Transcript 2.7 MB - KFUPM Resources v3

Percent
(%)
Evaluation
Attendance and Class Participation
5%
Assignments
5%
10%
Quizzes
5%
HYSYS Computer Assignments
Two Major Exams
40%
Final Exam
35%
TOTAL
Chapter
100%
Topic
Lectures
Chapter 7
Energy and Energy Balances
10
Chapter 8
Balances on Nonreactive Processes
10
Chapter 9
Laboratory Computer Class
Balances on Reactive Processes
Aspen HYSYS –
10
5
7- 1
Major Exam
Major Exam I: 28 Feb 2013, 10:00 AM
Major Exam II: 4 April 2013, 10:00 AM
Final Exam: homepage
7- 2
ENERGY BALANCE (ChE 202)
Chapter 7
Energy & Energy Balances
Dr. Shamsuzzoha, PhD
7- 3
7- 4
7- 5
7.1-7.2
Energy & 1st Law of
Thermodynamics
- What is energy?
- Forms of Energy
-
Energy due to the translational motion of the system as a whole
relative to some frame of reference
Kinetic energy (KE)
Energy due to the position of the system in a potential field
-
Potential energy (PE)
Internal energy (U)
PE  mgz
energy due to the motion of molecules relative to the
center of mass of the system, to the rotational and
vibrational motion and the electromagnetic interactions of
the molecules
Total Energy , E = KE + PE + U
7- 6
Change in kinetic energy:
1
KE  KE2  KE1  m(V22  V12 )
2
Change in potential energy
PE  PE2  PE1  mg( z2  z1 )
Change in Internal energy
U  U  U
2
1
Note: Δ means “change” and is always calculated as
“final value minus initial value”
7- 7
TEST YOURSELF
1. What forms of energy may a system possess? In what forms may
energy be transferred to and from a closed system?
2. Kinetic, potential, internal; heat, work
2. Why is it meaningless to speak of the heat possessed by a system?
Heat is only defined in terms of energy being transferred.
3. Suppose the initial energy of a system (internal + kinetic + potential)
is Ej, the final energy is Ef , an amount of energy Q is transferred from
the environment to the system as heat, and an amount W is transferred
from the system to the environment as work.
According to the first law of thermodynamics, how must Ei, Ef , Q, and W
be related?
E; + Q - W = Ef
7- 8
How energy can be transferred between a system and its
surroundings?
Heat – energy that flows as a result of
temperature difference between a system and its
surrounding ; heat is defined positive when it is
transferred to the system from the surroundings.
Work – energy that flows in response to any
driving force other than a temperature difference.
; work is defined positive when it is done by the
system on the surroundings.
7- 9
Types of Work
• Flow work (Wfl) - energy carried across the
boundaries of a system with the mass flowing across
the boundaries (i.e. internal, kinetic & potential
energy)
• Shaft work (Ws) - energy in transition across the
boundaries of a system due to a driving force other
than temperature, and not associated with mass flow
(an example would be mechanical work due to a
piston, pump or compressor)
7- 10
ENERGY – CONVERSION UNITS
1 newton (N) = 1 kg. m/s2
1 dyne = 1 g.cm/s2
1 lbf = 32.174 lbm.ft/s2
7- 11
Kinetic Energy Transported by a Flowing Stream
Example 7.2-11: Water flows into a process unit through a 2-cm ID pipe
at a rate of 2.00 m3/h. Calculate Ėk for this stream in joules/second.
SOLUTION
7- 12
Potential Energy Increase of a Flowing Fluid
Example: 7.2-2: Crude oil is pumped at a rate of 15.0
kg/s from a point 220 meters below the earth's surface
to a point 20 meters above ground level. Calculate the
attendant rate of increase of potential energy.
SOLUTION
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Problems
7.1. A certain gasoline engine has an efficiency of 30%; that is, it converts
into useful work 30% of the heat generated by burning a fuel. If the engine
consumes 0.80 L/h of a gasoline with a heating value of 3.5 x 104 kJ/L, how
much power does it provide? Express the answer both in kW and
horsepower.
7.2. Consider an automobile with a mass of 5500 Ibm braking to a stop from
a speed of 55 miles/h.
(a) How much energy (Btu) is dissipated as heat by the friction of the
braking process?
(b) Suppose that throughout the United States, 300,000,000 such braking
processes occur in the course of a given day. Calculate the average rate
(megawatts) at which energy is being dissipated by the resulting friction.
7- 14
General Balance Equation
A balance on conserved quantity (i.e. mass, energy,
momentum) in a process system may be written as:
Input + generation - output - consumption
= accumulation
A system is termed open or closed according to whether or not mass
crosses the system boundary during the period of time covered by the
energy balance.
A batch process system is, by definition, closed, and semibatch and
continuous systems are open.
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7.3 Energy Balance on Closed Systems
• How do you describe a closed system control
volume?
• What effect does this have on the mass and
energy balances?
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•
•
There is no mass transfer into a closed system
The only way energy can get into or out of a closed
system is by heat transfer or work
Q
Ws
a. Heat transfer (Q):
b. Work (Ws):
Note: * Work is any boundary interaction that is not
heat (mechanical, electrical, magnetic, etc.)
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First Law of Thermodynamics
Energy can neither be created nor destroyed ; It can
only change forms
Input + generation - output - consumption
0
0
= accumulation
 Input - output = accumulation
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In a closed system,


no mass crosses the boundary, hence the input &
output terms are eliminated
energy can be transferred across the boundary as heat
& work, hence the accumulation term may be defined
as the change in total energy in the system, i.e.
 Final total Energy   Initial Total Energy   Change in the total 

  
  

 in the System
  in the System
  system energy

Ef
-
Ei
Q-W
s
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E  KE 
ΔE  E f  E i
PE 
U
ΔE  Q  Ws
Q = heat transferred to the system
Ws = work done by the system
E  KE  PE  U
KE  PE  U  Q  Ws
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E  U + PE + KE = Q – W
Note:
Q   Qi
i
system
Ws   Ws,i
i
boundary)
(Summation of all heat
transfer across
boundary)
(Summation of all work
across system
7- 21
For a closed system what is E equal to?
E  KE  PE  U  Q  W
s
• Is it steady state ? (if yes, E = 0)
• Is it adiabatic? (if yes, Q = 0)
• Are there moving parts, e.g. do the walls move? (if
no, Ws = 0)
• Is the system moving? (if no, KE = 0)
• Is there a change in elevation of the system? (if no,
PE = 0 )
• Does temperature, phase, chemical composition
change, or pressure change less than a few
atmospheres ? (if no to all, U = 0)
7- 22
Example 2
1. A closed system of mass 5 kg undergoes a process in
which there is work of magnitude 9 kJ to the system
from the surroundings. The elevation of the system
increases by 700 m during the process. The specific
internal energy of the system decreases by 6 kJ/kg
and there is no change in kinetic energy of the
system. The acceleration of gravity is constant at
g=9.6 m/s2. Determine the heat transfer, in kJ.
heat is defined positive when it is transferred to the system from the surroundings.
work is defined positive when it is done by the system on the surroundings.
7- 23
Solution
7- 24
7.4 Energy Balances on Open
Systems
How are open systems control volumes different from
closed systems
What effect does this have on the energy balance?
7- 25
7.4 ENERGY BALANCES ON OPEN
SYSTEMS AT STEADY STATE
7.4a Flow Work and Shaft Work
7.4b Specific Properties and Enthalpy
7.4c The Steady-State Open-System
Energy Balance
7- 26
Flow Work and Shaft Work
The net rate of work done by an open system on its
surroundings may be written as
Ẇ= Ẇs + Ẇfl
Ẇs = shaft work, or rate of work done by the process fluid on a
moving part within the system (e.g., a pump rotor)
Ẇfl = flow work, or rate of work done by the fluid at the system
outlet minus the rate of work done on the fluid at the system inlet
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heat is defined positive when it is transferred to the system from the
surroundings.
work is defined positive when it is done by the system on the surroundings.
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To derive an expression for Ẇfl ,we initially consider the
single-inlet-single-outlet system
The fluid that enters the system has work done on it by
the fluid just behind it at a rate
If several input and output streams enter and leave the system. the
products for each stream must be summed to determine Ẇfl
7- 29
7.4b Specific Properties and Enthalpy
The properties of a process material are either extensive
(proportional to the quantity of the material) or intensive
(independent of the quantity)
Mass, number of moles, and volume (or mass flow rate,
molar flow rate and volumetric flow rate for a continuous
stream), and kinetic energy, potential energy, and internal
energy (or the rates of transport of these quantities by a
continuous stream) are extensive properties
Intensive: temperature, pressure, and density
7- 30
We will use the symbol ᶺ to denote a specific property
A property that occurs in the energy balance equation
for open systems is the specific enthalpy, defined as
7- 31
Calculation of Enthalpy
The specific internal energy of helium at 300 K and 1 atm is
3800 J/mol, and the specific molar volume at the same
temperature and pressure is 24.63 L/mol. Calculate the specific
enthalpy of helium at this temperature and pressure, and the
rate at which enthalpy is transported by a stream of helium at
300 K and 1 atm with a molar flow rate of 250 kmol/h.
Solution
7- 32
TEST YOURSELF
The specific internal energy of a fluid is 200 cal/g.
1. What is the internal energy of 30 g of this fluid?
2. If the fluid leaves a system at a flow rate of 5 g/min, at
what rate does it transport internal energy out of the
system?
3. What would you need to know to calculate the specific
enthalpy of this fluid?
7- 33
Example 3
1.
Air at 300oC and 130 kPa flows through a horizontal 7 cm ID pipe at
a velocity of 42 cm/sec
7 cm ID
Air
1
T1 =300oC
P1=130 kPa
V1 = 42 m/s
a)
b)
c)
Q
2
T2 =400oC
P2=130 kPa
V2 = ? m/s
Write and simplify the energy balance
Calculate the rate of kinetic energy (W), if the air is heated to 400oC at
constant pressure, assuming ideal gas behaviour
Why would be correct to say that the rate of heat transfer to the gas equals
the rate of change of kinetic energy? Why?
7- 34
a)
Write and simplify the energy balance
H + Ek + Ep = Q - Ws
0
b)
0
Calculate Ek (W), assuming ideal gas behaviour
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c)
If the air is heated to 400oC at constant pressure what is Ek (300oC
 400oC)?
d)
Why would be incorrect to say that the rate of heat transfer to the
gas in part (c) must equal the rate of change of kinetic energy?
Q = H + Ek ….hence Q ≠ Ek
7- 36
7.4b Specific properties and Enthalpy
Total Energy of a flowing fluid (open system)
U  KE  PE  Q  W
U  KE  PE  Q  (W fl  W s )
W fl  PoutVout  PinVin
The fluid possesses an additional form of
energy –the flow energy (flow work)
Shaft work
H  KE  PE  Q  W s
H  U  PV ....... Enthalpy (Joule, cal ..)
Hˆ  Uˆ  PVˆ ...... Specific Enthalpy( J / kg, cal / kg...)
7- 37
7.4c Energy balance on an open system at
steady state
Input
-
Output
=
Accumulation

 


2
2

ˆ
ˆ
 ˆ

 ˆ
 Ecv
Vin
Vout
Q   min  H in 
 gzin   Ws   m out  H out 
 gzout  
2
2
t










The flow work
is included in
the enthalpy
term
This work represents everything but
the flow work
7- 38
Energy Balance on Open Systems at Steady
State


m
in
 m
out
E
0
t
cv





2
2





V̂in
V̂out
Q   min  Ĥ in  2  gzin  Ws   mout  Ĥ out  2  gzout   0
















2
2





V̂out
V̂in
 mout  Ĥ out  2  gzout    min  Ĥ in  2  gzin   Q Ws









7- 39
For an open system what is E equal to?
 W
  ΔH
  ΔE
  ΔE
 Q

ΔE
k
p
s
• Is it adiabatic? (if yes, Q = 0)
• Are there moving parts, e.g. pump, compressor,
turbine ? (if no, Ws = 0)
• Does the average velocity of the fluid change
between the input and the output? ? (if no, KE = 0)
• Is there a change in elevation of the system between
the input and the output? ? (if no, PE = 0 )
• Does temperature, phase, chemical composition or
pressure change? (if no to all, H = 0)
7- 40
Single Stream Steady Flow
System

Nozzles    
2
2
Vout  Vin

ˆ
ˆ
Q  Ws  m H out  H in 
 g zout  zin 


Diffusers
2


Often the change in kinetic energy
of the fluid is small, and the
change in potential energy of the
fluid is small
7- 41
Nozzles and Diffusers
nozzle
A nozzle is a device that
increases the velocity of a
fluid at the expense of
pressure
diffuser
A diffuser is a device that
slows a fluid down
7- 42


2
2
Vout  Vin

ˆ
ˆ
Q  Ws  m H out  H in 
 g zout  zin 


2





Is there work in this system?
NO
Is there heat transfer?
Usually it can be ignored
Does the fluid change
elevation?
NO

0  Hˆ out  Hˆ in

 2

 Vout  Vin2 


2




enthalpy is converted
into kinetic energy
7- 43
Recall…
1. E is always measured relative to reference point!
•
Reference plane for PE
•
Reference frame for KE
•
Reference state for Û or Ĥ (i.e. usually, but not
necessarily Û or Ĥ = 0)
And…
1. Changes in E are important, not total values of E
2. E depends only on beginning and end states
3. Q and W depend on process path (could get to the same
end state with different combinations of Q and W)
7- 44