Transcript Reflection of Buddhism in Contemporary Cinema

ENGR 2213 Thermodynamics
F. C. Lai
School of Aerospace and Mechanical
Engineering
University of Oklahoma
First Law of Thermodynamics
Closed Systems
E  Q  W
E: total energy
includes kinetic energy, potential energy and
other forms of energy
All other forms of energy are lumped together as
the internal energy U.
Internal energy U is an extensive property.
Specific internal energy u = U/m
is an intensive property
Energy Analysis for a Control Volume
Conservation of Mass
Net Change in = Total Mass Entering CV
Mass within CV
Total Mass
Leaving CV
mCV   mi  me
dmCV
  mi   me
dt
Steady State
AV
m  AV 
v
 mi   me
Steady-Flow Process
Conservation of mass
 mi   me
Conservation of energy
QCV  WCV




Ve2
Vi2
  me  he 
 gze    mi  hi 
 gzi 
2
2




Steady-Flow Process
For single-stream steady-flow process
Conservation of mass
mi  me  m
Conservation of energy


(Ve2  Vi2 )
QCV  WCV  m  (he  hi ) 
 g(ze  zi ) 
2


QCV WCV
(Ve2  Vi2 )

 (he  hi ) 
 g(ze  zi )
m
m
2
Uniform-Flow Process
Conservation of Mass
mCV   mi  me
Conservation of Energy
ECV




Ve2
Vi2
  mi  hi 
 gzi    me  he 
 gze   QCV  WCV
2
2




QCV  WCV




Ve2
Vi2
  me  he 
 gze    mi  hi 
 gzi 
2
2




+ (m2u2 – m1u1)CV
Second Law of Thermodynamics
Kelvin-Planck Statement
It is impossible for any device that operates on a
cycle to receive heat from a single reservoir and
produce an equivalent amount of work.
No heat engine can have a thermal efficiency of
100%
The impossibility of having 100% efficiency heat
engine is not due to friction or other dissipative
effects.
Second Law of Thermodynamics
Clausius Statement
It is impossible to construct a device that operates
on a cycle and produce no effect other than the
transfer of heat from a low-temperature body to a
high-temperature body.
Equivalence of the two statements
A violation of one statement leads to the violation
of the other statement.
Second Law of Thermodynamics
Carnot Principles
1. The efficiency of an irreversible heat engine is
always less than that of a reversible one
operating between the same two reservoirs.
2. The efficiencies of all reversible heat engines
operating between the same two reservoirs
are the same.
A violation of either statement results in the
Violation of the second law of thermodynamics.
Entropy Change of an Ideal Gas
T ds = du + p dv
du p
ds 
 dv
T T
For an ideal gas,
dT
dv
ds  c v
R
T
v
s2  s1 
2
1 c v
du = cv dT,
pv = RT
 v2 
dT
dT
2
2 dv
 1 c v  R ln  
 R 1
T
T
v
 v1 
Entropy Change of an Ideal Gas
T ds = dh - v dp
dh v
ds 
 dp
T T
For an ideal gas,
dh = cp dT,
pv = RT
dT
dp
ds  c p
R
T
p
 p2 
dT
dT
2
2
2 dp
 1 cp  R ln  
s2  s1  1 cp
 R 1
T
T
p
 p1 
Isentropic Processes of Ideal Gases
 v2 
dT
s2  s1 
 Rln  
T
 v1 
 p2 
dT
2
s2  s1  1 cp
 Rln  
T
 p1 
2
1 c v
1. Constant Specific Heats
 T2 
 v2 
(a) s2  s1  c v ln 
  Rln  
 T1 
 v1 
 T2 
 p2 
(b) s2  s1  c p ln 
  Rln  
 T1 
 p1 
Isentropic Processes of Ideal Gases
1. Constant Specific Heats
 T2 
 v2 
(a) s2  s1  c v ln 
  Rln    0
 T1 
 v1 
R / cv 

 v1 
 T2 
R  v2 

ln     ln    ln  
c v  v1 
 v 2 

 T1 
R / cv
T2  v1 
 
T1  v 2 
k 1
T2  v1 
 
T1  v 2 
R = c p – cv
k = cp/cv
R/cv = k – 1
Isentropic Processes of Ideal Gases
1. Constant Specific Heats
 T2 
 p2 
(b) s2  s1  cp ln 
  Rln    0
 T1 
 p1 
R / cp 

 p2 
 T2  R  p2 

ln    ln    ln  
 p1 

 T1  cp  p1 
R / cp
T2  p2 
 
T1  p1 
k 1
k
T2  p2
 
T1  p1 
R = c p – cv
k = cp/cv
R/cp = (k – 1)/k
Isentropic Processes of Ideal Gases
1. Constant Specific Heats
k 1
k
T2  p2
 
T1  p1 
k 1
 v1 
 
 v2 
k
 p2   v1 
  
 p1   v 2 
p1V1k = p2V2k
Polytropic Processes
pVn = constant
n=0
constant pressure
isobaric processes
n=1
constant temperature
isothermal processes
n=k
constant entropy
isentropic processes
n = ±∞ constant volume
isometric processes
Isentropic Processes of Ideal Gases
2. Variable Specific Heats
 p2 
s2  s1  s (T2 )  s (T1)  R ln    0
 p1 
 p2  s (T2 )  s (T1)
ln   
R
 p1 
 s (T2 )  s (T1) 
p2
 exp 

p1
R


exp s (T2 ) / R 
pr2


exp s (T1) / R 
pr1
Relative Pressure
pr = exp[sº(T)/R]
► is not truly a pressure
► is a function of
temperature
Isentropic Processes of Ideal Gases
2. Variable Specific Heats
p2 pr2

p1 pr1
v 2 RT2 / p2 RT2 / pr2 v r2



v1 RT1 / p1 RT1 / pr1 v r1
Relative Volume
vr = RT/pr(T)
► is not truly a volume
► is a function of
temperature
Work
w
2
1 p
wrev 
dv
2
1 v
reversible work in closed systems
dp
reversible work associated with
an internally reversible process
an steady-flow device
► The larger the specific volume, the larger the
reversible work produced or consumed by the
steady-flow device.
Ideal Rankine Cycles
Process 1-2: isentropic compression in a pump
Process 2-3: constant-pressure heat addition in a
boiler
Process 3-4: isentropic expansion in a turbine
Process 4-1: constant-pressure heat rejection in a
condenser
3
T
2
Boiler
Pump
3
Turbine
2
1
1
Condenser
4
4
S
Ideal Reheat Rankine Cycles
2
T
Boiler
3
3
Pump
Turbine
2
1
1
4
4
Condenser
S
2
Boiler
3
T
3
5
4
Pump
1
4
Condenser
5
6
2
1
6
S
Ideal Regenerative Rankine Cycles
Open Feedwater Heater
4
5
Boiler
P2
3
5
T
4
6
Turbine
FWH
3
2
2
1
P1
Condenser
1
7
6
7
S
Ideal Regenerative Rankine Cycles
Closed Feedwater Heater
3
4
Boiler
Turbine
T
4
y
1-y
5
6
•
1
FWH
P
8
1
Trap
7
y
2
Condenser
2
7
3
8
5
1-y
6
S
Otto Cycles
Nikolaus A. Otto (1876) – four-stroke engine
Beau de Rochas (1862)
Diesel Cycles
Rudolph Diesel (1890)
Brayton Cycles