Post on 13-Jan-2016
description
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 1
Formulas Termodinmicas
TP
=V1 11 T
P V2 22
m=V
( )f
( )f
P n TR=V
P m TR=VM
P m T=VRM( )
P m T=V
( )
R( )
P = TR( )mV( )
P = TR( )( )
P = TR( )( )1
P = TR( )( )
n = P VTR = m
V =MV
TR( )
P z == =TR
P ( )
z = Factor de Comprensibilidad
= Volumen especifico del gas (Real)
= Volumen especifico del gas (ideal)( )
= Ctte. especifico del gasR
= Ctte. universal de los gasesR
error%( ) =P2 P1
P1* 100( )
[Lbm/mol]=mM
m = masa del gas
M = Peso molecular
n = # de moles
[gr/mol]
[gr]
[mol]
[kg/Kmol]
[kg]
[kmol]
[Lbm]
[mol]
[ft/s ]= m am = masa
a = aceleracin
F = Fuerza
[gr] [kg] [Lbm]
. [cm/s ]22
[m/s ]2
[kg. m/s ]2
2
[Lbf ]
gr. cms2
=dina
kg. m
s2=N
[gr. cm/s ]
=1 Lbf 32,174ft
2
Lbm .
s[ ]=1 Kgf 9,81m
2
Kgm .
s[ ]
= m.g
=g 9,806 [m/s ]2(SI)
=g 32,18 [ft/s ]2(INGLES)
= gravedad
w = peso [gr. cm/s ]
m = masa [gr] [kg] [Lbm]
[cm/s ]2
2
[m/s ]2
[kg. m/s ]2
[ft/s ]2
[Lbf ]
g
gr. cms2
=dina
kg. m
s2=N
=1 Lbf 32,174ft
2
Lbm .
s[ ]=1 Kgf 9,81m
2
Kgm .
s[ ]
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 2
=RH2O = densidad relativaR
[gr/cm ]3 [kg/m ]3 [Lbm/ft ]3[kg/L ] = densidad del aguaH2O
= densidad [gr/cm ]3 [kg/m ]3 [Lbm/ft ]3[kg/L ]
= 1 [gr/cm ]3H2O = 13,6 [gr/cm ]3Hg
= 1000 [kg/m ]3H2O
= 62,4 [Lbm/ft ]3H2O = 850 [Lbm/ft ]3Hg= 13.600Hg [kg/m ]3
= 1 [kg/L ]H2O
[kmol/ m ]3 = densidad especifica [gr/cm ]3 [kg/m ]3 [Lbm/ft ]3[kg/L ]
=m
V
m = masa [gr] [kg] [Lbm]
= VolumenV [m ]3[cm ]3 [ft ]3[L ]
[kg] [kmol]
[m ]3
=m V.
V = A . h( )( )
=mV
= volumen especifico [cm /gr ]3 [m /kg ]3 [ft /Lbm ]3
m = masa [gr] [kg] [Lbm]
= Volumen especificaV [m ]3[cm ]3 [ft ]3
[m /kmol ]3
[kmol]
[m ]3
[Lbmol]
[ft ]3
[ft /Lbmol ]3[L /kg ]
[kg]
[L ]
=1
=mV
= volumen especifico [cm /gr ]3 [m /kg ]3 [ft /Lbm ]3
m = masa [gr] [kg] [Lbm]
= Volumen especificaV [m ]3[cm ]3 [ft ]3
[m /kmol ]3
[kmol]
[m ]3
[Lbmol]
[ft ]3
[ft /Lbmol ]3[L /kg ]
[kg]
[L ]
w =wV = volumen especifico [dinas /cm ]3 [N/m ]3
= Volumen
= pesowV
[dinas] [N] [Lbf ]
[m ]3[cm ]3 [ft ]3
[Lbf /ft ]3w
w = g. =V A . h( )
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 3
=V
= volumen especifico [cm /gr ]3 [m /kg ]3 [ft /Lbm ]3
m = Flujo masico
= Flujo VolumetricoV
[L /kg ]
m
[gr /s ] [Kg /s ] [Lbm /s ][Kg /s]
[cm /s ]3 [m /s ]3 [ft /s ]3[L /s ]
=A = Area
= VelocidadV
[cm ] [m ] [ft ][m ]
[cm /s ] [m /s ] [ft /s ][Km /s ]V V A
= Flujo VolumetricoV [cm /s ]3 [m /s ]3 [ft /s ]3[L /s ]
2 2 2 2
m=V
= A = Area= VelocidadV
[cm ] [m ] [ft ][m ]
[cm /s ] [m /s ] [ft /s ][Km /s ]
V V A= Flujo VolumetricoV [cm /s ]3 [m /s ]3 [ft /s ]3[L /s ]
2 2 2 2
1 atm = 760 [mmHg] 76 [cmHg] 0,760 [mHg]= =1 atm = 101325 [Pa] 101,325 [KPa] 1,01325 [bar]= =
1 atm = 29,921 [inHg] 2,493 [ftHg]=1 atm = 14,7 [Lbf/in ]2 = 14,7 [psi ]
1 bar = 10 [Pa] 10 [KPa]= 0,1 [MPa]=25 =1 Lbf 32,174
ft2
Lbm .
s[ ]=1 Kgf 9,81m
2
Kgm .
s[ ]
[in ]
F = Fuerza
A = rea
P = Presin
[dinas] [kg] [Lbf ]
[cm ]2
2
[m ]2
[N/m ]2
2
[Lbf/in ]
Nm2=
Pa
[dinas/cm ]
=FA 2 =1 N 10 dinas5
=1 Kgf 9,8 N
Patm
manP
absP
P vacio
Pabs
Pabs Patm Pman> +PmanPabs Patm
Pabs = [psia]Pman = [psig]{
Pabs Patm Pman= +Patm PabsPvac =
Pbaro
Pvacio
=Pbaro PabsPvac =Patm PabsPman
BAROMETRO
1
Pabs
2
h Pman
Patm
MANOMETRO
Pabs Patm Pman= +Pabs Patm (.g.h)= +
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 4
= mV
T
T
= fg +V V
fmm g +
= mV
= f+fmm g +
g m g fm
=fmm g +
g m g +fmm g +
f fm
= g fx)( + 1 - x)(
X =m g
fmm g +X =
g
fg +V VV
X =m g
mX =
g
totalVV
total
= g fx)( + 1 - x)(
= g fx)( + x)(- f
= x+ g )( - ff
Donde = g )( - ffg
= x+ fg )(f
=+ fgf
x
CALIDAD DE VAPOR ( )X
masa Vapor saturado
Calidad de VaporX =m g =
masa Liquido saturadom f =Volumen de Vapor saturado=gVVolumen de Liquido saturado=fVVolumen especifico del Vaporg =Volumen especifica del Liquidof =Volumen especifica entre (Vp - Lq) saturado=fg
Escalas Absoluta ( K , R )
Senala el cero de la temperatura, como el cero absoluto
o o
Escalas Relativa ( C , F )
No senala el cero de la temperatura, como el cero absoluto
o o
=5
Co
= =5
Ko - 273
9
Ro - 492 Fo
9
- 32
LEY CERO DE TERMODINAMICA
Cuando dos sistemas, se encuentran en equilibrio termico con un 3er sistemaEste 3er sistema, es un termonetro
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 5
0.01704 18.04
0.07811 78.11
86.469
0.04401 44.01
0.02801 28.01
0.11203 112.03
0.03007 30.07
0.02805 28.05
0.004003 4.003
0.002016 2.016
0.01604 16.04
0.02801 28.01
0.03200 32.00
0.04409 44.09
0.06406 64.06
0.03402 34.02
Amoniaco
Bencelo
Dioxido de Carbono
Monoxido de Carbono
Refrigerante 134a
Etano
Etileno
Helio
Hidrogeno
Metano
Oxigeno
Dioxido de Azufre
Agua Oxigenada
Nitrogeno
Propano
masa molecular (M) molKg[ Kmol
Kg[
0.01802 18.02Agua ( )H2O
NH3
C6H6
CO2
CO
C2F4H2
C2H6
C2H4
H2
He
CH4
N2
O2
C3H8
SO2
H2O2
0.03994 39.94Argon Ar
0.02897 28.97Aire
( )
( )
0.086469Refrigerante R-22 ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
R-22
0.02604 26.04Acetileno ( )C2H2
masa molecular (M) molKg[ Kmol
Kg[
0.02697 26.97
0.01201 12.01
0.05585 55.85
0.20720 207.20
0.20060 200.60
0.039096 39.096
0.10788 107.88
0.022997
42.08
0.07215 72.15
0.11422 114.22
0.03205 32.05
0.04607 46.07
0.070914 70.914
Aluminio
Carbon
Hierro
Plomo
Mercuirio
Potasio
Plata
Sodio
n-Octano
Alcohol Etilico
Cloro
n-Pentano
Alcohol Metilico
Al
C
Fe
Pb
Hg
K
Ag
Na
C5H12
C8H18
CH3OH
C2H5OH
Cl2
22.997
0.03800 38.00
0.017008 17.008
0.030008
0.034086 34.086
0.070914 70.914
Hidroxilo
Sulfuro de Hidrogeno
Oxido Nitroso
Fluor
Oxido Nitroso
F2
OH
NO
H2S
N2O
30.008
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
0.05812n-Butano C4H10( )
0.04208Propileno C3H6( ) 42.08
P
T
PT
PC
a f
d
b
a fLiquido Sub-enfriado
f bVapor Sobre-calentado
a
dLiquido Comprimido
Solido
Liquido
Vapor
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 6
P
T
PT
PC
a f
d
b
a fLiquido Sub-enfriado
f bVapor Sobre-calentado
a
dLiquido Comprimido
Solido
Liquido
Vapor
P
T
a f
TSAT
P SAT
PT
T
P
T
a
d
P
PT
P C
TSAT
P SAT
P
TTSAT
P SAT
PT
PC
f b
T
PC
Ing. Franz Vallejos lvarez ingeltvaf@gmail.com 7
SISTEMA TERMODINMICO
Es una porcin limitada de espacio, que se elige arbitratoriamente, para realizar un estudio termodinmico
P
T
a f
TSAT
P SAT
PT
T
PC
P
T
a
d
P
PT
P C
TSAT
P SAT
P
TTSAT
P SAT
PT
PC
f b
T
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