves.

▪ Heat transfer per unit mass of a system is denoted q and is determined from
Q
q= (kJ / kg )
m

Engineering Thermodynamics -I SMiE, AAiT-AAU 10

 Energy transport by work
▪ Work is also a form of energy transferred, like heat, and has energy units kJ.

▪ The work done during a process between states 1 and 2 is denoted by W12, or simply W.

▪ The work done per unit time is called power and is denoted by .
The unit of power is kJ/s, or kW.

▪ The work done per unit mass of a system is denoted by w and is expressed as
W (kJ / kg )
w=
m Example:
A rising piston
A rotating shaft

Engineering Thermodynamics -I SMiE, AAiT-AAU 11

 Sign convention for energy transported by heat and work
▪ Heat and work are directional quantities.

▪ Their complete description requires the specification of both the magnitude and
direction.

Engineering Thermodynamics -I SMiE, AAiT-AAU 12

 Sign convention for energy transported by heat and work
▪ The generally accepted formal sign convention for heat and work
interactions is as follows:
✓ Heat transfer to a system and work done by a system are positive;
✓ Heat transfer from a system and work done on a system are negative

work done by the work done on the

system (positive) system (negative)

Engineering Thermodynamics -I SMiE, AAiT-AAU 13

 More on heat and work
▪ Both are recognized at the boundaries of a system as they cross
the boundaries.
▪ Systems possess energy, but not heat or work.
▪ Both are associated with a process, not a state.
▪ Both are path functions, i.e., their magnitudes depend on the
path followed during a process as well as the end states.

Engineering Thermodynamics -I SMiE, AAiT-AAU 14

 Boundary work
▪ The work associated with a moving boundary is called boundary
work.
▪ The expansion and compression work is often called boundary
work.

Engineering Thermodynamics -I SMiE, AAiT-AAU 15

 Boundary work
2
Wb =   Wb
1

𝐹
𝛿𝑊𝑏 = 𝐹𝑑𝑠 = 𝐴𝑑𝑠 = 𝑃𝑑𝑉
𝐴

2
Wb =  PdV
1

2 2
𝐴𝑟𝑒𝑎 = 𝐴 = න 𝑑𝐴 = න 𝑃𝑑𝑉
1 1

Engineering Thermodynamics -I SMiE, AAiT-AAU 16

 Boundary work at some typical processes
▪ Boundary work at a constant volume process

If the volume is held constant,

=0
And the boundary work equation
becomes
2
Wb =  PdV = 0
1

Engineering Thermodynamics -I SMiE, AAiT-AAU 17

 Boundary work at some typical processes
▪ Boundary work at a constant pressure process

If the pressure is held constant, the boundary work equation becomes

2 2
𝑊𝑏 = න 𝑃𝑑𝑉 = 𝑃 න 𝑑𝑉 = 𝑃(𝑉2 − 𝑉1 )
1 1

Engineering Thermodynamics -I SMiE, AAiT-AAU 18

 Boundary work at some typical processes
▪ Boundary work at a constant temperature (isothermal process)
mRT
P=
V
2 2
𝑚𝑅𝑇
𝑊𝑏 = න 𝑃𝑑𝑉 = න 𝑑𝑉
1 1 𝑉

mRT = C = PV
2 dv
Wb = C 
1 V
V2
Wb = Cln
V1
If the temperature of an ideal gas system is held constant, 𝑉2 𝑉2
then the equation of state provides the pressure-volume 𝑊𝑏 = 𝑚𝑅𝑇𝑙𝑛 = 𝑃1 𝑉1 ln
𝑉1 𝑉1
relation.

Engineering Thermodynamics -I SMiE, AAiT-AAU 19

 Boundary work at some typical processes
▪ Boundary work at Polytropic Process
✓ During actual expansion and compression processes of gases,
pressure and volume are often related by PVn = C., where n and C
are constants
2
Wb =  PdV
1

𝟐 −𝒏+𝟏 −𝒏+𝟏
𝑽𝟐 − 𝑽𝟏 𝑷𝟐 𝑽𝟐 − 𝑷𝟏 𝑽𝟏
𝑾𝒃 = න 𝑪𝑽−𝒏 𝒅𝑽 = 𝑪 =
𝟏 −𝒏 + 𝟏 𝟏−𝒏

mR(T2 − T1 )
Wb = For ideal gases
1− n

Engineering Thermodynamics -I SMiE, AAiT-AAU 20

 Boundary work at some typical processes
▪ For the special case of n = 1, the system is an isothermal process, and
the boundary work becomes
2 2
𝑉2
𝑊𝑏 = න 𝑃𝑑𝑉 = න 𝐶𝑉 −𝑛 𝑑𝑉 = 𝑃𝑉 𝑙𝑛
1 1 𝑉1

Engineering Thermodynamics -I SMiE, AAiT-AAU 21

 Other than Compression and expansion
Shaft Work
▪ A force F acting through a moment arm r generates a torque T

T= F r

𝑊𝑏 = F ∙ S

Engineering Thermodynamics -I SMiE, AAiT-AAU 22

 Energy transferred by Mass
▪ When mass enters a control volume, the energy of the control volume
increases because the entering mass carries some energy with it.
▪ When some mass leaves the control volume, the energy contained
within the control volume decreases because some of the mass leaving
takes out some energy with it.

Engineering Thermodynamics -I SMiE, AAiT-AAU 23