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Conservation of Energy
Conservation of Energy
Chapter One
Chapter One
Section 1.3
Section 1.3
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View Full Document Alternative Formulations
• Alternative Formulations
Time Basis:
At an instant
or
Over a time interval
Type of
System:
Control volume
Control surface
• An important tool in heat transfer analysis, often
providing the
basis for determining
the
temperature
of a system.
CONSERVATION OF ENERGY
(FIRST LAW OF THERMODYNAMICS)
•A
t
a
n
Instant of Time:
Note representation of system by a
control surface (dashed line)
at the boundaries.
Surface Phenomena
,
energy transfer across the control
su
:
rate of thermal and/or mechanical
due to heat transfer, fluid flow and/or wor
rfa
k i
c
nteract
io .
e
ns
in
out
EE
±±
Volumetric Phenomena
rate of
due to conversion from another enegy form
(e.g., electrical, nuclear, or chemical); energy conversion proc
thermal ener
ess occurs w
gy generatio
ithin the sy e
n
m.
st
g
E
±
energy storage in the system
:
rate of change
.
of
st
E
±
Conservation of Energy
in
out
g
st
dE
st
dt
E
E
−+
=≡
±
±
(1.11c)
Each term has units of J/s or W.
APPLICATION TO A
CONTROL VOLUME
•O
v
e
r
a
Time Interval
Each term has units of J.
in
out
g
st
E
E
=
Δ
(1.11b)
CV at an Instant and over a Time Interval
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View Full Document At an
instant
t
dU
q
W
dt
−=
±
• Special Cases (Linkages to Thermodynamics)
(i) Transient
Process for a
Closed System
of Mass (
M) Assuming Heat Transfer
to the System (Inflow) and Work Done by the System (Outflow).
Over a
time interval
tot
st
QE
W
Δ
(1.11a)
Closed System
For negligible changes in potential or kinetic energy
t
QW
U
−
=Δ
Internal
thermal energy
Example 1.3: Application to thermal response of a conductor with Ohmic
heating (generation):
• Involves change in
thermal energy
and for an incompressible substance.
t
dU
dT
Mc
dt
dt
=
• Heat transfer is from the conductor (negative
)
q
• Generation may be viewed as
electrical work
done on the system (negative
)
W
±
Example 1.3
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View Full Document Example 1.4: Application to isothermal solidliquid phase change in a container:
Latent Heat
of Fusion
t1
a
t
s
f
UU
M
Δ=
Δ
=
h
Example 1.4
(ii) Steady State
for Flow through an
Open System
without Phase Change or
Generation:
()
flow
o
wrk
pv
→
•
enthalp
y
t
up
vi
+≡
→
•
ideal gas
constant specific h
For an
w
eat
ith
:
in
out
p
in
out
ii
c
TT
−=
−
•
For an
:
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This note was uploaded on 04/02/2008 for the course MAE 310 taught by Professor Kuznetsov during the Spring '08 term at N.C. State.
 Spring '08
 Kuznetsov
 Heat Transfer

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