The Haber-Bosch Process Reversible Reactions and Dynamic Equilibrium.
7-10 REVERSIBLE STEADY-FLOW WORKvps/ME321/TABLES/29.pdf · 7-10 REVERSIBLE STEADY-FLOW WORK δ δq...
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7-10 REVERSIBLE STEADY-FLOW WORK rev rev q w dh dke dpe δ δ - = + + Energy balance rev q Tds dh vdP δ = = - nd 2 Gibbs equation rev w vdP dke dpe δ = - - - 2 rev ,net ,out 1 w vdP ke pe Δ Δ =- - - ∫ ( ) 7-51 = - ∫ 2 rev ,out 1 w vdP ( ) 7-52 turbine = ∫ 2 rev ,in 1 w vdP compressor rev ,out act ,out w w ≥ rev ,in act ,in w w ≤ 7-11 Compression work for ideal gas (p.364) ( ) k 1 k 1 2 comp ,in 2 1 1 kRT P k w RT T 1 k 1 k 1 P - = - = - - - ( ) n 1 n 1 2 comp ,in 2 1 1 nRT P n w RT T 1 n 1 n 1 P - = - = - - - 2 comp ,in 1 P w RT ln P = Incompressible fluid ( v const = , 7-51) ⇒ ( ) rev 2 1 w vP P ke pe Δ Δ = - - - - ( ) 7-54 Bernoulli equation (steady flow of incompressible fluid through the simple pipe without friction) ( ) 2 2 2 1 2 1 2 1 P P V V g z z 0 2 ρ - - + + ⋅ - = ( ) 7-55 ( ) Danila Bernoulov 1700 1782 - act act rev rev act rev act rev rev act rev act Tds rev act act gen q w dh dke dpe q w dh dke dpe q q w w 0 w w q q w w q ds s 0 T T δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ - = + + - = + + - - + = - = - - = - = ≥ pipe inlet state w 0 = outlet state 1 2 q δ inlet state w δ outlet state 1 2 k Isentropic process Pv const = Isothermal process Pv const = n Polytropic process Pv const = - = 1 k v cP - = 1 n v cP 1 v cP - = P v 1 P 2 P ( ) isothermal n 1 = ( ) polytropic 1 n k < < ( ) isentropic n k = Flow through the pipe which involves no work interaction Pv RT = Ideal gas Reversible work output for steady-flow and closed systems ( ) for ke pe 0 Δ Δ = = Equations 7-57 a,b,c out Q maximum heat transfer Q 0 = T const = rev ,out act ,out w w ≥ reversible actual turbine compression P v 1 v 2 v 1 2 1 P 2 P turbine in derivation, we assume that both processes are between the same states turbine compression Steady-flow devices deliver the most and consume the least work when the process is reversible ≥ rev ,net ,out act ,net ,out w w δ δ ≥ rev act w w Eq.7-9 minimum heat transfer comp ,in w By cooling compressor, the requiered work input can be minimized to achive the same pressure increase temperature is increased P v 1 v 2 v 1 2 1 P 2 P rev ,out w turbine
Transcript of 7-10 REVERSIBLE STEADY-FLOW WORKvps/ME321/TABLES/29.pdf · 7-10 REVERSIBLE STEADY-FLOW WORK δ δq...
7-10 REVERSIBLE STEADY-FLOW WORK
rev rev
q w dh dke dpeδ δ− = + + Energy balance
rev
q Tds dh vdPδ = = − nd2 Gibbs equation
rev
w vdP dke dpeδ = − − −
2
rev ,net ,out
1
w vdP ke pe∆ ∆= − − −∫ ( )7-51
= − ∫2
rev ,out
1
w vdP ( )7-52 turbine
= ∫2
rev ,in
1
w vdP compressor
rev ,out act ,out
w w≥
rev ,in act ,in
w w≤
7-11 Compression work for ideal gas (p.364)
( )
k 1
k1 2
comp ,in 2 1
1
kRT Pkw R T T 1
k 1 k 1 P
− = − = − − −
( )
n 1
n1 2
comp ,in 2 1
1
nRT Pnw R T T 1
n 1 n 1 P
− = − = − − −
2
comp,in
1
Pw RT ln
P=
Incompressible fluid ( v const= , 7-51) ⇒ ( )rev 2 1w v P P ke pe∆ ∆= − − − − ( )7-54
Bernoulli equation (steady flow of incompressible fluid through the simple pipe without friction)
( )2 2
2 1 2 1
2 1
P P V Vg z z 0
2ρ
− −+ + ⋅ − = ( )7-55
( )
Danila Bernoulov
1700 1782−
�
act act
rev rev
act rev act rev
rev act rev act
Tds
rev act act
gen
q w dh dke dpe
q w dh dke dpe
q q w w 0
w w q q
w w qds s 0
T T
δ δ
δ δ
δ δ δ δ
δ δ δ δ
δ δ δ
− = + +
− = + +
− − + =
− = −
−= − = ≥
pipe
inlet state
w 0=
outlet state
1 2
qδinlet state
wδ
outlet state
1 2
k
Isentropic process
Pv const=
Isothermal process
Pv const=
n
Polytropic process
Pv const=
−
=1
kv cP
−
=1
nv cP
1v cP
−=
P
v
1P
2P
( )isothermal n 1=
( )polytropic 1 n k< <
( )isentropic n k=
Flow through the pipe which involves no work interaction
Pv RT=Ideal gas
Reversible work output for
steady-flow and closed systems
( )for ke pe 0∆ ∆= =
Equations 7-57 a,b,c
outQ maximum
heat transfer
Q 0=
T const=
rev ,out act ,outw w≥
reversible
actual
turbine
compression
P
v1
v2
v
1
2
1P
2P
turbine
in derivation, we assume that both
processes are between the same states
turbine
compression
Steady-flow devices
deliver the most and
consume the least work
when the process is
reversible
≥rev ,net ,out act ,net ,out
w w
δ δ≥rev act
w w
Eq.7-9
minimum
heat transfercomp ,in
w
By cooling compressor, the requiered work input
can be minimized to achive the same pressure increase
temperature
is increased
P
v1
v2
v
1
2
1P
2P
rev ,outw
turbine
