conductividad-lab iq

TABLA Nº1: Condiciones de Laboratorio

Presión(mmHg) 756

Temperatura(℃) 20

TABLA Nº2: Propiedades del Aluminio

ρExper .(Kg

m3 ) 2695.51

Cp( JKg∗K ) 910

K ( Wm∗K ) 205

TABLA Nº3: Propiedades del Cobre

ρExper .(Kg

m3 ) 9289.07

Cp( JKg∗K ) 390

K ( Wm∗K ) 385

TABLA Nº4: Dimensiones (diámetro y longitud), Volumen del área, Área superficial de Aluminio

D(m) 0.05L(m) 0.149

As (m2 ) 0.02733

V (m3 ) 2.93 x10−4

TABLA Nº5: Dimensiones (diámetro y longitud), Volumen del área, Área superficial de Cobre

D(m) 0.0049L(m) 0.149

As (m2 ) 0.02671

V (m3 ) 2.81 x10−4

TABLA Nº6: Variación de la temperatura con el tiempo para el cilindro de aluminio –1ra corrida

t (s ) 0 5 10 15 20 25 30 35 40

T (℃) 119.2 112.3 108.7 104.2 99.2 93.9 88.7 83.6 78.5

t (s ) 45 50 55 60 65 70 75 80 85

T (℃) 73.9 69.5 65.5 61.8 58.4 55.4 52.6 50.2 47.8

t (s ) 90 95 100 105 110 115 120 125 130

T (℃) 45.8 43.9 42.2 40.7 39.2 37.9 36.7 35.6 34.6

t (s ) 135 140 145 150 155 160 165 170 175

T (℃) 33.6 32.8 31.9 31.3 30.6 30 29.4 28.9 28.3

t (s ) 180 185 190 195 200 205 210 215 220

T (℃) 27.9 27.5 27.2 26.8 26.5 26.3 26 25.7 25.5

t (s ) 225 230 235 240 245 250 255 260 265

T (℃) 25.3 25.1 24.8 24.7 24.5 24.4 24.2 24 23.9

t (s ) 270 275 280 285 290 295 300 305 310

T (℃) 23.7 23.6 23.6 23.4 23.3 23.2 23.1 23 23

t (s ) 315 320 325 330 335 340 345 350 355

T (℃) 22.9 22.8 22.7 22.6 22.6 22.6 22.5 22.4 22.4

t (s ) 360 365 370 375 380 385 390 395 400

T (℃) 22.3 22.3 22.2 22.2 22.2 22.2 22.2 22.1 22.1

t (s ) 405 410 415 420 425 430 435 440 445

T (℃) 22.1 22.1 22.1 22 22 21.8 21.8 21.8 21.8

t (s ) 450 455 460 465 470 475 480 485 490

T (℃) 21.7 21.7 21.7 21.7 21.6 21.6 21.6 21.6 21.6

t (s ) 495 500 505

T (℃) 21.6 21.6 21.6

TABLA Nº7: Variación de la temperatura con el tiempo para el cilindro de aluminio –2da corrida

t (s ) 0 5 10 15 20 25 30 35 40

T (℃) 119 112.1 108.2 100.1 94.9 87.8 81.4 74.4 68.2

t (s ) 45 50 55 60 65 70 75 80 85

T (℃) 63 58.4 54.5 51 48.2 46.1 43.1 40.9 39.1

t (s ) 90 95 100 105 110 115 120 125 130

T (℃) 37.6 36.2 35 33.9 32.9 31.9 31.1 30.5 29.8

t (s ) 135 140 145 150 155 160 165 170 175

T (℃) 29.3 28.7 28.2 27.7 27.3 26.9 26.6 26.3 26

t (s ) 180 185 190 195 200 205 210 215 220

T (℃) 25.7 25.5 25.3 25.1 24.8 24.7 24.5 24.4 24.2

t (s ) 225 230 235 240 245 250 255 260 265

T (℃) 24 24 23.8 23.7 23.6 23.5 23.4 23.3 23.2

t (s ) 270 275 280 285 290 295 300 305 310

T (℃) 23.2 23.1 23 23 22.9 22.8 22.7 22.7 22.6

t (s ) 315 320 325 330 335 340 345 350 355

T (℃) 22.6 22.5 22.5 22.4 22.4 22.4 22.4 22.3 22.3

t (s ) 360 365 370 375 380 385 390 395 400

T (℃) 22.2 22.2 22.2 22.2 22.2 22.2 22.1 22.1 22.1

t (s ) 405 410 415 420 425 430 435 440 445

T (℃) 22.1 22 22 22 22 22 22 21.9 21.9

t (s ) 450 455 460 465 470 475 480 485 490

T (℃) 21.9 21.9 21.9 21.9 21.9 21.9 21.9 21.9 21.9

t (s ) 495 500 505 510 515 520 525 530

T (℃) 21.8 21.8 21.8 21.8 21.8 21.8 21.8 21.8

TABLA Nº8: Variación de la temperatura con el tiempo para el cilindro de cobre –1ra corrida

t (s ) 0 5 10 15 20 25 30 35 40

T (℃) 143.4 123.9 115.9 110 103.2 96.9 91 85.8 81.1

t (s ) 45 50 55 60 65 70 75 80 85

T (℃) 76.9 72.9 69.3 66.7 63.6 60.8 57.7 55.5 53.4

t (s ) 90 95 100 105 110 115 120 125 130

T (℃) 51.5 49.8 48.2 46.7 45.3 44.1 42.9 41.7 40.7

t (s ) 135 140 145 150 155 160 165 170 175

T (℃) 39.8 38.9 38 37.2 36.4 35.9 35.1 34.4 33.9

t (s ) 180 185 190 195 200 205 210 215 220

T (℃) 33.4 32.7 32.3 31.8 30.9 30.6 30.2 29.8 29.5

t (s ) 225 230 235 240 245 250 255 260 265

T (℃) 29.1 28.8 28.5 28.2 27.9 27.6 27.3 27.1 26.9

t (s ) 270 275 280 285 290 295 300 305 310

T (℃) 26.7 26.6 26.4 26.2 26.1 25.9 25.7 25.6 25.5

t (s ) 315 320 325 330 335 340 345 350 355

T (℃) 25.4 25.3 25.1 25.1 24.9 24.8 24.7 24.5 24.4

t (s ) 360 365 370 375 380 385 390 395 400

T (℃) 24.3 24.1 24 23.9 23.8 23.7 23.6 23.5 23.4

t (s ) 405 410 415 420 425 430 435 440 445

T (℃) 23.4 23.4 23.4 23.2 23.2 23.1 23.1 23 23

t (s ) 450 455 460 465 470 475 480 485 490

T (℃) 23 23 22.9 22.9 22.8 22.8 22.8 22.7 22.7

t (s ) 495 500 505 510 515 520 525 530

T (℃) 22.7 22.6 22.6 22.6 22.6 22.6 22.6 22.6

TABLA Nº9: Variación de la temperatura con el tiempo para el cilindro de cobre –2da corrida

t (s ) 0 5 10 15 20 25 30 35 40

T (℃) 142.9 123 114.1 109.3 104.2 98.7 92.5 86.6 81

t (s ) 45 50 55 60 65 70 75 80 85

T (℃) 75.2 71.2 67.1 63.4 60.2 57.3 54.8 52.5 50.5

t (s ) 90 95 100 105 110 115 120 125 130

T (℃) 48.6 46.9 45.3 43.9 42.6 41.4 40.4 39.3 38.4

t (s ) 135 140 145 150 155 160 165 170 175

T (℃) 37.5 36.7 35.9 35.1 34.6 33.9 33.4 32.8 32.3

t (s ) 180 185 190 195 200 205 210 215 220

T (℃) 31.8 31.2 30.8 30.4 30 29.6 29.2 28.9 28.5

t (s ) 225 230 235 240 245 250 255 260 265

T (℃) 28.2 27.9 27.6 27.4 27.2 26.9 26.7 26.6 26.4

t (s ) 270 275 280 285 290 295 300 305 310

T (℃) 26.1 25.9 25.8 25.7 25.5 25.4 25.3 25.1 25

t (s ) 315 320 325 330 335 340 345 350 355

T (℃) 24.8 24.8 24.7 24.5 24.4 24.4 24.2 24.1 24

t (s ) 360 365 370 375 380 385 390 395 400

T (℃) 24 23.9 23.8 23.7 23.7 23.6 23.5 23.4 23.3

t (s ) 405 410 415 420 425 430 435 440 445

T (℃) 23.3 23.2 23.2 23.1 23.1 23 22.9 22.9 22.8

t (s ) 450 455 460 465 470 475 480 485 490

T (℃) 22.8 22.8 22.7 22.7 22.6 22.6 22.6 22.5 22.5

t (s ) 495 500 505 510 515 520 525 530 535

T (℃) 22.5 22.5 22.5 22.4 22.4 22.4 22.3 22.3 22.3

t (s ) 540 545 550 555 560 565 570 575

T (℃) 22.2 22.2 22.2 22.2 22.2 22.2 22.2 22.2

TABLA Nº10: Temperatura del Agua

T w 20℃

TABLA Nº 11: Valores de T−T w

T0−Tw

Y ln ( T−T w

T 0−T w) para el cilindro de aluminio – 1ra corrida

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

190 27.2 7.2 -2.62305699195 26.8 6.8 -2.6802154200 26.5 6.5 -2.72533584205 26.3 6.3 -2.75658838210 26 6 -2.80537855215 25.7 5.7 -2.85667184220 25.5 5.5 -2.89238992225 25.3 5.3 -2.92943119230 25.1 5.1 -2.96789747235 24.8 4.8 -3.0285221240 24.7 4.7 -3.04957551245 24.5 4.5 -3.09306062250 24.4 4.4 -3.11553347255 24.2 4.2 -3.16205349260 24 4 -3.21084365265 23.9 3.9 -3.23616146270 23.7 3.7 -3.28880519275 23.6 3.6 -3.31620417280 23.6 3.6 -3.31620417285 23.4 3.4 -3.37336258290 23.3 3.3 -3.40321555

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

0 119.2 5 112.3 92.3 -0.07209387

10 108.7 88.7 -0.1118781215 104.2 84.2 -0.1639430920 99.2 79.2 -0.2251617225 93.9 73.9 -0.2944251930 88.7 68.7 -0.3673888235 83.6 63.6 -0.4445245440 78.5 58.5 -0.5281112645 73.9 53.9 -0.6100075450 69.5 49.5 -0.6951653455 65.5 45.5 -0.7794256960 61.8 41.8 -0.8642416765 58.4 38.4 -0.9490805570 55.4 35.4 -1.0304261975 52.6 32.6 -1.1128257380 50.2 30.2 -1.1892960985 47.8 27.8 -1.2721019990 45.8 25.8 -1.3467635295 43.9 23.9 -1.42325956

100 42.2 22.2 -1.49704573

295 23.2 3.2 -3.4339872300 23.1 3.1 -3.4657359305 23 3 -3.49852573310 23 3 -3.49852573315 22.9 2.9 -3.53242728320 22.8 2.8 -3.5675186325 22.7 2.7 -3.60388624330 22.6 2.6 -3.64162657335 22.6 2.6 -3.64162657340 22.6 2.6 -3.64162657345 22.5 2.5 -3.68084728350 22.4 2.4 -3.72166928355 22.4 2.4 -3.72166928360 22.3 2.3 -3.76422889365 22.3 2.3 -3.76422889370 22.2 2.2 -3.80868065375 22.2 2.2 -3.80868065

105 40.7 20.7 -1.56700431110 39.2 19.2 -1.64222774115 37.9 17.9 -1.7123373120 36.7 16.7 -1.78172929125 35.6 15.6 -1.8498671130 34.6 14.6 -1.91611649135 33.6 13.6 -1.98706822140 32.8 12.8 -2.04769284145 31.9 11.9 -2.12059961150 31.3 11.3 -2.17233529155 30.6 10.6 -2.23628401160 30 10 -2.29455292165 29.4 9.4 -2.35642833170 28.9 8.9 -2.41108674175 28.3 8.3 -2.4808825180 27.9 7.9 -2.53027525185 27.5 7.5 -2.58223499

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

380 22.2 2.2 -3.80868065385 22.2 2.2 -3.80868065390 22.2 2.2 -3.80868065395 22.1 2.1 -3.85520067400 22.1 2.1 -3.85520067405 22.1 2.1 -3.85520067410 22.1 2.1 -3.85520067415 22.1 2.1 -3.85520067420 22 2 -3.90399083425 22 2 -3.90399083430 21.8 1.8 -4.00935135435 21.8 1.8 -4.00935135440 21.8 1.8 -4.00935135445 21.8 1.8 -4.00935135450 21.7 1.7 -4.06650976455 21.7 1.7 -4.06650976460 21.7 1.7 -4.06650976465 21.7 1.7 -4.06650976470 21.6 1.6 -4.12713439475 21.6 1.6 -4.12713439480 21.6 1.6 -4.12713439485 21.6 1.6 -4.12713439490 21.6 1.6 -4.12713439495 21.6 1.6 -4.12713439500 21.6 1.6 -4.12713439505 21.6 1.6 -4.12713439


T0−Tw Y ln ( T−T w

T 0−T w)

para el cilindro de aluminio – 2da corrida

t (s )T (℃)

T−T w

T0−Tw

ln ( T−T w

T 0−T w)

200 24.8 4.8

-3.0265039

3

205 24.7 4.7

-3.0475573

4

210 24.5 4.5

-3.0910424

5

215 24.4 4.4

-3.1135153

1

220 24.2 4.2

-3.1600353

2

225 24 4

-3.2088254

9

230 24 4

-3.2088254

9

235 23.8 3.8

-3.2601187

8

240 23.7 3.7

-3.2867870

3245 23.6 3.6 -3.314186

250 23.5 3.5

-3.3423568

8

255 23.4 3.4

-3.3713444

2

260 23.3 3.3

-3.4011973

8

265 23.2 3.2

-3.4319690

4

270 23.2 3.2

-3.4319690

4

275 23.1 3.1

-3.4637177

4

280 23 3

-3.4965075

6

285 23 3

-3.4965075

6

290 22.9 2.9

-3.5304091

1

295 22.8 2.8

-3.5655004

3-

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

0 119 5 112.1 92.1 -0.07224491

10 108.2 88.2 -0.1155128915 100.1 80.1 -0.21184420 94.9 74.9 -0.2789659625 87.8 67.8 -0.3785576630 81.4 61.4 -0.4777100135 74.4 54.4 -0.598755740 68.2 48.2 -0.7197608345 63 43 -0.8339197350 58.4 38.4 -0.9470623955 54.5 34.5 -1.0541605360 51 31 -1.1611326565 48.2 28.2 -1.2557978770 46.1 26.1 -1.3331845475 43.1 23.1 -1.4552872380 40.9 20.9 -1.5553706985 39.1 19.1 -1.6454315290 37.6 17.6 -1.7272209595 36.2 16.2 -1.81010861

100 35 15 -1.88706965105 33.9 13.9 -1.96323101110 32.9 12.9 -2.03789254115 31.9 11.9 -2.11858145120 31.1 11.1 -2.18817474125 30.5 10.5 -2.24374459130 29.8 9.8 -2.31273746135 29.3 9.3 -2.36510545140 28.7 8.7 -2.43179682145 28.2 8.2 -2.4909857150 27.7 7.7 -2.55389952155 27.3 7.3 -2.6072455160 26.9 6.9 -2.66359844165 26.6 6.6 -2.7080502170 26.3 6.3 -2.75457022175 26 6 -2.80336038180 25.7 5.7 -2.85465368185 25.5 5.5 -2.89037176190 25.3 5.3 -2.92741303195 25.1 5.1 -2.96587931

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

400 22.1 2.1 -3.85318251405 22.1 2.1 -3.85318251

410 22 2 -3.90197267415 22 2 -3.90197267420 22 2 -3.90197267425 22 2 -3.90197267430 22 2 -3.90197267435 22 2 -3.90197267440 21.9 1.9 -3.95326596445 21.9 1.9 -3.95326596450 21.9 1.9 -3.95326596455 21.9 1.9 -3.95326596460 21.9 1.9 -3.95326596465 21.9 1.9 -3.95326596470 21.9 1.9 -3.95326596475 21.9 1.9 -3.95326596480 21.9 1.9 -3.95326596485 21.9 1.9 -3.95326596490 21.9 1.9 -3.95326596495 21.8 1.8 -4.00733319500 21.8 1.8 -4.00733319505 21.8 1.8 -4.00733319510 21.8 1.8 -4.00733319515 21.8 1.8 -4.00733319520 21.8 1.8 -4.00733319525 21.8 1.8 -4.00733319530 21.8 1.8 -4.00733319


T0−Tw Y

ln ( T−T w

T 0−T w) para el cilindro de cobre – 1ra

corrida

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

200 30.9 10.9 -2.42666832205 30.6 10.6 -2.45457711210 30.2 10.2 -2.49304339215 29.8 9.8 -2.53304873220 29.5 9.5 -2.56413931225 29.1 9.1 -2.6071567230 28.8 8.8 -2.64067939235 28.5 8.5 -2.67536495240 28.2 8.2 -2.71129696245 27.9 7.9 -2.74856835250 27.6 7.6 -2.78728286255 27.3 7.3 -2.82755676260 27.1 7.1 -2.85533633265 26.9 6.9 -2.8839097270 26.7 6.7 -2.91332359275 26.6 6.6 -2.92836146280 26.4 6.4 -2.95913312285 26.2 6.2 -2.99088182290 26.1 6.1 -3.00714234295 25.9 5.9 -3.04047876300 25.7 5.7 -3.07496494305 25.6 5.6 -3.09266451310 25.5 5.5 -3.11068302315 25.4 5.4 -3.12903216320 25.3 5.3 -3.14772429325 25.1 5.1 -3.18619057330 25.1 5.1 -3.18619057335 24.9 4.9 -3.22619591340 24.8 4.8 -3.24681519345 24.7 4.7 -3.2678686350 24.5 4.5 -3.31135371355 24.4 4.4 -3.33382657360 24.3 4.3 -3.35681609365 24.1 4.1 -3.40444414370 24 4 -3.42913675375 23.9 3.9 -3.45445456380 23.8 3.8 -3.48043004385 23.7 3.7 -3.50709829390 23.6 3.6 -3.53449727395 23.5 3.5 -3.56266814

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

0 143.4 5 123.9 103.9 -0.17200221

10 115.9 95.9 -0.2521251315 110 90 -0.3156214420 103.2 83.2 -0.3941837625 96.9 76.9 -0.4729252330 91 71 -0.5527512335 85.8 65.8 -0.6288112740 81.1 61.1 -0.7029192545 76.9 56.9 -0.7741357750 72.9 52.9 -0.8470277755 69.3 49.3 -0.9175070360 66.7 46.7 -0.9716869565 63.6 43.6 -1.0403739670 60.8 40.8 -1.1067490375 57.7 37.7 -1.1857710280 55.5 35.5 -1.2458984185 53.4 33.4 -1.3068752190 51.5 31.5 -1.3654435795 49.8 29.8 -1.42092272

100 48.2 28.2 -1.47610913105 46.7 26.7 -1.53076755110 45.3 25.3 -1.58462672115 44.1 24.1 -1.63321927120 42.9 22.9 -1.6842942125 41.7 21.7 -1.73811885130 40.7 20.7 -1.78529741135 39.8 19.8 -1.82974917140 38.9 18.9 -1.87626919145 38 18 -1.92505935150 37.2 17.2 -1.97052173155 36.4 16.4 -2.01814978160 35.9 15.9 -2.049112165 35.1 15.1 -2.10073637170 34.4 14.4 -2.1482029175 33.9 13.9 -2.18354227180 33.4 13.4 -2.2201764185 32.7 12.7 -2.27382912190 32.3 12.3 -2.30583185195 31.8 11.8 -2.34733158

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

400 23.4 3.4 -3.59165568

405 23.4 3.4 -3.59165568

410 23.4 3.4 -3.59165568

415 23.4 3.4 -3.59165568

420 23.2 3.2 -3.6522803

425 23.2 3.2 -3.6522803

430 23.1 3.1 -3.684029

435 23.1 3.1 -3.684029

440 23 3 -3.71681882

445 23 3 -3.71681882

450 23 3 -3.71681882

455 23 3 -3.71681882

460 22.9 2.9 -3.75072037

465 22.9 2.9 -3.75072037

470 22.8 2.8 -3.78581169

475 22.8 2.8 -3.78581169

480 22.8 2.8 -3.78581169

485 22.7 2.7 -3.82217934

490 22.7 2.7 -3.82217934

495 22.7 2.7 -3.82217934

500 22.6 2.6 -3.85991967

505 22.6 2.6 -3.85991967

510 22.6 2.6 -3.85991967

515 22.6 2.6 -3.85991967

520 22.6 2.6 -3.85991967

52 22.6 2.6 -3.85991967

553

0 22.6 2.6 -3.85991967


T0−Tw Y

ln ( T−T w

T 0−T w) para el cilindro de cobre – 2da

corrida

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

0 142.9 5 123 103 -0.17664203

10 114.1 94.1 -0.2670129715 109.3 89.3 -0.3193695320 104.2 84.2 -0.378176125 98.7 78.7 -0.4457278630 92.5 72.5 -0.5277844535 86.6 66.6 -0.6126664440 81 61 -0.7004971545 75.2 55.2 -0.8004080650 71.2 51.2 -0.8756314855 67.1 47.1 -0.9590980260 63.4 43.4 -1.0409115865 60.2 40.2 -1.1175040270 57.3 37.3 -1.1923776975 54.8 34.8 -1.2617536380 52.5 32.5 -1.3301309385 50.5 30.5 -1.3936443390 48.6 28.6 -1.4579643

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

200 30 10 -2.50878592205 29.6 9.6 -2.54960792210 29.2 9.2 -2.59216753215 28.9 8.9 -2.62531974220 28.5 8.5 -2.67130485225 28.2 8.2 -2.70723686230 27.9 7.9 -2.74450826235 27.6 7.6 -2.78322277240 27.4 7.4 -2.80989102245 27.2 7.2 -2.83728999250 26.9 6.9 -2.8798496255 26.7 6.7 -2.90926349260 26.6 6.6 -2.92430137265 26.4 6.4 -2.95507303270 26.1 6.1 -3.00308225275 25.9 5.9 -3.03641867280 25.8 5.8 -3.0535131285 25.7 5.7 -3.07090484290 25.5 5.5 -3.10662292295 25.4 5.4 -3.12497206300 25.3 5.3 -3.1436642305 25.1 5.1 -3.18213048310 25 5 -3.2019331315 24.8 4.8 -3.2427551320 24.8 4.8 -3.2427551325 24.7 4.7 -3.26380851330 24.5 4.5 -3.30729362335 24.4 4.4 -3.32976648340 24.4 4.4 -3.32976648345 24.2 4.2 -3.37628649350 24.1 4.1 -3.40038404355 24 4 -3.42507666360 24 4 -3.42507666365 23.9 3.9 -3.45039446370 23.8 3.8 -3.47636995375 23.7 3.7 -3.5030382380 23.7 3.7 -3.5030382385 23.6 3.6 -3.53043717390 23.5 3.5 -3.55860805395 23.4 3.4 -3.58759558

95 46.9 26.9 -1.51924473100 45.3 25.3 -1.58056662105 43.9 23.9 -1.63749256110 42.6 22.6 -1.69342111115 41.4 21.4 -1.74798009120 40.4 20.4 -1.79583612125 39.3 19.3 -1.85126592130 38.4 18.4 -1.89902035135 37.5 17.5 -1.94917014140 36.7 16.7 -1.9959623145 35.9 15.9 -2.04505191150 35.1 15.1 -2.09667627155 34.6 14.6 -2.13034949160 33.9 13.9 -2.17948218165 33.4 13.4 -2.21611631170 32.8 12.8 -2.26192585175 32.3 12.3 -2.30177175180 31.8 11.8 -2.34327149185 31.2 11.2 -2.39545724190 30.8 10.8 -2.43182488195 30.4 10.4 -2.46956521

t (s ) T (℃)T−T w

T0−Tw

ln ( T−T w

T 0−T w)

400 23.3 3.3 -3.61744855405 23.3 3.3 -3.61744855410 23.2 3.2 -3.64822021415 23.2 3.2 -3.64822021420 23.1 3.1 -3.67996891425 23.1 3.1 -3.67996891430 23 3 -3.71275873435 22.9 2.9 -3.74666028440 22.9 2.9 -3.74666028445 22.8 2.8 -3.7817516450 22.8 2.8 -3.7817516455 22.8 2.8 -3.7817516460 22.7 2.7 -3.81811924465 22.7 2.7 -3.81811924470 22.6 2.6 -3.85585957475 22.6 2.6 -3.85585957480 22.6 2.6 -3.85585957485 22.5 2.5 -3.89508028490 22.5 2.5 -3.89508028495 22.5 2.5 -3.89508028500 22.5 2.5 -3.89508028505 22.5 2.5 -3.89508028510 22.4 2.4 -3.93590228

515 22.4 2.4 -3.93590228520 22.4 2.4 -3.93590228525 22.3 2.3 -3.97846189530 22.3 2.3 -3.97846189535 22.3 2.3 -3.97846189540 22.2 2.2 -4.02291366545 22.2 2.2 -4.02291366550 22.2 2.2 -4.02291366555 22.2 2.2 -4.02291366560 22.2 2.2 -4.02291366565 22.2 2.2 -4.02291366570 22.2 2.2 -4.02291366575 22.2 2.2 -4.02291366

TABLA Nº 15: Valores de la pendiente de la grafica ln ( T−T w

T 0−T w)vs Tiempo y coeficiente

de convección del Aluminio

1ra Corrida 2da Corridam -0.008 -0.006

h( w

m2∗K ) 210.05 157.54

TABLA Nº 16: Valores de la pendiente de la grafica ln ( T−T w

T 0−T w)vs Tiempo y coeficiente

de convección del Cobre


h( w

m2∗K ) 228.67 228.67

TABLA Nº 17: Valores de Biot del Aluminio y del Cobre en las 2 corridas

1ra Corrida 2da Corrida

Al 0.0109676 0.0082257

Cu 0.0062485 0.0062485

TABLA Nº 18: Valores de ln ( T−T w

T 0−T w) Y Bi−1 x ln ( T−T w

T 0−T w)para el cilindro de aluminio

– 1ra corrida

t (s )ln ( T−T w

T 0−T w) Bi−1 x ln ( T−T w

T 0−T w)

0 5 -0.07209387 -6.57334092

10 -0.11187812 -10.200770615 -0.16394309 -14.947925520 -0.22516172 -20.52968825 -0.29442519 -26.844959930 -0.36738882 -33.49760335 -0.44452454 -40.530647940 -0.52811126 -48.151877845 -0.61000754 -55.618977750 -0.69516534 -63.383455955 -0.77942569 -71.066105560 -0.86424167 -78.799417365 -0.94908055 -86.534816470 -1.03042619 -93.951710575 -1.11282573 -101.46469680 -1.18929609 -108.43707485 -1.27210199 -115.98711290 -1.34676352 -122.79456595 -1.42325956 -129.769284

100 -1.49704573 -136.496925105 -1.56700431 -142.875576110 -1.64222774 -149.734261115 -1.7123373 -156.126678120 -1.78172929 -162.453668125 -1.8498671 -168.666305130 -1.91611649 -174.70676

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

265

-3.2361614

6 -295.065194

270

-3.2888051

9 -299.865119

275

-3.3162041

7 -302.3632928 - -302.36329

t (s ) ln ( T−T w


T 0−T w)

135 -1.98706822 -181.175963140 -2.04769284 -186.703566145 -2.12059961 -193.351025150 -2.17233529 -198.068156155 -2.23628401 -203.898842160 -2.29455292 -209.211657165 -2.35642833 -214.853304170 -2.41108674 -219.836922175 -2.4808825 -226.200727180 -2.53027525 -230.704236185 -2.58223499 -235.441797190 -2.62305699 -239.163845195 -2.6802154 -244.375408200 -2.72533584 -248.489378205 -2.75658838 -251.338907210 -2.80537855 -255.787474215 -2.85667184 -260.464269220 -2.89238992 -263.720956225 -2.92943119 -267.098287230 -2.96789747 -270.605547235 -3.0285221 -276.13315240 -3.04957551 -278.052748245 -3.09306062 -282.017613250 -3.11553347 -284.066632255 -3.16205349 -288.308212260 -3.21084365 -292.756779

t (s ) ln ( T−T w


T 0−T w)

405 -3.85520067 -351.507657410 -3.85520067 -351.507657415 -3.85520067 -351.507657420 -3.90399083 -355.956223425 -3.90399083 -355.956223430 -4.00935135 -365.562735435 -4.00935135 -365.562735440 -4.00935135 -365.562735445 -4.00935135 -365.562735450 -4.06650976 -370.774297455 -4.06650976 -370.774297460 -4.06650976 -370.774297465 -4.06650976 -370.774297470 -4.12713439 -376.3019475 -4.12713439 -376.3019480 -4.12713439 -376.3019485 -4.12713439 -376.3019490 -4.12713439 -376.3019495 -4.12713439 -376.3019500 -4.12713439 -376.3019505 -4.12713439 -376.3019

03.3162041

7

285

-3.3733625

8 -307.574853

290

-3.4032155

5 -310.296772295 -3.4339872 -313.102456

300 -3.4657359 -315.997223

305

-3.4985257

3 -318.986918

310

-3.4985257

3 -318.986918

315

-3.5324272

8 -322.077978320 -3.5675186 -325.277518

325

-3.6038862

4 -328.593429

330

-3.6416265

7 -332.034499

335

-3.6416265

7 -332.034499

340

-3.6416265

7 -332.034499

345

-3.6808472

8 -335.610547

350

-3.7216692

8 -339.332595

355

-3.7216692

8 -339.332595

360

-3.7642288

9 -343.213075

365

-3.7642288

9 -343.21307537 - -347.266077

03.8086806

5

375

-3.8086806

5 -347.266077

380

-3.8086806

5 -347.266077

385

-3.8086806

5 -347.266077

390

-3.8086806

5 -347.266077

395

-3.8552006

7 -351.507657

400

-3.8552006

7 -351.507657


T 0−T w) Y Bi−1 x

ln ( T−T w

T 0−T w)para el cilindro de aluminio – 2da

corrida

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

210 -3.09104245 -375.778136215 -3.11351531 -378.510162220 -3.16003532 -384.165602225 -3.20882549 -390.097023230 -3.20882549 -390.097023235 -3.26011878 -396.332751240 -3.28678703 -399.574811245 -3.314186 -402.905705250 -3.34235688 -406.330439255 -3.37134442 -409.854455260 -3.40119738 -413.483681265 -3.43196904 -417.224593270 -3.43196904 -417.224593275 -3.46371774 -421.084283280 -3.49650756 -425.070543285 -3.49650756 -425.070543290 -3.53040911 -429.191956295 -3.56550043 -433.458008300 -3.60186808 -437.879224305 -3.60186808 -437.879224310 -3.63960841 -442.467317315 -3.63960841 -442.467317320 -3.67882912 -447.235381325 -3.67882912 -447.235381330 -3.71965111 -452.198112335 -3.71965111 -452.198112340 -3.71965111 -452.198112345 -3.71965111 -452.198112350 -3.76221073 -457.372086355 -3.76221073 -457.372086360 -3.80666249 -462.776088365 -3.80666249 -462.776088370 -3.80666249 -462.776088375 -3.80666249 -462.776088380 -3.80666249 -462.776088385 -3.80666249 -462.776088390 -3.85318251 -468.431528395 -3.85318251 -468.431528400 -3.85318251 -468.431528

t (s )ln ( T−T w

T 0−T w) Bi−1 x

t (s ) Ln( T−T w

T0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

0 5 -0.07224491 -8.78281578

10 -0.11551289 -14.042905615 -0.211844 -25.753881820 -0.27896596 -33.913901225 -0.37855766 -46.02126730 -0.47771001 -58.075222735 -0.5987557 -72.790750340 -0.71976083 -87.501348445 -0.83391973 -101.3796550 -0.94706239 -115.13440755 -1.05416053 -128.15433160 -1.16113265 -141.15893565 -1.25579787 -152.6673970 -1.33318454 -162.07528975 -1.45528723 -176.91931880 -1.55537069 -189.08646885 -1.64543152 -200.03516590 -1.72722095 -209.97830995 -1.81010861 -220.054965

100 -1.88706965 -229.411121105 -1.96323101 -238.67006110 -2.03789254 -247.746665115 -2.11858145 -257.556019120 -2.18817474 -266.016478125 -2.24374459 -272.772106130 -2.31273746 -281.159572135 -2.36510545 -287.52595140 -2.43179682 -295.633622145 -2.4909857 -302.829215150 -2.55389952 -310.477651155 -2.6072455 -316.962924160 -2.66359844 -323.813752165 -2.7080502 -329.217755170 -2.75457022 -334.873195175 -2.80336038 -340.804617180 -2.85465368 -347.040344185 -2.89037176 -351.382593190 -2.92741303 -355.885701195 -2.96587931 -360.562048200 -3.02650393 -367.932186205 -3.04755734 -370.491649

ln ( T−T w

T 0−T w)

405 -3.85318251 -468.431528410 -3.90197267 -474.36295415 -3.90197267 -474.36295420 -3.90197267 -474.36295425 -3.90197267 -474.36295430 -3.90197267 -474.36295435 -3.90197267 -474.36295440 -3.95326596 -480.598677445 -3.95326596 -480.598677450 -3.95326596 -480.598677455 -3.95326596 -480.598677460 -3.95326596 -480.598677465 -3.95326596 -480.598677470 -3.95326596 -480.598677475 -3.95326596 -480.598677480 -3.95326596 -480.598677485 -3.95326596 -480.598677490 -3.95326596 -480.598677495 -4.00733319 -487.171631500 -4.00733319 -487.171631505 -4.00733319 -487.171631510 -4.00733319 -487.171631515 -4.00733319 -487.171631520 -4.00733319 -487.171631525 -4.00733319 -487.171631530 -4.00733319 -487.171631


T 0−T w) Y Bi−1 x

ln ( T−T w

T 0−T w)para el cilindro de cobre – 1ra corrida

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

0 5 -0.17200221 -27.5271289

10 -0.25212513 -40.349951315 -0.31562144 -50.511862120 -0.39418376 -63.084928125 -0.47292523 -75.686664930 -0.55275123 -88.46196935 -0.62881127 -100.63457140 -0.70291925 -112.49476545 -0.77413577 -123.89221550 -0.84702777 -135.55780655 -0.91750703 -146.83726360 -0.97168695 -155.50818465 -1.04037396 -166.50081170 -1.10674903 -177.12343775 -1.18577102 -189.77006780 -1.24589841 -199.39281985 -1.30687521 -209.15150890 -1.36544357 -218.52475295 -1.42092272 -227.403601

100 -1.47610913 -236.235602105 -1.53076755 -244.9831110 -1.58462672 -253.602689115 -1.63321927 -261.379412120 -1.6842942 -269.553412125 -1.73811885 -278.167476130 -1.78529741 -285.717904135 -1.82974917 -292.831937140 -1.87626919 -300.276972145 -1.92505935 -308.08532150 -1.97052173 -315.36109155 -2.01814978 -322.983454160 -2.049112 -327.93863165 -2.10073637 -336.200562170 -2.1482029 -343.797077175 -2.18354227 -349.452768180 -2.2201764 -355.315672185 -2.27382912 -363.902219190 -2.30583185 -369.023917195 -2.34733158 -375.665508

t (s )ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

210

-2.4930433

9 -398.985137

215

-2.5330487

3 -405.387567

220

-2.5641393

1 -410.363285225

-2.6071567 -417.247761

230

-2.6406793

9 -422.612712

235

-2.6753649

5 -428.163768

240

-2.7112969

6 -433.914304

245

-2.7485683

5 -439.879195

250

-2.7872828

6 -446.075042

255

-2.8275567

6 -452.520452

260

-2.8553363

3 -456.966277265

-2.8839097 -461.539142

270

-2.9133235

9 -466.246522

275

-2.9283614

6 -468.653175

280

-2.9591331

2 -473.577852

285

-2.9908818

2 -478.658894

290

-3.0071423

4 -481.261218

295

-3.0404787

6 -486.596358

300

-3.0749649

4 -492.115505

305

-3.0926645

1 -494.948134-

200 -2.42666832 -388.362512205 -2.45457711 -392.829017

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

405 -3.59165568 -574.806375410 -3.59165568 -574.806375415 -3.59165568 -574.806375420 -3.6522803 -584.508702425 -3.6522803 -584.508702430 -3.684029 -589.589745435 -3.684029 -589.589745440 -3.71681882 -594.837408445 -3.71681882 -594.837408450 -3.71681882 -594.837408455 -3.71681882 -594.837408460 -3.75072037 -600.262991465 -3.75072037 -600.262991470 -3.78581169 -605.878985475 -3.78581169 -605.878985480 -3.78581169 -605.878985485 -3.82217934 -611.69924490 -3.82217934 -611.69924495 -3.82217934 -611.69924500 -3.85991967 -617.739179505 -3.85991967 -617.739179510 -3.85991967 -617.739179515 -3.85991967 -617.739179520 -3.85991967 -617.739179525 -3.85991967 -617.739179530 -3.85991967 -617.739179


T 0−T w) Y Bi−1 x ln ( T−T w

T 0−T w)para el cilindro de cobre –

2da corrida

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

0 5 -0.17664203 -28.269682

10 -0.26701297 -42.732592215 -0.31936953 -51.111703720 -0.3781761 -60.523070725 -0.44572786 -71.334013930 -0.52778445 -84.466300835 -0.61266644 -98.050761640 -0.70049715 -112.10713545 -0.80040806 -128.09681650 -0.87563148 -140.13552655 -0.95909802 -153.49345960 -1.04091158 -166.58685165 -1.11750402 -178.84465970 -1.19237769 -190.82739575 -1.26175363 -201.93027880 -1.33013093 -212.87333985 -1.39364433 -223.03798590 -1.4579643 -233.33171395 -1.51924473 -243.138996

100 -1.58056662 -252.952914105 -1.63749256 -262.063306110 -1.69342111 -271.014077115 -1.74798009 -279.745664120 -1.79583612 -287.404512125 -1.85126592 -296.275464130 -1.89902035 -303.918054135 -1.94917014 -311.943995140 -1.9959623 -319.432583145 -2.04505191 -327.288855150 -2.09667627 -335.550786155 -2.13034949 -340.939827160 -2.17948218 -348.802993165 -2.21611631 -354.665897170 -2.26192585 -361.997227175 -2.30177175 -368.374142180 -2.34327149 -375.015733185 -2.39545724 -383.367509

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

215 -2.62531974 -420.154563220 -2.67130485 -427.513992225 -2.70723686 -433.264529230 -2.74450826 -439.22942235 -2.78322277 -445.425267240 -2.80989102 -449.693237245 -2.83728999 -454.078152250 -2.8798496 -460.889367255 -2.90926349 -465.596747260 -2.92430137 -468.0034265 -2.95507303 -472.928077270 -3.00308225 -480.611443275 -3.03641867 -485.946583280 -3.0535131 -488.682366285 -3.07090484 -491.46573290 -3.10662292 -497.18203295 -3.12497206 -500.118615300 -3.1436642 -503.110092305 -3.18213048 -509.266212310 -3.2019331 -512.435413315 -3.2427551 -518.96854320 -3.2427551 -518.96854325 -3.26380851 -522.337914330 -3.30729362 -529.297245335 -3.32976648 -532.893787340 -3.32976648 -532.893787345 -3.37628649 -540.338822350 -3.40038404 -544.195379355 -3.42507666 -548.14717360 -3.42507666 -548.14717365 -3.45039446 -552.199016370 -3.47636995 -556.356117375 -3.5030382 -560.624087380 -3.5030382 -560.624087385 -3.53043717 -565.009002390 -3.55860805 -569.517452395 -3.58759558 -574.1566400 -3.61744855 -578.93425

190 -2.43182488 -389.187765195 -2.46956521 -395.227704200 -2.50878592 -401.504563205 -2.54960792 -408.03769210 -2.59216753 -414.848904

t (s ) ln ( T−T w

T 0−T w)

Bi−1 x

ln ( T−T w

T 0−T w)

405 -3.61744855 -578.93425410 -3.64822021 -583.858927415 -3.64822021 -583.858927420 -3.67996891 -588.939969425 -3.67996891 -588.939969430 -3.71275873 -594.187633435 -3.74666028 -599.613216440 -3.74666028 -599.613216445 -3.7817516 -605.22921450 -3.7817516 -605.22921455 -3.7817516 -605.22921460 -3.81811924 -611.049465465 -3.81811924 -611.049465470 -3.85585957 -617.089404475 -3.85585957 -617.089404480 -3.85585957 -617.089404485 -3.89508028 -623.366263490 -3.89508028 -623.366263495 -3.89508028 -623.366263500 -3.89508028 -623.366263505 -3.89508028 -623.366263510 -3.93590228 -629.89939515 -3.93590228 -629.89939520 -3.93590228 -629.89939525 -3.97846189 -636.710605530 -3.97846189 -636.710605535 -3.97846189 -636.710605540 -4.02291366 -643.824637545 -4.02291366 -643.824637550 -4.02291366 -643.824637555 -4.02291366 -643.824637560 -4.02291366 -643.824637565 -4.02291366 -643.824637570 -4.02291366 -643.824637575 -4.02291366 -643.824637

TABLA Nº 21: Valores de la pendiente de la grafica Bi−1∗ln( T−Tw

T 0−T w) vs tiempo y

conductividad térmica experimental del Aluminio


K ( wm∗K ) 205.163 228.209

TABLA Nº 22: Valores de la pendiente de la grafica Bi−1∗ln( T−Tw

T 0−T w) vs tiempo y

conductividad térmica experimental del Cobre


K ( wm∗K ) 433.820 403.750

TABLA Nº23: Porcentaje de error de conductividad térmica – Aluminio


% Error 0.08 11.32

TABLA Nº24: Porcentaje de error de conductividad térmica – Cobre


% Error 12.68 4.87

EJEMPLOS DE CALCULOS

Determinación del coeficiente de convección del aluminio – 1era corrida

Se usa la siguiente ecuación

−m=−h x A s

ρ xV xCp… ..(1)

Donde:

m : pendiente de la grafica ln( T−T w

T 0−T w) vs tiempo

h :Coeficiente de conveccion( W

m2 x s )ρ :Densidad delmaterial de la barra(Kg

m3 )Cp :Capacidad calorificadelmaterial ( J

Kgx K )V :Volumendel area de labarra (m3 )

As :Area de la barra (m2 )

La pendiente lo hallamos de la grafica ln ( T−T w

T 0−T w)vs Tiempo y lo podemos observar en

la tabla Nº15 y en la grafica Nº 1

m = - 0.008

Luego, hallamos el área de la barra (As)

A s=2π D2

4+πDL

Donde:

A s: Area de labarra (m2 )

D :Diametro de labarra (m )

L :Longitud de la barra (m )

A s=2π (0.05m)2

4+πx0.05mx 0.149m

A s=0.02733m2

Después, el volumen del área (V)

V= π D2L4

Donde:

V :Volumendel area de labarra (m3 )

D :Diametro de labarra (m )

L :Longitudde la barra (m )

V=π (0.05m)2 x 0.149m

4

V=2.93x 10−4m3

A continuación hallamos la densidad de la barra

ρ= MasaVolumen

ρ= 0.78860.000293

ρ=2695.508 Kg

m3

Nota 1: Los datos del diámetro, longitud, área y volumen lo observamos en la tabla Nº4, en tanto la densidad en la tabla Nº2

Finalmente, nuestros datos obtenidos lo reemplazamos en la ecuación 1.

h=mx ρ xV x CpA s

h=0.08x 2700

Kg

m3x 2.93 x10−4m3 x 910

JKg∗K

0.02733m2

h=210.05 W

m2K

Nota 2: Los datos de densidad y capacidad calorífica lo observamos en la tabla Nº 2, así como la pendiente y el coeficiente de convección en la tabla 15.

Determinación del número de Biot

Bi=h x ( VA s

)K t

Donde:

Bi: Numero de biot

h :Coeficiente de conveccion( W

m2 x s )V :Volumendel area de labarra (m3 )


K t :Conductividad termica teorica( Wm xK )

Bi=210.40

Wm2K

x ( 2.93 x10−4m3

0.02733m2 )205

Wmx K

Bi=0.01096762

Nota 3: La conductividad térmica teórica (K) lo observamos en la tabla Nº2 y el numero de biot (Bi) en la tabla Nº 17.

Determinación de la conductividad térmica experimental

−m=−K e

ρ xCp x ( VAs )2… ..(2)

Donde:

m : pendiente de la grafica Bi−1∗ln( T−T w

T 0−T w)vs tiempo

ρ :Densidad delmaterialde labarra(Kg

m3 )Cp :Capacidad calorificadelmaterial ( J

Kgx K )V :Volumendel area de labarra (m3 )


K e :Conductividad termicaexperimental( Wm xK )

La pendiente lo hallamos de la grafica Bi−1∗ln( T−Tw

T 0−T w)vs Tiempo y lo podemos

observar en la tabla Nº21 y en la grafica Nº 5

m = - 0.729

Luego, lo reemplazamos en la ecuación (2)

K e=0.729 x 910J

Kg∗Kx2700

Kgm3

x ( 2.93 x10−4m3

0.02733m2 )2

K e=205.163W

mx K

Por ultimo, el porcentaje de error de la conductividad térmica.

%Error=Valor teorico−Valor ExperimentaValor Teorico

x 100

%Error=205−205.163205

x100

%Error=0.08%

GRAFICAS

GRAFICA Nº1: ln ( T−T w

T 0−T w)vs Tiempo para la barra de Aluminio – 1ra corrida


T 0−T w)vs Tiempo para la barra de Aluminio – 2da corrida


T 0−T w)vs Tiempo para la barra de Cobre – 1ra corrida

0 100 200 300 400 500 600

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

f(x) = − 0.00801262500967566 x − 0.73027007321007

ALUMINIO 1

ALUMINIO 1Linear (ALUMINIO 1)

0 100 200 300 400 500 600

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

f(x) = − 0.00668243218916652 x − 1.18511010254187

ALUMINIO 2



T 0−T w)vs Tiempo para la barra de Cobre – 2da corrida

GRAFICA Nº5: Bi−1∗ln( T−Tw

T 0−T w)vs Tiempo para la barra de Aluminio – 1ra corrida

0 100 200 300 400 500 600 700

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

f(x) = − 0.00629541299587836 x − 0.964073688338154

COBRE 2

COBRE 2Linear (COBRE 2)

0 100 200 300 400 500 600

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

f(x) = − 0.00676087498203695 x − 0.801815463343947

COBRE 1


0 100 200 300 400 500 600

-400

-350

-300

-250

-200

-150

-100

-50

0

f(x) = − 0.730571320519947 x − 66.5842181653372

ALUMINIO 1



T 0−T w)vs Tiempo para la barra de Aluminio – 2da corrida

0 100 200 300 400 500 600

-600

-500

-400

-300

-200

-100

0

f(x) = − 0.812383507748356 x − 144.073875337156

ALUMINIO 2



T 0−T w)vs Tiempo para la barra de Cobre – 1ra corrida

0 100 200 300 400 500 600

-700

-600

-500

-400

-300

-200

-100

0

f(x) = − 1.08200629089043 x − 128.322055618012

COBRE 1



T 0−T w)vs Tiempo para la barra de Cobre – 2da corrida

0 100 200 300 400 500 600 700

-700

-600

-500

-400

-300

-200

-100

0

f(x) = − 1.00751403973476 x − 154.28976255815

COBRE 2


conductividad-lab iq

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