The First Law of
Thermodynamics
Cengel & Boles,
Chapter 4
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The First Law of
Thermodynamics
• The First Law of Thermodynamics is
also known as
– Conservation of energy principle
– Energy balance equation
– The “First Law”
• In basic terms, it states:
Ein  Eout  Esystem
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Energy Balance for a
Closed System
• For a closed system,
Esystem  E final  Einitial
 U  KE  PE
 m(u2  u1 )  12 m(V22 V12 )  mg ( z2  z1 )
and
Ein  Win  Qin
Eout  Wout  Qout
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Energy Balance for a
Closed System, cont.
• The energy balance statement
becomes
Qin  Qout  Win  Wout  Esystem
Qnet ,in  Wnet ,out  Esystem
or,
Q  W  Esystem
• Rate form:
  W 
Q
dEsystem
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dt
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Closed System Energy
Balance: Special Cases
• Stationary system (KE, PE = 0)
Q  W  U
• Adiabatic system (Q = 0)
 W  E
• No work interactions (W = 0)
Q  E
• Cycle (initial state = final state)
Q  W  E  0 or Qcycle  Wcycle
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Energy Balance for
Control Volumes
• Balance of energy transfer by work,
heat, and mass flow across system
boundary plus stored energy within
control volume:
Q  W  E in,mass  E out,mass 
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dEsystem
dt
6
Energy Transport by Mass
• Recall from Chapter 3:

E in,mass   m i hi  12 Vi 2  gzi
i


2
1


Eout,mass   me he  2 Ve  gze

e
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Energy Balance for
Steady-Flow Systems
• At steady-state, dEsystem/dt = 0, thus:
Q  W  E in,mass  E out,mass  0
or
 e (he  12Ve2  gze ) 
Q  W   m
e
1 2

m
(
h

 i i 2Vi  gzi )
i
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Energy Balance for
Steady-Flow Systems, cont.
• For single-stream control volumes,
Q  W 



2
2
1

m h2  h1  2 V2 V1  g ( z2  z1 )

• Dividing by mass flow rate gives the
energy balance on a unit-mass basis:
qw


h2  h1  12 V22  V12  g ( z 2  z1 )
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Steady-Flow
Engineering Devices
•
•
•
•
•
•
•
Nozzles and diffusers
Turbines, compressors, and pumps
Throttling valves
Mixing chambers
Heat exchangers
Pipe and duct flow
See section 4-4 in text and PDF file
ME152SSdevices.pdf on website
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Energy Balance for
Unsteady-Flow Processes
• Unsteady = transient
• Examples:
– Filling and discharging of tanks
– Start-up and shut-down of turbines,
compressors, hxers, etc.
• Mathematically,
d
  0
dt
– need to solve 1st order differential
equation
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