Ciclo brayton termodinâmica

3. 1
2 2
1 1
k
kT P
T P
−
=
2 2 1
1 1 2
P T V
P T V
=
1
1 2
2 1
k
V P
V P
=
2 1
12 2 1
s s
w u u
=
= −
1 1
1
2 2
2
PV
mR
T
PV
mR
T
=
=
1 1 2 2
k k
PV PV=
PV mRT=
k
PV C=
{
2
1
p
P
r
P
=
∆ ∆ ∆
1
2
1
k
k
p
T
r
T
−
=

4. 2
2 2
3
3 3
V mR
T P
V mR
T P
=
=
3 3
2 2
T V
T V
=PV mRT=
( )23 2 3 2
23 23 3 2
0
w P v v
q w u u
s
= −
− = −
∆ >
2 3P P=
( ) ( ) ( )23 3 2 2 3 2 3 2 3 2in pq q u u P v v h h c T T= = − + − = − ≅ −
∆ ∆ ∆

5. 3 3
3
4 4
4
PV
mR
T
PV
mR
T
=
=
3 3 4
4 4 3
P T V
P T V
=
1
34
3 4
kPV
V P
=3 3 4 4
k k
PV PV=
4 3
34 4 3
s s
w u u
=
= −
PV mRT=
k
PV C=
{
∆ ∆ ∆
1
3 3
4 4
k
kT P
T P
−
=
32
1 4
p
PP
r
P P
= =
1
3 2
4 1
k
k
p
T T
r
T T
−
= =
2 3
4 1
P P
P P
=
={

6. 4
4 4
1
1 1
V mR
T P
V mR
T P
=
=
4 4
1 1
T V
T V
=PV mRT=
( )41 4 1 4
41 41 4 1
0
w P v v
q w u u
s
= −
− = −
∆ >
1 4P P=
( ) ( ) ( )41 1 4 4 1 4 1 4 1 4out pq q u u P v v h h c T T= = − + − = − ≅ −
∆ ∆ ∆

7. 1
_ 1
k
k
th Brayton prη
−
= −
( )
( )
3 2 3 2
4 1 4 1
in p
out p
q h h c T T
q h h c T T
= − ≅ −
= − ≅ −
_ 1liq out
th Brayton
in in
w q
q q
η = = −
( )
( )
4 1
_
3 2
1
p
th Brayton
p
c T T
c T T
η
−
= −
−
4
1
1
_
3
2
2
1
1
1
th Brayton
T
T
T
T
T
T
η
−
= −
−
3 4
2 1
1
2
1
k
k
p
T T
T T
T
r
T
−
=
=
Brayton_Real 35% 45%η ≅ −
1,4k =

8. 1
3 2
4 1
k
k
p
T T
r
T T
−
= =

14. η

15. 2
1
1
1,4
8
300 K
p
k
P
r
P
T
=
= =
=
0,2857
2 300 8 543,43 KT = × =
1
2
2 1
1
k
kP
T T
P
−
=
32
1 4
3
1,4
8
1.300 K
p
k
PP
r
P P
T
=
= = =
=
4 0,2857
1.300
717,66 K
8
T = =
1
3 2
4 1
k
k
p
T T
r
T T
−
= =
1
2
300 K
543,43 K
T
T
=
=
1
2
300,19 kJ/kg
547,914 kJ/kg
h
h
=
=
3
4
1.300 K
717,66 K
T
T
=
=
3
4
1.395,97 kJ/kg
732,297 kJ/kg
h
h
=
=

16. 1
_ 1 1
k
k liqout
th Brayton p
in in
wq
q q
rη
−
= = − =−
liq in outw q q= − 760,353 419,748 340,605 kJ/kgliqw = − =
0,2857
_
419,748 340,605
1 8 1
760,353 760,353
th Braytonη −
= − = − = _ 44,79%th Braytonη =
( )23 3 2in pq q c T T= ≅ − ( )1,005 1.300 543,43 760,353 kJ/kginq = − =
( )41 4 1out pq q c T T= ≅ − ( )1,005 717,66 300 419,748 kJ/kgoutq = − =
c
ct
t
w
r
w
=
2 1cw h h= −
3 4tw h h= −
547,914 300,19 247,72 kJ/kgcw = − =
1.395,97 732,297 663,67 kJ/kgtw = − =
247,72
37,3%
663,67
ctr = = ∆

17. 2
2
544,18 kJ/kg
539,836 K
h
T
=
=
2 2
1 1
1
8
1,3860
r
p
rs
r
P P
r
P P
P
= = =
=
2 8 1,3860 11,088rP = × =
1 300 KT =
1
1
300,19 kJ/kg
1,3860r
h
P
=
=
3 1.300 KT =
3
3
1.395,97 kJ/kg
330,9r
h
P
=
=

18. 4
4
789,386 kJ/kg
872,422 K
h
T
=
=
3 3
4 4
3
8
330,9
r
p
rs
r
P P
r
P P
P
= = =
=
4
330,9
41,3625
8
rP = =
_ 1 liqout
th Brayton
in in
wq
q q
η = − =
liq in outw q q= − 851,79 489,196 362,259 kJ/kgliqw = − =
_
489,196 362,259
1
851,79 851,79
th Braytonη = − = _ 42,53%th Braytonη =
( )23 3 2inq q h h= = − ( )1.395,97 544,18 851,79 kJ/kginq = − =
( )41 4 1outq q h h= = − ( )789,386 300,19 489,196 kJ/kgoutq = − =
_ 44,79%th Braytonη =

19. c
ct
t
w
r
w
=
2 1cw h h= −
3 4tw h h= −
544,18 300,19 243,99 kJ/kgcw = − =
1.395,97 789,386 606,584 kJ/kgtw = − =
243,99
40,2%
606,584
ctr = =
247,72
37,3%
663,67
ctr = =
liq t c
liq in out
w w w
w q q
= −
= −
415,95 kJ/kg
340,605 kJ/kg
liq
liq
w
w
=
=
liq t cw w w= − 606,584 243,99 362,594 kJ/kgliqw = − =

20. 2 1
2 1
cs s
c
cr r
w h h
w h h
η
−
= ≅
−
3 4
3 4
tr r
t
ts s
w h h
w h h
η
−
= ≅
−

21. η
η
η

22. cs
c
cr
w
w
η =
tr
t
ts
w
w
η =
243,99 kJ/kgcsw =
0,80cη =
243,99
304,99 kJ/kg
0,8
cs
cr
c
w
w
η
= = =
0,85cη =
606,584 kJ/kgtsw =
0,85 606,584 515,6 kJ/kgtr t tsw wη= × = × =
cr
ctr
tr
w
r
w
=
304,99
59,2%
515,6
ctrr = =
_ 40,2%ct idealr =

23. liq
th
in
w
q
η =
liq tr crw w w= − 515,6 304,99 210,66 kJ/kgliqw = − =
3 2in rq h h= −
2 1cr rw h h= − 2 1r crh h w= +
1
3
300,19 kJ/kg
1.395,97 kJ/kg
h
h
=
=
2 300,19 304,9 605,09 kJ/kgrh = + =
1.395,97 605,09 790,88 kJ/kginq = − =
_
210,66
26,6%
790,88
liq
th Brayton
in
w
q
η = = =
_ 42,53%th Braytonη =
_ 44,79%th Braytonη =

24. 3 4tr rw h h= −
3 1.395,97 kJ/kgh =
4 1.395,97 515,6 880,37 kJ/kgrh = − =
4 3r trh h w= −
4 852,88 KrT =
4 852,88 KrT =
2 605,09 kJ/kgrh = 2 598,62 KrT =
254,18 KT∆ =