02 เธอร์โมไดนามิกส์-power-point-10

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Thermodynamics

.

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/

:

1.

2. 3.

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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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( SUBCOOLED /COMPRESSED LIQUID )

:-1 (T

S)

2 (PS)

3

(vf)

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/ (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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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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(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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() ()

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


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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

.


KELVIN-PLANCK STATEMENT

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THQ

H

WT

WT= QH

th

= 1 .


CLAUSIUS STATEMENT

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THQ

H

(Evaporator)QL T

L

Expansion Valve

COP = QL/W

C

WC= 0

COP= .


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)

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