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. 1
Thermodynamics
.
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. 2
/
:
1.
2. 3.
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. 3
m kg( lb) V m3 ( ft3, ) kg/m3 ( lb/ft3) v , m3/kg (ft3/lb) v = 1 /
= x ( m = V. )oC, K=273+oC
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F (m)
(a) m/s2
(ft/s
2
)
F = m.a kg.m/s2 N
[ lbf (1 lbf=4.448 N ) kg
f (1 kgf= 9.81 N) ]
P N/m2 Pa ( psi =lbf/in2)
:
= + kPa = kPag + 101.3 ( psia = psig + 14.7 )
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PVAP =X .L. g + PATM Pa P
VAP=
X.L. g
120 mm.Hg 120
=13,600x(120/1000)x9.81=16,010 Pa = 16,010 + 101,325 =117,335 Pa
PVAP
Y X
L
PATM
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38 Pa 2 m2? F = A.DP = 2 m2 x 38 N/m2 = 76 N 76/9.81 =7.7kg
P=38 Pa
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101.325 kPa 10.33 m 760 mm
u SI-> kJ/kg (PI)->Btu/lb
h(u+Pv) SI-> kJ/kg (PI)->Btu/lb
s
SI-> kJ/(kg.K) (PI)->Btu/(lb.F) s s
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(Saturated liquid and Saturated Vapour)(Saturation)
(Saturation/Saturated
Point/State) ... (SATURATED....TABLE) 101.3 kPa
100oC
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PS, kPa T
S, oC v
f,m3/kg
vfg,m
3/kg -
vg,m3/kg
5 32.88 0.001005 28.1900 - 0.001005 28.1900
1.6729
0.3749
0.1944
101.3 100 0.001044 1.6729 - 0.001044
500 151.86 0.001093 0.3749 - 0.001093
1000 179.91 0.001127 0.1944 - 0.001127
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m3/kg
(oC) (kPa) T P vf vfg vg
0.01 0.6113 0.001000 206.131 206.132
5 0.8721 0.001000 147.117 147.118
10 1.2276 0.001000 106.376 106.377
15 1.705 0.001001 77.924 77.925
20 2.339 0.001002 57.7887 57.7897
25 3.169 0.001003 43.3583 43.3593
30 4.246 0.001004 32.8922 32.8932
35 5.628 0.001006 25.2148 25.2158
40 7.384 0.001008 19.5219 19.5229
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/Compressed/Subcooled Liquid
30oC
4.246 kPa 101.3 kPa
30oC
30oC
/
9.9 m
0.76 m
=(101.3-4.246)x1000/(1000x9.81) =9.9 m
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Satured Liquid
100oC
101.3 kPa
101.3 kPa
100oC
100oC
100oC 30
oC 0.03 kPa ( 101.3 )
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\ 134a 22 290(Propane)
F C psig kPag psig kPag psig kPag
26 -3.3 22.9 158 49.9 344 47.3 326
28 -2.2 24.5 169 52.4 361 49.5 342
30 -1.1 26.1 180 54.9 379 51.8 357
32 0.0 27.8 192 57.5 396 54.1 373
34 1.1 29.5 203 60.1 414 56.5 389
36 2.2 31.3 216 62.8 433 58.9 406
38 3.3 33.1 228 65.6 452 61.4 423
40 4.4 35.0 241 68.5 472 63.9 441
42 5.6 37.0 255 71.5 493 66.5 459
44 6.7 39.0 269 74.5 514 69.2 477
46 7.8 41.1 283 77.6 535 71.9 496
48 8.9 43.2 298 80.8 557 74.7 515
50 10.0 45.4 313 84.0 579 77.6 535
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\ 134a 22 290(Propane)
F C psig kPag psig kPag psig kPag
100 37.8 124.1 856 195.9 1351 173.9 1199
102 38.9 128.4 885 201.8 1391 178.8 1233
104 40.0 132.7 915 207.7 1432 183.9 1268
106 41.1 137.2 946 213.8 1474 189.0 1303
108 42.2 141.7 977 220.0 1517 194.2 1339
110 43.3 146.4 1009 226.4 1561 199.6 1376
112 44.4 151.1 1042 232.8 1605 205.0 1413114 45.6 155.9 1075 239.4 1651 210.6 1452
116 46.7 160.9 1109 246.1 1697 216.2 1491
118 47.8 166.0 1145 252.9 1744 221.9 1530120 48.9 171.1 1180 259.9 1792 227.8 1570
122 50.0 176.4 1216 267.0 1841 233.3 1611
124 51.1 181.8 1254 274.3 1891 239.8 1653
126 52.2 187.3 1291 281.6 1942 245.9 1695
128 53.3 192.9 1330 289.1 1993 252.2 1739
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101.3 kPa 30oC
10%
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. 16
( SUBCOOLED /COMPRESSED LIQUID )
:-1 (T
S)
2 (PS)
3
(vf)
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. 18
/ (SUPERHEATED VAPOUR)1 (TS)
2 (PS)
3
R22 (Saturated R 22)
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R22 (Saturated R-22)
m3/kg
kJ/kg
o
C kPa T P v v v u u u-10 354.3 0.000759 0.06458 0.06534 32.74 190.25 222.99-5 421.3 0.000768 0.05457 0.05534 38.44 186.33 224.77
0 497.6 0.000778 0.04636 0.04714 44.20 182.30 226.505 583.8 0.000789 0.03957 0.04036 50.03 178.15 228.1710 680.7 0.000800 0.03391 0.03471 55.92 173.87 ?29.7915 789.1 0.000812 0.02918 0.02999 61.88 169.47 231.3520 909.9 0.000824 0.02518 0.02590 67.92 164.92 232.85
25 1043.9 0.000838 0.02179 0.02262 74.04 160.22 234.2630 1191.9 0.000852 0.01889 0.01974 80.23 155.35 235.5935 1354.8 0.000867 0.01640 0.01727 86.53 150.30 236.8240 1533.5 0.000884 0.01425 0.01514 92.92 145.02 237.94
45 1729.0 0.000902 0.01238 0.01328 99.42 139.50 238.9350 1942.3 0.000922 0.01075 0.01167 106.06 133.70 239.7655 2174.4 0.000944 0.00931 0.01025 112.85 127.56 240.4160 2426.6 0.000969 0.00803 0.00900 119.83 121.01 240.8465 2699.9 0.000997 0.00689 0.00789 127.04 113.94 240.98
70 2995.9 0.00103 0.00586 0.00689 134.54 106.22 240.7675 3316.1 0.001069 0.00491 0.00598 142.44 97.61 240.05
R22 (Saturated R-22) ()
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R22 (Saturated R-22) ()
,kJ/kg kJ/kg.K
o
C kPa T P hf hfg hg sf sfg sg-10 354.3 33.01 213.13 246.14 0.1324 0.8099 0.9422-5 421.3 38.76 209.32 248.09 0.1538 0.7806 0.93440 497.6 44.59 205.36 249.95 0.1751 0.7518 0.92695 583.8 50.49 201.25 251.73 0.1963 0.7235 0.919710 680.7 56.46 196.96 253.42 0.2173 0.6956 0.912915 789.1 62.52 192.49 255.02 0.2382 0.6680 0.906220 909.9 68.67 187.84 256.51 0.2590 0.6407 0.8997
25 1043.9 74.91 182.97 257.88 0.2797 0.6137 0.893430 1191.9 81.25 177.87 259.12 0.3004 0.5867 0.887135 1354.8 87.70 172.52 260.22 0.3210 0.5598 0.880940 1533.5 94.27 166.8s 261.15 0.3417 0.5329 0.874645 1729.0 100.98 160.91 261.9 0.3624 0.5058 0.8682
50 1942.3 107.85 154.58 262.43 0.3832 0.4783 0.861555 2174.4 114.91 147.80 262.71 0.4042 0.4504 0.854660 2426.6 122.18 140.50 262.68 0.4255 0.4217 0.847265 2699.9 129.73 132.55 262.28 0.4472 0.3920 0.8391
70 2995.9 137.63 123.77 261.40 0.4695 0.3607 0.830275 3316.1 145.99 113.90 259.89 0.4927 0.3272 0.8198
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R22(Superheated R-22)
oC m
3/kg kJ/kg kJ/kg.K m
3/kg kJ/kg kJ/kg.K m
3/kg kJ/kg kJ/kg.K
T v h s v h s v h s
Pressure 1000 kPa Pressure 1200 kPa Pressure 1400 kPaSat. 0.0236 257.46 0.8954 0.0196 259.18 0.8868 0.0167 260.48 0.879230 0.0246 262.91 0.9136 40 0.0260 271.04 0.9400 0.0209 267.60 0.9141 0.0171 263.86 0.8901
50 0.0273 279.05 0.9651 0.0221 276.01 0.9405 0.0183 272.77 0.918160 0.0286 286.97 0.9893 0.0232 284.26 0.9657 0.0193 281.40 0.944470 0.0298 294.86 1.0126 0.0243 292.42 0.9898 0.0203 289.86 0.969480 0.0310 302.73 1.0352 0.0253 300.51 1.0131 0.0213 298.20 0.9934
90 0.0322 310.6 1.0572 0.0264 308.57 1.0356 0.0222 306.47 1.0165100 0.0334 318.49 1.0786 0.0274 316.62 1.0574 0.0231 314.70 1.0388
R22 (Superheated R-22)
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. 22
R22(Superheated R-22)
o
C m3
/kg kJ/kg kJ/kg.K m3
/kg kJ/kg kJ/kg.K m3
/kg kJ/kg kJ/kg.K
T v h s v h s v h s
Pressure 1600 kPa Pressure1800 kPa Pressure 2000 kPa
Sat. 0.0145 261.43 0.8724 0.0127 262.10 0.8659 0.0113 262.53 0.8598
50 0.0154 269.26 0.8969 0.0131 265.42 0.8763
60 0.0164 278.36 0.9246 0.0140 275.10 0.9057 0.0121 271.56 0.8873
70 0.0173 287.17 0.9507 0.0149 284.33 0.933 0.0130 281.31 0.9161
80 0.0182 295.80 0.9755 0.0158 293.28 0.9588 0.0138 290.64 0.9429
90 0.0190 304.30 0.9992 0.0166 302.05 0.9832 0.0146 299.7 0.9682100 0.0198 312.73 1.0221 0.0173 310.68 1.0067 0.0153 308.57 0.9923
110 0.0206 321.10 1.0442 0.0180 319.24 1.0293 0.0160 317.32 1.0155
120 0.0214 329.46 1.0658 0.0187 327.75 1.0512 0.0166 325.99 1.0378
170 0.0250 371.39 1.1661 0.022 370.19 1.1528 0.0197 368.97 1.1407
180 0.0257 379.87 1.1851 0.0227 378.74 1.1719 0.0203 377.60 1.1600
190 0.0264 388.40 1.2037 0.0233 387.33 1.1907 0.0208 386.25 1.1788
200 0.0271 396.97 1.222 0.0239 395.96 1.2091 0.0214 394.94 1.1974
P T 3
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P-v-Tsurface of a substancethat contractson freezing. P-v-Tsurface of a substance thatexpandson freezing (like water).
P-v-T 3
2 P-v T-v
- (P-h Diagram)
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-(P-h Diagram)
T4T3T2T1P
(Critical Point)
T=5oC
h
-40oC 5oC 50oC
3
2
1
50oC
-40oC
s1s2
s3
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oC
MPa
m3/kg
kg/ m3
374.14 22.09 0.003155 317CO
231.05 7.39 0.002143 467
O2
118.35 5.08 0.002438 410
N2
146.95 3.39 0.003215 311
H2
239.85 1.3 0.032192 31
CH4=NGV 82.75 4.6 0.00615 163
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100 kPa 100 m3
101 kPa m3?
(V)(T)P
1/m
1=P
2/m
2
m2=(P
2/P1)m
1
m2=(101/100)m
1=1.01m
1
() 1% 1 m3
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N-m J J/s W 2
(Heat),Q (Work), W (Power)
(Q)(W)
(Heat) Q
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(Heat),Q
25OC 500
OC 25
OC
273OC
(Work),W (E)(I) W = E.I W=E.I cos
3 W = 1.732E.I cos
(U)(KE)
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(U)(KE) (PE)(U) uf= 0 kJ/kg 0.01 oC
Propane (R-290)
(H)
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(H)(U) PV()(Flow work) H = U + PV h = u + Pv
m kg
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m kg V m/s
KE =mV2/2000 .(1.8)
ke = V2/2000 .(1.8a)
KE kJ ke kJ/kg
m kg g m/s2
PE = mgZ/1000.(1.9)
pe = gZ /1000 .(1.9a)
KE kJ pe kJ/kg
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E = mc2 E (J)m c 3x10
8E = mx(3x108)2=9x1016m (J)
1 .
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.
34
9x1016
J
1 J 1/(9x1016) = 1.1x10-17
(1)
mi1
mi -me =mCV2- mCV1 =mCV
mi2
mi3
me1
me2
mCV1 mCV2
(2)
1 Thermodynamics
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1
()
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() (Q)(W) :
Q =W (Q+W)in=(Q+W)out (Q
L) 10
kW(WC) 2 kW
QH= QL+WC= 10+2 = 12 kW
QH
QL
WC
1
23
4
QH+ QL= WC QL+WC = QH
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1 (PROCESS)
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1Q
2= (E
2-E
1) +
1W
2
1Q
2=E +
1W
2
1Q2= (U2-U1) + (mV2
2/2 - mV2
1/2) + (mgZ2-mgZ1)+ 1W2(1.12b)Q =U+KE+PE+W (1.12c)
1q
2=(u
2-u
1) + (V
2
2-V
2
1)/2+(Z
2-Z
1)g +
1w
2(1.12d)
u1+V21/2+Z1g
m
u2+V22/2+Z2g
m
1Q
2 1W2/
1Q
2-1W
2=E
1Q
2- 1W2 = (U2-U1) + (mV
22/2 - mV2
1/2) + (mgZ
2-mgZ
1)
Q - W =U+KE+PE1
q2
-1
w2
=(u2
-u1
) + (V2
2
-V2
1
)/2+(Z2
-Z1
)g
1 2
1 (PROCESS) ( )
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1 (PROCESS)()
U = 0
Q = WE
WE
Q
Q =U+KE+PE+W Q-W =U+KE+PE
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W= dPV
dV
Q
Q = d(U+PV) = dH q = dhQ = H
2-H
1= m (h
2-h
1)
q = h2- h1
Q = dU+ W =dU+PdV
W d(PV)
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W=d(PV)
dV
WE
-WE = d(U+PV) = dH -wE = dh-W
E= H
2-H
1= m (h
2-h
1)
-wE = h2- h1
-WE
= dU+ W =dU+PdV
W d(PV)
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W =d(PV)
dV
WE
Q - WE = d(U+PV) = dH q - wE = dhQ -W
E= H
2-H
1= m (h
2-h
1)
q-wE = h2- h1
Q
Q-WE
= dU+ W =dU+PdV
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20O
C 21O
C1kg 1kg
qV
20OC
1kg
qP
21OC
1kg
qV= q
P?
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20OC 21OC
1kg 1kg
q q = u2- u1
20OC
1kg
q
q = h2- h
1
21OC
1kg
q = dh
q = du
CV
=
CP=
CV= 0.717 kJ/(kg.K)
CP
= 1.004 kJ/(kg.K)
u2- u
1= C
V(T
2-T
1)
h2- h1= CP(T2-T1)
25OC, 100 kPa
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,
Cpo Cvo k kg/m3 kJ/kg-K kJ/kg-K
0.0231 1.872 1.410 1.327
1.05 1.699 1.380 1.231
1.169 1.004 0.717 1.400
0.694 2.130 1.642 1.297 1.613 0.520 0.312 1.667 C
P= C
V= C
Dh =D
u = CD
T
1 (PROCESS)
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.47
(1)
mi1
mi2
mi3
me1
me2
mCV1 mCV2
(2)
mi -me =mCV2- mCV1 =mCV
1 (PROCESS)
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(Steady Flow Process)
(mCV = 0)
kg/s5
im =
kg/s5em =
(1.26a)......emim
=
)(1.26......emim =
m3/s-
1 (PROCESS)
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(Uniform Flow Process)
() ()
(1) (2)
mi1
(h+V2/2+Zg)i1
W [(1)(2)]
Q [(1)(2)]Q W = m
e(h + V
2/2+Zg )
e- m
i(h + V
2/2+Zg )
i+ E
CV2- E
CV1
Q W = me (h + V2/2+Zg )e - mi (h + V2/2+Zg )i +(ECV2- ECV1)/t
mi2(h+V2/2+Zg)i2
mi3
(h+V2/2+Zg)i3
me1
(h+V2/2+Zg)e1
me2
(h+V2/2+Zg)e2
ECV1
ECV2
1 (PROCESS)(Steady Flow Process)
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(Steady Flow Process)
() ()
mi1
(h+V2/2+Zg)i1
W [(1)(2)]
Q W = me
(h + V2/2+Zg )
e- m
i(h + V
2/2+Zg )
i
Q W = me (h + V2/2+Zg )e - mi (h + V2/2+Zg )i(1) (2)Q [(1)(2)]
mi2(h+V2/2+Zg)i2
mi3
(h+V2/2+Zg)i3
me1
(h+V2/2+Zg)e1
me2
(h+V2/2+Zg)e2
mCV
= 0 ECV
= 0
(Steady Flow Process)()
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Q = me(h + V2
/2+Zg )e mi(h + V2
/2+Zg )i + W kJ.(1.27)
Q =
me(h + V2
/2+Zg )e
mi (h + V2
/2+Zg )i +
W kW .(1.27
Q = mehe mi h i +W kJ ...(1.27Q =
mehe
mi h i +
W kW .(1.27
(Steady Flow Process)
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1 1
Q =
m h + W kW (1.27j)
Q = h + W kJ (1.27k)q = h +w kJ/kg (1.27l)
WQ
hi he
m m
Cengel-Boles
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Q = 0 (q=0), W = We+WshW
eW
sh
when kinetic and potential energychanges are negligible
1000 kJ
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-P
e>>P
i
W = m h+ Q w = h+q
W =
m (Pv +u)+ Q w = (Pv+u)+q
v u= CT W =
m (vP + CT)+ Q
w = ( vP+ CT)+q ..(1.28)
() Q q 0 u= CT = 0 (
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Q q (
) W =
m vP = V P w = vP ..(1.29)
1.23 0.1 m3/s101 kPa 303 kPa
() W =
V P
m .v =V m
3/s 0.1 m3/s , Pi = 101 kPa
Pe
= 303 kPa
W = 0.1 ( 303 101 ) = 20. 2kW
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DZ
Q =
m [(he-hi) + (V
2
e/2 -V2
i/2) + g (Ze-Zi)] +W
++++= W)g]Z-(Z/2)V-/2(V)vPv(P)u[(umQ ie2
i
2
eiieeie
W =
m (Zi Ze)g
W
()
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DZ
W=
m (Z
i
Ze
)g Watt, W = m (Zi
-Ze
)g Joul
W
100 m 1 m3 kW.h
W = (1m3
*1000kg/m
3
)*100m*9.81m/s
2
=981000 N.mW = 981000 J = 981000/3,600,000 kW.h =0.2725 kW.h
1 = 1 kW.h = 3.6 MJ = 3,600 kJ = 3,600,000 J
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Q = mh = m ( h h )m =
kg/s
h = kJ/kgQH
23
QL
14
m m
QH
= m ( h3 h
2) Q
L= m ( h
1 h
4)
hb- ha= CP(Tb-Ta)
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. 59
W = Q mh =Q m ( h h )
W = mh(-)
W = mh (QLoss
)
W = mh + QLoss W
1
2
m
QLoss
R-22
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. 60
1942.3 kPa, 50OC 101.3 kPa,40.8OC
1942.3 kPa 101.3 kPa
40.8OC
-40.8o
C
hi = he
-(P-h Diagram)
( )
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. 61
T4T
3T2T1P
(Critical Point)
T=5oC
h
h
-40oC 5oC 50oC
3
2
1
50oC
-40o
C
(Bernoulli Equation)
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. 62
(Bernoulli Equation)i e
q = he hi + (2
2
eV
2
2
iV
)+(zegzig) + w ( w = 0 )
q = ue+ Peve (ui+ Pivi )+ ( 2
2
eV
2
2
iV
)+(zegzig)
Pi Pe+(
PF Z
F
v
Vi
2
2
v
Ve
2
2
)+ (zig/v zeg/v ) = [(ueui) q]/v = PF Pa
Pivi/g Peve/g +(g
Vi
2
2
g
Ve
2
2
)+ (zi ze ) = [(ueui) q]/g = ZF m
(Bernoulli Equation)()
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. 63
( q )( )i e
Pi- Pe+( v
Vi
2
2
- v
Ve
2
2
)+ (zig/v - zeg/v ) = 0
Pivi/g - Peve/g +(g
Vi
2
2
-g
Ve
2
2
)+ (zi - ze ) = 0
P1+V12
/(2v1)+Z1g/v1=P2+V22
/(2v2)+Z2g/v2
2
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TH
QH
WT
(Boiler)
(Condenser)Q
L
TL
WP
(Heat Engine Cycle)
Turbine
Pump
TH
QH
WC
(Evaporator)
QL
TL
(Refrigeration Cycle)
Compressor
Expansion Valve
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. 65
=
=
=
=
1 (100%)
T (Heat Engine Cycle)
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TH
QH
WT
(Boiler)
(Condenser)QL
TL
W
P
Turbine Generator
WE,T
Pump W
E,P
Motor
WPS W
TS
th
=(WT- W
P) / Q
H
th,S
=(WTS
- WPS
) / QH
th,O
=(WE,T
- WE,P
) / QH
T= WT / WTS
G= W
E,T/ W
T
P= W
PS/ W
P
M
= WP
/ WE,P
S WPS WTS .
T (Heat Engine Cycle)
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TH
QH
WT
(Boiler)
(Condenser)QL
TL
W
P
TurbinePump
(WT- WP) = QH- QL
th
=(QH- Q
L) / Q
H
th 1 (100%)
th
=(WT- W
P) / Q
H
.
()
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()() 10 km/
.
T (Refrigeration Cycle)
= W / W
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TH
QH
(Evaporator)QL
WC
TL
Comp. Motor
WE,M
Expansion Valve WCS
COP= QL/W
CS
C
= WCS
/ WC
M
= WC
/ WE,M
COP= QL/W
C
COP= QL/W
E,M
S WCS .
T (Refrigeration Cycle)
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TH
QH
WC
(Evaporator)QL
TL
Compressor
Expansion Valve
COP = QL
/WC
WC= Q
H- Q
L
COP= QL/(Q
H- Q
L)
COP 1 (100%).
()
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10 kW 10 kW 20 kW
COP (kW.h kJ)()
.
T (Heat Pump Cycle)
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TH
QH
WC
(Evaporator)
QL
TL
Comp.
Expansion Valve
COP = QH
/WC
WC= Q
H- Q
L
COP= QH/(Q
H- Q
L)
COP 1 (100%).
T
= W / W
(Internally Reversible Refrigeration Cycle)
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TH
QH
(Evaporator)
QL
WC
TL
W
T
Comp. Motor
WE,M
Turbine
WTS W
CS
COP= QL/(W
CS- W
TS)
C
WCS
/ WC
M
= WC
/ WE,M
T= W
T
/ WTS COP= Q
L/(W
C- W
T)
COP= QL/(W
E,M- W
T)
S WCS WTS .
2- (2nd Law of Thermo.)
KELVIN-PLANCK STATEMENT
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THQ
H
WT
(Boiler)
WP
Turbine
Pump
th=(WT- WP) / QH(W
T- W
P) = Q
H
th= 1
.
2- (2nd Law of Thermo.)
KELVIN-PLANCK STATEMENT
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THQ
H
WT
WT= QH
th
= 1 .
2- (2nd Law of Thermo.)
CLAUSIUS STATEMENT
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THQ
H
(Evaporator)QL T
L
Expansion Valve
COP = QL/W
C
WC= 0
COP= .
2- (2nd Law of Thermo.)
CLAUSIUS STATEMENT
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THQ
H
QL
TL
QL= Q
H
.
T/ (Carnot/Reversible Cycle)
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H
QH
WT
QL
TL
W
P
TurbinePump
QH/T
H= Q
L/ T
L
Comp
Turbine
QH/TH- QL/ TL= 0
=0TQ
QL/QH= TL/ TH
100% .
T =500oC (Carnot Heat Engine Cycle)
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H
QH
WT
499.9oC
32.1oC
QL
TL= 32oC
W
P
TurbinePump
th=(WT- WP) / QH(W
T- W
P) = Q
H- Q
L
th=(QH- QL) / QH
th= [(500+273) (32+273)] / (500+273) = 0.6054=60.54%
th
= (TH-T
L)/T
H
.
T =500oC (Carnot Heat Engine Cycle)
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H
QH
WT
QL
TL= 32oC
W
P
TurbinePump
/ 100%0.6054 60.54%.
TH
=35O
C
( CARNOT REFRIGERATOR )
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. 81
TE=24.99OC
TC=35.01OC
QL
QH
WC
COPCARNOT
=QL/W
C=T
L/(T
H-T
L)
EERCARNOT
=3.412TL/(T
H-T
L) = 102
EVAPORATOR
CONDENSER
TC=
Condenser
TE=
Evaporator
COPCARNOT
= (25+273)/[(35+273)-(25+273)]= 30
TL=25
O
C QH= QL+WC W
C= QH - QL
1
23
4
TH
=35O
C
( CARNOT REFRIGERATOR )
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. 82
QL
QH
WC
EVAPORATOR
CONDENSER
TL=25
O
C
1
23
4
/ 100%
COP 30 EER102
(Carnot Cycle)HEAT ENGINE/ REFRIGERATOR/
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THQ
H
Wnet
QL T
L
th= (TH-TL)/TH
THQ
H
Wnet
QL T
L
COP = TL/ (TH-TL)
HEAT ENGINE/T
H
TL 30OC(303K)
.
(Entropy) T
H
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QH
WT
Q
L
TL
WP
Turbine
Pump
Comp
Turbine
QH
/TH
- QL/ T
L= 0
= 0TQ
T
QdS =
(Carnot)
0T
QO =dS
T
Q
T DS = Q/T.
(Entropy)()
2 (Reversible Process)
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T
QdS =
=1
TdSQTdS=Q
(Internally reversible).
(Entropy in Carnot Cycle)
T
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HQ
H
WT
Q
L
TL
WP
TurbinePump
Comp
Turbine
1 2
34
1 2
34
s
T
.
(Entropy in Carnot Cycle)() T
H
QH
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WT
QL
TL
WP
TurbinePump
Comp
Turbine
1 2
34
1 2
34
T TH
s
TL
1-2 QH= TH(S2-S1) = 1-2 TH 2-3 Q =0 , S
2=S
3 (Isentropic)
3-4 QL= TL(S4-S3) = 3-4 T
L
2-3 Q =0 , S4=S
1 (Isentropic)
QH- Q
L= Q
NET= W
T-W
P=W
NET= 1-2-3-4-1
.
(Clausius Inequality)
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0TQ
0T
QO
= 0TQ
0TQO =
< 0T
Q 0
T
QO
0 .(1)
.(2)
.
=
e
i
vdPmW
= e
idPVW
KE &PE
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W= m = v= dP =
W =
kW
V= -m3/s
P =kPa H kg/m3:
P = 9.81 H/1000
- v V
PvmW = PVW =
.
=e
i
vdPmW
= e
idPVW
KE &PE
()
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W = kWV= -m3/s
P =kPa(a)-
(b)-
P.....(a)vmW =
.(b)P.........VW
=
.
(Air Compressor)
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h
W = V =P1
= P2
=
P2
P1
P2
P1
P2
P1
dW = VdP
W = V(P2-P1) = VP V
P1
P2
P2- FrictionFriction 0.5
Air Compressor
PumpPump Fan
= e
idPVW V
.
P2-P1 = h + F
F V2( 3)
W = V*(h+F)
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W (h*V+k*V3)(F =0) W = V*h
W V W2/W1=V2/V1
() W = V * F W V3 W2/W1=[V2/V]3
V
h
( h
)
100 / 100 kW 50 / 50 kW
100 / 100 kW 50 / 12.5 kW
hP
2
P1
Pump
P2P1
Pump FanP
2
P1
.
P
1P
2P
2- Friction
Air Compressor
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=
e
i
vdPmWW = (
V /0.286)*P1 [ (P2/P1)
0.286-1]
W = (
m R/0.286)*T1 [ (P2/P1)
0.286
-1]W = kWV = m3/s
P1 = kPa 101 kPaP2 = kPaR = 0.287 kJ/(kg.K)
T1 = KOC+273
=
e
idPVW
dW = VdP V (Isentropic) PV1.4=
Air Compressor
.
()
W / W = [ (P /P )0.286 1] / [ (P /P )0.286 1]
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(dP )
= 1122 W)V/V(W
Wb/ W a= [ (Pb/P1)0.286-1] / [ (Pa/P1)
0.286-1]
c 75%
=
W
=
ACTW
1 8 100 kW 7 100*(70.286-1)/*(80.286-1) = 91.6 kW
100 / 10 kW VSD 50 / 5 kW
c ACTW/W
=
.
P-hP
3
223
T1
T3 T3
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h
1
2
1
23
4
12 (s2 =s1 = constant) 34 (h4= h
3= Constant )
23 41 (P2=P3 P4 = P1)
1 3 T3
T1
T1
T3
COP = (h1-h
4) / (h
2-h
1) = (h
1-h
3) / (h
2-h
1) .
TH=35OC
TC=50oC,T
E=5oC
R-22
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96
TE=5OC (70 psig)
TC
=50OC (267psig)
QL
QH
WC
COP=Q /W =Q /(Q -Q ) = (h -h ) / (h -h )= 4.78
P=267-70= 197psi
TL=25OC
TH=35OC
TC=
Condenser
TE=
Evaporator
1 psi=6.9kPa
kPa =kPag+101.325
QH= QL+WC W
C= QH - QL
1
23
4
L C L H L 1 4 2 1
EER=3.412QL/(Q
H-Q
L) =3.412 (h
1-h
4) / (h
2-h
1) =16.3
T
1=5oC P
1=P
S= 583.8kPa
h1= h
g= 251.73 kJ/kg
s1
= sg
= 0.9197 kJ/kg.K
T2=50oC P
2=P
S=1942.3kPa
s2=s
1=0.9197 h
2= 281.8kJ/kg
h3= 107.85 kJ/kg h
4=h
3
qL= h
1-h
4= 251.73 - 107.85
= 143.88 kJ/kg
wC=h2-h1=281.8-251.73
=30.07 kJ/kg
COP=qL/w
C=143.88/30.07
=4.78
m = 10kg/s QL=1438.8kW
.
TH=32OC
TC=40
oC,T
E=5
oC
()
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. 97
TE=5OC (70 psig)
TC
=40OC (208psig)
QL
QH
WC
P=208-70= 138psi1 psi=6.9kPa
kPa =kPag+101.325
TL=25OC
TH 32 C
TC=
Condenser
TE=
Evaporator
QH= QL+WC W
C= QH - QL
1
23
4
COP=QL/WC=QL/(QH-QL) = (h1-h4) / (h2-h1)= 6.58 (TC=50
o
C 4.78)EER=3.412QL/(Q
H-Q
L) =3.412 (h1-h4) / (h2-h1) =22.45 (T
C=50oC 16.3)