Transcript Reflection of Buddhism in Contemporary Cinema

ENGR 2213 Thermodynamics
F. C. Lai
School of Aerospace and Mechanical
Engineering
University of Oklahoma
Increase-in-Entropy Principle
(ΔS)adiabatic ≥ 0
A system plus its surroundings constitutes an
adiabatic system, assuming both can be enclosed
by a sufficiently large boundary across which there
is no heat or mass transfer.
(ΔS)total
= (ΔS)system + (ΔS)surroundings
≥0
surroundings
system
Increase-in-Entropy Principle
Sgen = (ΔS)total
> 0 irreversible processes
= 0 reversible processes
< 0 impossible processes
Causes of Entropy Change
► Heat Transfer
► Irreversibilities
Isentropic Process
A process involves no heat transfer (adiabatic) and no
Irreversibilities within the system (internally reversible).
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 
Entropy Change of an Ideal Gas
Standard-State Entropy
s (T) 
T
0 c p
s2  s1 
2
1 cp
dT
T
Reference state: 1 atm and 0 K
 p2 
dT
 Rln  
T
 p1 
 p2 
dT 1 dT

 0 cp
 R ln  
T
T
 p1 
 p2 
 s (T2 )  s (T1)  R ln  
 p1 
2
0 cp
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.
Work
wrev 
2
1 v
dp
To minimize the work input during a compression
process
► Keep the specific volume of the working fluid
as small as possible.
To maximize the work output during an expansion
process
► Keep the specific volume of the working fluid
as large as possible.
Work
Why does a steam power plant usually have a
better efficiency than a gas power plant?
Steam Power Plant
► Pump, which handles liquid water that has a
small specific volume, requires less work.
Gas Power Plant
► Compressor, which handles air that has a
large specific volume, requires more work.
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
Real Rankine Cycles
Efficiency of Pump
w s h2  h1
p 

w a h2'  h1
T
3
h2’ = (h2 – h1)/ηp + h1
2’
Efficiency of Turbine
w a h3  h4'
t 

w s h3  h4
h4’ = h3 – ηp(h3 – h4)
2
1
4 4’
S
Increase the Efficiency of a Rankine Cycle
1. Lowering the condenser
pressure
T
2. Superheating the steam
to a higher temperature
3. Increasing the boiler
pressure
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 Reheat Rankine Cycles
3
T
wp = h2 – h1 = v(p2 – p1)
qin = (h3 – h2) + (h5 – h4)
wt = (h3 – h4) + (h5 – h6)
5
4
2
1
qout = h6 – h1
h6  h1
w net
qout
 1

 1
(h3  h2 )  (h5  h4 )
qin
qin
wp
h2  h1
back work ratio 

w t (h3  h4 )  (h5  h6 )
6
S