Post on 24-Feb-2021
transcript
Energy, energy transfer, and general energy analysis
Chapter 3
Md. Mizanur Rahman MEng(Sweden), PhD (Finland), CEng Chartered Energy Engineer (EI, UK) Certified Energy Manager School of Mechanical Engineering Universiti Teknologi Malaysia Email: mizanur@mail.fkm.utm.my
INTRODUCTION
• As a result of the conversion of electric
energy consumed by the device to heat, the
room temperature will rise.
2
A refrigerator
operating with its
door open in a well-
sealed and well-
insulated room
A fan running in a
well-sealed and
well-insulated room
will raise the
temperature of air in
the room.
FORMS OF ENERGY • Energy can exist in numerous forms such as thermal, mechanical,
kinetic, potential, electric, magnetic, chemical, and nuclear, and their sum constitutes the total energy, E of a system.
• Thermodynamics deals only with the change of the total energy.
• Macroscopic forms of energy: Those a system possesses as a whole with respect to some outside reference frame, such as kinetic and potential energies.
• Microscopic forms of energy: Relate to the molecular structure and molecular activity of a system
• Internal energy, U: The sum of all the microscopic forms of energy.
3
The macroscopic energy of an
object changes with velocity and
elevation.
• Kinetic energy, KE: The energy
that a system possesses as a result
of its motion relative to some
reference frame.
• Potential energy, PE: The energy
that a system possesses as a result
of its elevation in a gravitational
field.
4
Total energy
of a system
Energy of a system
per unit mass
Potential energy
per unit mass
Kinetic energy
per unit mass
Potential energy
Total energy
per unit mass
Kinetic energy
Mass flow rate
Energy flow rate
Some Physical Insight to Internal Energy
5
Sensible energy:
The portion of the
internal energy of
a system
associated with
the kinetic
energies of the
molecules.
• Latent energy: The internal energy associated with the phase of a system.
• Chemical energy: The internal energy associated with the atomic bonds in a molecule.
• Nuclear energy: The tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself.
6
Internal = Sensible + Latent + Chemical + Nuclear
Thermal = Sensible + Latent
7
macroscopic kinetic energy:
organized, more useful
microscopic kinetic energy:
disorganized
• The total energy of a system, can
be contained or stored in a
system, and thus can be viewed as
the static forms of energy.
• The forms of energy not stored in
a system can be viewed as the
dynamic forms of energy or as
energy interactions.
• The dynamic forms of energy are
recognized at the system boundary
as they cross it, and they represent
the energy gained or lost by a
system during a process.
• The only two forms of energy
interactions associated with a
closed system are heat transfer
and work.
• The difference between heat transfer and work: An energy interaction is
heat transfer if its driving force is a temperature difference. Work is energy
transfer associated with force acting through a distance
Mechanical Energy
8
Mechanical energy: The form of energy that can be converted to
mechanical work completely and directly by an ideal mechanical device such as an ideal turbine.
Kinetic and potential energies: The familiar forms of mechanical energy.
Mechanical energy of a
flowing fluid per unit mass
Rate of mechanical
energy of a flowing fluid
Mechanical energy change of a fluid during incompressible flow per unit mass
Rate of mechanical energy change of a fluid during incompressible flow
ENERGY TRANSFER BY HEAT
9
Energy can cross the
boundaries of a closed system
in the form of heat and work.
Temperature difference is the driving
force for heat transfer. The larger the
temperature difference, the higher is the
rate of heat transfer.
Heat: The form of energy that is
transferred between two
systems (or a system and its
surroundings) by virtue of a
temperature difference.
10
Energy is
recognized
as heat
transfer only
as it crosses
the system
boundary.
During an adiabatic process, a system
exchanges no heat with its surroundings.
Heat transfer
per unit mass
Amount of heat transfer
when heat transfer rate
changes with time
Amount of heat transfer
when heat transfer rate
is constant
Historical Background on Heat
• Kinetic theory: Treats molecules as tiny balls that are in motion and thus possess kinetic energy.
• Heat: The energy associated with the random motion of atoms and molecules.
Heat transfer mechanisms:
• Conduction: The transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interaction between particles.
• Convection: The transfer of energy between a solid surface and the adjacent fluid that is in motion, and it involves the combined effects of conduction and fluid motion.
• Radiation: The transfer of energy due to the emission of electromagnetic waves (or photons).
11
In the early nineteenth century, heat was
thought to be an invisible fluid called the
caloric that flowed from warmer bodies to
the cooler ones.
ENERGY TRANSFER BY WORK • Work: The energy transfer associated with a force acting through a distance.
– A rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions
• Formal sign convention: 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.
• Alternative to sign convention is to use the subscripts in and out to indicate direction. This is the primary approach in this text.
12
Specifying the directions
of heat and work.
Work done
per unit mass
Power is the
work done per
unit time (kW)
Heat vs. Work • Both are recognized at the boundaries
of a system as they cross the boundaries. That is, both heat and work are boundary phenomena.
• Systems possess energy, but not heat or work.
• Both are associated with a process, not a state.
• Unlike properties, heat or work has no meaning at a state.
• Both are path functions (i.e., their magnitudes depend on the path followed during a process as well as the end states).
13
Properties are point functions; but
heat and work are path functions
(their magnitudes depend on the
path followed). Properties are point functions
have exact differentials (d ).
Path
functions
have inexact
differentials ( )
Electrical Work
14
Electrical power in terms of resistance
R, current I, and potential difference V.
Electrical power
When potential difference
and current change with time
When potential difference
and current remain constant
MECHANICAL FORMS OF WORK • There are two requirements for a work interaction between a
system and its surroundings to exist:
– there must be a force acting on the boundary.
– the boundary must move.
15
The work done is proportional to the force
applied (F) and the distance traveled (s).
Work = Force Distance
When force is not constant
If there is no movement,
no work is done.
Spring Work
16
Elongation
of a spring
under the
influence of
a force.
When the length of the spring changes by
a differential amount dx under the influence
of a force F, the work done is
For linear elastic springs, the displacement
x is proportional to the force applied
k: spring constant (kN/m)
Substituting and integrating yield
x1 and x2: the initial and the final
displacements
The
displacement
of a linear
spring doubles
when the force
is doubled.
Shaft Work
17
A force F acting through
a moment arm r
generates a torque T
This force acts through a distance s
The power transmitted through the shaft
is the shaft work done per unit time
Shaft
work
MOVING BOUNDARY WORK
18
Moving boundary work (P dV work):
The expansion and compression work
in a piston-cylinder device.
The work associated
with a moving
boundary is called
boundary work. A gas does a
differential
amount of work
Wb as it forces
the piston to
move by a
differential
amount ds.
Quasi-equilibrium process:
A process during which the system
remains nearly in equilibrium at all
times.
Wb is positive for expansion
Wb is negative for compression
19
The area under the process
curve on a P-V diagram
represents the boundary work.
The boundary
work done
during a process
depends on the
path followed as
well as the end
states.
The net work done
during a cycle is the
difference between
the work done by
the system and the
work done on the
system.
20
Polytropic, Isothermal, and Isobaric processes
Schematic and
P-V diagram for
a polytropic
process.
For expansion and compression of ideal gases, relation between P and V is often PVn = C, where C and n are constants, n is also called as polytropic exponent. This type of process is called polytropic process. For isentropic process, n=γ, We also know for ideal gas eq. of state: PV=mRT, R is gas constant (kJ/kg-K)
Boundary work for polytropic process, 2
2 2 1 1
1 1b
PV PVW PdV
n
Boundary work for isothermal or constant temp. process,
Boundary work for isobaric or constant pressure process, 2
2 11
( )bW PdV P V V
Boundary work for isometric or constant volume process, 2
10bW PdV
or
22 2
1 1 2 21
1 1
ln lnb
V VW PdV PV PV
V V
Energy Balance
21
Energy Change of a System, ΔEsystem
22
The change in the total energy of a system during a process is the sum of the
changes in its internal, kinetic, and potential energies and can be expressed as
Example 1: A piston–cylinder device initially contains 0.4 m3 of air at 100 kPa and 80°C. The air is now compressed to 0.1 m3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process.
Solution:
It is an isothermal process, so we will use equation,
Here given, p1=100 kPa= 100x103 Pa, V1=0.4 m3, V2=0.1 m3,
So, boundary work Wb= 100x 103 x0.4 x ln(0.1/0.4) J= -55451 J= -55.451 kJ
24
22 2
1 1 2 21
1 1
ln lnb
V VW PdV PV PV
V V
• Example 2: A piston–cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 120°C. The nitrogen is now expanded polytropically to a state of 100 kPa and 100°C. Determine the boundary work done during this process.
• Solution:
Here given, V1=0.07 m3, P1= 130 kPa, T1=120 ºC = (120+273) K= 393 K, P2=100 kPa, T2= 100 ºC= (100+273) K= 373 K, Wb= ?
The process is polytropic, so,
We also know for polytropic process, PVn=C, that means, P1V1n=P2V2n, so, n=ln(P1/P2)/ln(V2/V1)
For any ideal gas, we know, PV=mRT, here, R= gas constant= 0.2968 kJ/kg-K for Nitrogen
Therefore,
Done!
25
22 2 1 1
1 1b
PV PVW PdV
n
1 1
1
130 0.070.0780
0.2968 393
PVm kg
RT
22
2
0.078 0.2968 3730.0863 3
100
mRTV m
P
2 2 1 1 100 0.0863 130 0.071.86
1 1 1.248b
PV PVW kJ
n
ln(130 /100)1.248
ln(0.08637 / 0.07)n
Example 3: A piston–cylinder device initially contains 0.3 kg of steam at 1.0 MPa and 250 °C. Determine the boundary work if steam is expanded at constant pressure to 400 °C .
26
0.3
Ex. 2
A piston-cylinder device contains 2 kg of superheated water at
200 kPa and 300 oC. The superheated water is now cooled at
constant pressure until the temperature drops to 200 oC.
i. Determine the boundary work done during this process [kJ].
ii. Sketch the process on pressure versus volume (P-V) diagram
clearly showing the states and the direction of the process.
Solution in next slide>
27
28
Ex. 3
Air initially at 600 kPa and 250 oC is contained in a 0.30 m3 piston-
cylinder device. The air is now expanded slowly until the final pressure inside the cylinder is 200 kPa. The temperature of the air
remains constant during this process. Assume the air to be an ideal
gas with R = 0.287 kJ/kgK.
i. Determine the mass of the air in the cylinder (kg).
ii. Determine the boundary work done during this process (kJ).
iii. Sketch the process on pressure versus volume (P-V) diagram clearly showing the states and the direction of the process.
Solution in next slide >
29
30
Ex : A piston–cylinder device contains 0.10 kg of
air initially at 1 MPa and 250°C. The air is first
expanded isothermally to 500 kPa, then air is
compressed with constant volume to the initial
pressure. Determine the boundary work for each
process and the net-work done during the
processes.
Solution in next slide
31
• Example 4: A piston–cylinder device contains 0.05 m3 of a gas initially at 200 kPa. At this state, a linear spring that has a spring constant of 150 kN/m is touching the piston but exerting no force on it. Now heat is transferred to the gas, causing the piston to rise and to compress the spring until the volume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25 m2 , determine (a) the final pressure inside the cylinder, (b) the total work done by the gas, and (c) the fraction of this work done against the spring to compress it.
33
34
Forms of energy Question- what is total energy of a system?
• The sum of all forms of the energy a system possesses is called total energy. In the absence of magnetic, electrical and surface tension effects, the total energy of a system consists of the kinetic, potential, and internal energies.
Question- what is mechanical energy? How does it differ from thermal energy? What are the forms of mechanical energy of a fluid stream?
• The mechanical energy is the form of energy that can be converted to mechanical work completely and directly by a mechanical device such as a propeller. It differs from thermal energy in that thermal energy cannot be converted to work directly and completely. The forms of mechanical energy of a fluid stream are kinetic, potential, and flow energies.
35
Energy transfer by heat and work • In what forms can energy cross the boundaries of a closed system?
• Energy can cross the boundaries of a closed system in two forms: heat and work.
• When is the energy crossing the boundaries of a closed system heat and when is it work?
• The form of energy that crosses the boundary of a closed system because of a temperature difference is heat; all other forms are work.
• What is an adiabatic process? What is an adiabatic system?
• An adiabatic process is a process during which there is no heat transfer. A system that does not exchange any heat with its surroundings is an adiabatic system.
36
Energy transfer by heat and work • A gas in a piston–cylinder device is compressed, and as a
result its temperature rises. Is this a heat or work interaction?
• It is a work interaction.
• A room is heated by an iron that is left plugged in. Is this a heat or work interaction? Take the entire room, including the iron, as the system.
• It is a work interaction
• A room is heated as a result of solar radiation coming in through the windows. Is this a heat or work interaction for the room?
• It is a heat interaction since it is due to the temperature difference between the sun and the room.
37
38
Mechanical energy of a flowing fluid per unit mass
Rate of mechanical energy of a flowing fluid
Total energy of a system
Energy of a system per unit mass
• Example 5: Determine the total energy required to accelerate a 1300 kg car from 10 km/h to 60 km/h on an uphill road with a vertical rise of 40 m.
39
• Example 6: A person gets into an elevator at the lobby level of a hotel together with his 30-kg suitcase, and gets out at the 10th floor 35 m above. Determine the amount of energy consumed by the motor of the elevator that is now stored in the suitcase.
40
• Example 7: Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m3 /s at a location 90 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.
41
4–40 A piston–cylinder device initially contains 0.8 m3 of saturated water
vapor at 250 kPa. At this state, the piston is resting on a set of stops, and
the mass of the piston is such that a pressure of 300 kPa is required to
move it. Heat is now slowly transferred to the steam until the volume
doubles. Show the process on a P-v diagram with respect to saturation lines
and determine (a) the work done during this process, and (b) the total heat
transfer
4.10 example
A piston–cylinder device initially contains air at 150 kPa and 27°C. At this
state, the piston is resting on a pair of stops, as shown in Fig. 4–32, and the
enclosed volume is 400 L. The mass of the piston is such that a 350-kPa
pressure is required to move it. The air is now heated until its volume has
doubled. Determine (a) the final temperature, (b) the work done by the air
Test 1 14 October 2018 (Monday)
9-11 PM
DK5, P19
Syllabus for Test 1:
Chapter 1: Introduction and Basic concepts
Chapter 2: Properties of pure substances