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Unformatted text preview: Energy BalanceOverall 10/13/11 1 LEARNING OBJECTIVES By the end of this topic, you should be able to understand the
following:
•
•
•
• Definition of Energy
Conservation of Energy
Form of Energy
Energy Balance for Closed and Open Systems 10/13/11 2 CONSERVATION OF ENERGY The law of conservation of energy states that for any
process unit (s), energy can neither be created nor
destroyed but it can change from one form to another
forms of energy.
The law concludes that at a steady state: Total energy INPUT = Total energy OUTPUT 10/13/11 3 FORM OF ENERGY
There are 6 forms of energy
Work (W)
Heat (Q)
Kinetic energy (Ek)
Potential energy (Ep)
Internal energy (U)
Enthalpy (H)
10/13/11 4 FORM OF ENERGY
Work (W) form of energy that represent a transfer
form
between the system and surroundings. Work can not
stored. Work is positive when done on the system.
For example, work done by piston. state 2 W= ∫ Fds state1 10/13/11 5 FORM OF ENERGY
Heat (Q) heat flow or total energy flow across a
Heat
system boundary that is caused by a temperature
difference between the system and the
surroundings. Heat is not stored nor created. Heat
is positive when transferred to the system via
conduction, convection or radiation. Q = UA∆T
U=overall heat tranfer coefficient, A=surface area,
T=temperature
10/13/11
6 FORM OF ENERGY
Internal Energy (U) due to; motion of molecules relative to the centre
motion
of mass of the system, rotational, vibrational, and electromagnetic
rotational,
interactions of molecules, and interactions of the atomic and subatomic
interactions
constituents of the molecules
constituents
T2 U 2 − U1 = ∫ UCV dT
T1 10/13/11 7 FORM OF ENERGY
KINETIC AND POTENTIAL ENERGY 1
Ek = mu 2
2 s The kinetic energy portion is defined by s Thus you could calculate the kinetic energy of a portion of fluid with
mass m (kg) and uniform velocity u (m/s). s Now, for potential energy, E p = mgz where z = height of the object above a reference plane (potential
energy is assigned as 0) 10/13/11 8 FORM OF ENERGY
Enthalpy (H) the summation of internal energy and
the multiplication of pressure with volume H = U + pV 10/13/11 9 CLOSE AND OPEN SYSTEMS
CLOSE AND OPEN SYSTEMS
Closed system or nonflow system no transfer of mass
across the boundary
Open system or flow system exchange of mass occurs
across the boundary 10/13/11 10 CLOSE AND OPEN SYSTEMS
CLOSE AND OPEN SYSTEMS
s For a simple and closed system, energy may enter or
For
leave a closed system in only two ways:
leave
– As heat: a flow of heat into the system is a positive flow, a
As
flow out is negative.
flow – As work: thus the application of a force, torque, or voltage.
As
In this text, work, is positive when it is done on the system. s All of our energy balances is based on the first law of
All
thermodynamics, known as the conservation of
thermodynamics known
energy law (similar to conservation of mass law neither can be created nor destroyed). 10/13/11 11 ENERGY BALANCES
ENERGY BALANCE FOR CLOSED SYSTEMS
s The balance:
Final energy of syst. = initial energy of syst. + net energy
Final
transferred to syst.
transferred
•
•
• s Initial energy of the system = Ui + Eki + Epi
Initial
Final energy of the system = Uf + Ekf + Epf
Final
kf
Energy transferred = Q  W (heat energy transferred minus work done) Hence Hence Uf + Ekf + Epf = Ui + Eki + Epi + Q  W
kf Rearranging (Uf  Ui) + (Ekf  Eki) + (Epf  Epi) = Q – W
kf
pf Simplify U + Ek + Ep = Q – W “first law statement for a closed system” 10/13/11 12 ENERGY BALANCES
ENERGY BALANCE FOR CLOSED SYSTEMS
s The internal energy  dependent upon chemical composition, state of
The
aggregation, and temperature. If no changes in T, phase, or
aggregation,
no
chemical composition occur:
chemical
U0 s Well insulated syst., or the outside temp. is the same as the system,
Well
Q = 0 termed as adiabatic, no heat exchanged.
adiabatic no s Work done on the system can be done by a piston (compressing,
Work
exerting force), a propeller, or by an electric current.
If none of these things are done
W=0 10/13/11 13 ENERGY BALANCES
ENERGY BALANCE FOR OPEN SYSTEMS
s The previous equations applied to closed syst., that is, syst. in
The
which mass were conserved. What about an open system where
mass does cross the boundaries of the system?
mass s In an open system, several other "things" can impact the energy.
In
Have work done by propeller, called "shaft" work. s There is also "flow" work; the work done on the fluid as it enters
There
the system minus the work done by the fluid at the outlet.
the s This "flow" work is calculated by looking at the pressure P and
This
• volumetric flow rate, V
volumetric
s • • • Thus, Wfl (N.m/s) = Pout (N/m ) * Vout (m /s)  Pin (N/m ) * Viin (m3/s)
Thus,
/s)
n (m 10/13/11 2 3 2 14 ENERGY BALANCES
ENERGY BALANCE FOR OPEN SYSTEMS
s Another property of the energy balance for an open system is:
^ ^ ^ H =U +P V
s Note the symbol ^ on top of the letter H, U and V. This is a
Note
symbol to represent a specific property.
symbol s A specific property is obtained by dividing an extensive property
specific
by the total amount of the stream. s Thus, if the volume of a stream is 500ft3 and the mass is 100lbm,
5 ft3/Ibm . You can do this for
then the specific volume would be
then
You
other properties, including kinetic energy. 10/13/11 15 ENERGY BALANCES
ENERGY BALANCE FOR OPEN SYSTEMS
s Pages 322, 323 and 324 go through the derivation. You should
Pages
DEFINITELY look at this, but I won't go through the derivation.
The end result is 7.415, on pg. 324.
• • • Δ H + ∆ Ek + ∆ Ep = Q + Ws
s You can see that the difference between an open and closed
You
system is that we use enthalpy instead of internal energy. 10/13/11 16 Conclusions You have learnt
Definition of Energy
Conservation of Energy
Form of Energy
Energy Balance for Closed and Open Systems 10/13/11 17 ...
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 Spring '09
 DR.AZMI

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