Thermodynamics:
Equation Sheets:
Chap 1:
number of moles
m
n 
v 
M
v
M
Temperature Conversions:
R  1 .8 K
F  R  4 5 9 .6 7
C  K  2 7 3 .1 5
F  1 .8 C  3 2
--------------------------------------------------------------------------------------------------------------Chap 2: Energy balance of closed system
Energy Rate balance of close system
dE
U  KE  PE  Q  W
 Q W
dt
Work due to action of a force
Work due to compression of a fluid
r2
W 
V2
F
dr  F
W 
V
r1

pdV
V1
Kinetic Energy
KE 
1
mV
Gravitational Potential Energy
PE  m gz
2
2
Energy Balance: Power Cycle
Power Cycle Efficiency
 
W c y c le  Q in  Q o u t
W c y c le
Q in
Energy balance: Ref and Heat Pump
Refrigeration COP
 
W c y c le  Q in  Q o u t
Heat Pump COP
Q in
 
W c y c le
Q out
W c y c le
-----------------------------------------------------------------------------------------------------------------Chap 3:
Quality
Polytropic Process
v  v f  x (v g  v f )
x 
m vapor
u  u
m liq u id  m v a p o r
f
 x (u g  u f )
pV
N
 c o n s ta n t
h  h f  x (hg  h f )
Ideal Gas Model:
pv  RT
pV  m RT
or
 U  m  cv d T  m cv  T
c p  cv  R
cp 
kR
k 1
or
pV  nRT
H  m  c p dT  m c pT
cv 
R
k 1
Compressibility Model:
pv
Z 
pv

RT
p
pR 
RT
TR 
pc
Chap 4: Continuity Equation:
AV
m 

v
T
v 'R 
Tc
v
R Tc / p c
Mass balance for CV:
V
dm
v
dt


mi 
i

me
e
Energy Balance for CV
d E cv
 Q cv  W cv 
dt

Vi
m i ( hi 
2
i
Simplified Nozzle/Diffuser model:
2
 gzi ) 
m e ( he 
Ve
e
2
2
 gze )
Simplified Turbine model:

Vi  
Ve 
0   hi 
   he 

2  
2 

2

2
0   W cv  m ( hi  he )
Simplified Compressor/Pump model
Simplified Throttling model
0  hi  he
0   W cv  m ( hi  he )
Simplified Heat Exchanger model
0 

mi 

i
0 
me

m i hi 

i
e
m e he
e
----------------------------------------------------------------------------------------------------Chap 5: 2nd Law Efficiency
2nd Law COP
 m ax  1 
TC
 m ax 
TH
TC
 m ax 
T H  TC
TH
T H  TC
Clausius Inequality:

Q 

  
 T b
c y c le
------------------------------------------------------------------------------------------------------Chap 6: Closed System Entropy Balance
Closed System Entropy Rate Balance
2
S 2  S1 
Q 
 
T b
 
1
dS
c y c le
Control Volume Entropy Balance
dS
dt


Q
T


m i si 

m e se  
dt


Q
T

Isentropic Efficiencies:
Turbine
 tu r b in e 
W cv / m
W
cv
/m


s
Nozzle
h1  h 2
Compressor/Pump
2
 n o z z le 
h1  h 2 s
V2 / 2
 co m p ress 
2
(V 2 / 2 ) s
 W
cv
/m

s
W cv / m

h 2 s  h1
h 2  h1
Ideal Gas Model Relations:
s ( T 2 , v 2 )  s ( T 1 , v 1 )  c v ln
T2
 R ln
T1
v2
s ( T 2 , p 2 )  s ( T1 , p 1 )  c p ln
v1
T2
 R ln
T1
p2
p1
or
s ( T 2 , p 2 )  s ( T1 , p 1 )  s ( T 2 )  s ( T1 )  R ln
o
o
p2
p1
Isentropic Ideal Gas relationships (when s1 = s2)
 p2 
 

T1
 p1 
( k 1 ) / k
 v1 
 

T1
 v2 
T2
k 1
T2
p2
p1

p2
p1
pr2
v2
p r1
v1

 v1 
 

 v2 
k
vr 2
v r1
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