Transcript
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CHAPTER 3ENERGY
Sub chapter covered3.1 Introduction3.2 Energy transfer by heat and work 3.3 Energy balance
3.4 Work boundary
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3.1 Intro
Energy exist in numerous forms.
– thermal, mechanical, chemical etc.
Their sum constitute Total Energy on aunit mass, e
m
E e (kJ/kg)
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energy
Macroscopic E Microscopic E
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Macroscopic E: form of energy arethose a system possesses as a wholewith respect to some outside reference
frame. eg: kinetic, potential energy.
Microscopic E: energy related to themolecular structure of a system and thedegree of molecular activity.Independent of outside reference frame.
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Sum of all microscopic energy forms calledinternal energy, U
Macroscopic energy of a system is relatedto motion and the influence of someexternal effect (gravity, magnetism,electricity & surface tension).
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Internal Energy
1) Translational energy
2) Rotational kinetic energy
3) Vibrational kinetic energy
4) Spin energy
5) Sensible energy
6) Latent energy
7) Chemical energy
8) Nuclear energy
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Kinetic Energy (KE)?
Potential Energy (PE)?
Total E of the system?
Flow Energy
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Kinetic Energy (KE): energy that asystem possesses as a result of its
motion relative to some reference frame.
)(2
2kJ
V m KE
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Potential Energy (PE): energy thata system possesses as a result of its
elevation in a gravitational field.
)(kJ mgz PE (kJ)
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Total E of the system (closedsystem):
)(2
2
kJ mgz V
mU PE KE U E
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FLOW ENERGY
Closed system: stationary system
Open system (control vol.): involved
fluid flow
Mass flow rate, : amount of massflowing through a cross section perunit
time.
m
)/( skg V m
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3.2 ENERGY TRANSFER
E transfer
By heat,
Q
By work,
W
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Mechanisms:
ConductionConvection
Radiation
Directional quantity
Qin Qout
E transfer by heat,
Q
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Other than E by heatForce acting through
distance
Directional quantity:
Win Wout
E transfer by work,W
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E transfer by work,W
Electrical work, We
Shaft work, Wsh
Spring work, Wspring
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3.3 ENERGY BALANCE
The conservation of E can expressed as:
E E E in out system
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1) Mechanisms of EnergyTransfer, E
inand E
out
Heat transfer, Q = 0, for adiabatic system
Work transfer, W = 0, if no work involved
Mass transfer, m = 0, for closed system
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2) Energy change of thesystem, ∆E system
E system = E final - E initial = E 2 - E 1
E = U + KE + PE
where U = m (u2
–u1 )
KE = ½ (m )(V 22 - V 1
2) PE = mg ( z 2 – z 1 )
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systemout massinmassout inout inout in E E E W W QQ E E
Balance EnergyOverall
)()()( ,,
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Discussion on Problem 2.10
Assignment on:Problem 2-49Problem 2-50
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CHAPTER 3
HEAT, WORK AND MASS Sub-chapter covered
3.4 Work boundary
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Boundary Work
• Boundary work occurs because the mass of the substancecontained within the system boundary
2
1
2
1
2
1
2
1 PdV Ads
A
F FdsW W bb
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The boundary work is equal to the area under theprocess curve plotted on the pressure-volume
diagram
Note from the figure:
P is the absolute pressure and is
always positive.
When dV is positive, Wb ispositive.
When dV is negative, Wb isnegative.
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Some Typical Processes
a) Constant volume
If the volume is heldconstant, dV = 0, and the boundary work equation becomes
0
2
1 PdV W b
b) Constant pressure
If the pressure is held constant,the boundary work equation becomes
12
2
1
2
1
V V P dV P PdV W b
P-V diagram for V = constant P-V diagram for P = constant
P
V
1
2
P
V
12
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c) Constant temperature, ideal gas
If the temperature of an ideal gas system is held constant, then
the equation of state provides the pressure-volume relation
V
mRT P
Then, the boundary work is
1
22
1
2
1ln
V
V mRT dV
V
mRT PdV W b
Note: The above equation is the result of applying the ideal gasassumption for the equation of state. For real gases undergoingan isothermal (constant temperature) process, the integral inthe boundary work equation would be done numerically.
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d) The polytropic process
The polytropic process is one in which the pressure-volume
relation is given as PV n = C (where n and C is constant)
The exponent n may have any value from minus infinity to plusinfinity depending on the process. Some of the more common
values are given below.Process Exponent n
Constant pressure 0
Constant volume
Isothermal & ideal gas 1
Adiabatic & ideal gas k = CP/C V
Here, k is the ratio of the specific heat at constant pressure C P to
specific heat at constant volume C V .
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The boundary work done during the polytropic process is
found by substituting the pressure-volume relation intothe boundary work equation
2
1
2
1 dV V
Const
PdV W nb
1,ln
1,1
1
2
1122
nV
V PV
nn
V P V P
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For an ideal gas undergoing a polytropic process, the boundary work
2
1
2
1dV
V
Const PdV W
nb
1,ln
1,1
1
2
12
nV V mRT
nn
T T mR
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Discussion
1. A frictionless piston-cylinder device initially contains 200L of saturated liquid refrigerant R134a. The piston is free to moveand its mass is such that it maintains a pressure of 800 kPa onthe refrigerant. The refrigerant is now heated until itstemperature rises to 50°C. Calculate the work done during this
process and show the process in P-v diagram
2. Air enters a nozzle steadily at 2.21 kg/m3 and 30 m/s and leaveat 0.762 kg/m3 and 180 m/s. If the inlet area of the nozzle is 80
cm2
, determinea) the mass flow rate through the nozzle b) the exit area of the nozzle
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Assignment 5:
Problem 4.8, 4.9, 4.12, 4.18
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To be continue…………………
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