formula - termodinÁmica - vaf

Ing. Franz Vallejos Álvarez – [email protected] 1

Formulas Termodinámicas

TP

=V1 1

1 TP V2 2

2

m=V

( )f

( )f

P n TR=V

P m TR=VM

P m T=V RM( )

P m T=V

( )

R( )

P = TR( )mV( )

P = TR( )( )

P = TR( )( )1

P = TR( )( )

n =P V

TR = 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 = aceleración

F = Fuerza

[gr] [kg] [Lbm]

. [cm/s ]2

2

[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[ ]


=R

H2O = 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 ]3

Hg

= 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


= 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


= 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 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( )


=V


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 = Área

P = Presión

[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)= +


= mV

T

T

=fg +V Vfmm 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 F

o

9

- 32

LEY CERO DE TERMODINAMICA

Cuando dos sistemas, se encuentran en equilibrio termico con un 3er sistemaEste 3er sistema, es un termonetro


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) mol

Kg[ 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) mol

Kg[ 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


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


SISTEMA TERMODINÁMICO

Es una porción limitada de espacio, que se elige arbitratoriamente, para realizar un estudio termodinámico

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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