8/13/2019 Formula MECH390
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Mech 390 Formula Sheet
total energy, mass:
V
potkin dVgzuEEUE2
2
1V ,
V
dVm
Closed systems:
1stlaw, general form: WQdt
dE , 121212 WQEE , WQdE
reversible proc.:dt
dVpQ
dt
dU ,
2
1
1212 pdVQUU
specific work / heat in rev. proc.: 2
1
1212 pdv
m
Ww , 1212
2
1
1212 wuuTds
m
Qq
2ndlaw 0 genk k
k ST
Q
dt
dS
012 genk k
k ST
QSS
Open systems:
mass balance: out ein i mmdtdm
mass flow: Am V
1stlaw, general form: WQgzhmgzhmdt
dE
in
iiii
out
eeee
22
2
1
2
1VV , h=u+pv
specific work / heat in rev. proc.: 2
1
1212 vdp
m
Ww
2
1
1212 Tds
m
Qq
2ndlaw: 0 genk k
k
in
ii
out
ee ST
Qsmsm
dt
dS
Gibbs equation: pdvduTds , vdpdhTds
Liquid-vapor two phase systems (saturated states):
quality
fg
f
fg
f
fg
f
fg
f
s
ss
u
uu
vv
vv
h
hhx
properties fgf xhhh , gf xvvxv 1 , fgf xuuu , fgf xsss
Compressed liquid properties (approx.):
spec. volume TvpTv f,
spec. int. energy 00, uTTcTupTu f
specific enthalpy TppTvThpTh satff ,
entropy TspTs f,
Incompressible liquids/solids (const. specific heat):
thermal equation of state: .constv
caloric eq. of state: 00 uTTcu 000 hppvTTch
entropy:0
0
ln sT
Tcs
8/13/2019 Formula MECH390
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Ideal gases:
thermal equation of state: RTpv mRTpV RTp
gas constant, spec. heats:M
RR ,
Kkmol
kJ314.8R , Rcc vp ,
v
p
c
ck
caloric equation of state: 00
'' udTTcTuT
T v 0
0
'' hdTTcThT
T p
for const. specific heats: 00
uTTcuv
00
hTTchp
entropy 1
21
0
2
0
1122 ln,,p
pRTsTspTspTs
for const. specific heats: 1
2
1
21122 lnln,,
p
pR
T
TcpTspTs p
, 1
2
1
21122 lnln,,
v
vR
T
TcvTsvTs v
isentropic processes:
1
2
1
0
2
0
1
2
exp
exp
Tp
Tp
RTs
RTs
p
p
r
r , 1
2
1
2
Tv
Tv
v
v
r
r
for const. specific heats: .constpvk , .1 constTv k , .1
constTp kk
Carnot engines: heat engineH
LCth
T
T1, , refrigerator
1
1,
L
HCR
T
TCOP , heat pump
H
LCHP
T
TCOP
1
1,
Isentropic efficiency: compressorC
revC
Cw
w, , turbine
revT
TT
w
w
,
, nozzle2
2
rev
NV
V
Speed of sound:s
pa
|
in ideal gas: kRTa Mach number:
a
vM
Mixtures of ideal gases:
mole fraction:p
p
n
nX mass fraction:
M
MX
m
mc
molar/mass based properties, e.g. enthalpy: X hch
Psychrometrics:
humidity ratio:v
v
a
v
pp
p
m
m
622.0 relative humidity:
Tpp
sat
v
enthalpy, volume per unit mass of dry air: va hhh 1 p
TR
M
Mv a
v
a
11
Combustion:
1stlaw for open systems: WQhhNhhNnin
RfR
outPfPFuel
00
(steady state) where RR pThpThh ,,
