Viscosidad Labos 3 Fico

May 2, 2019 | Author: darwinunorte | Category: Liquids, Phases Of Matter, Physical Sciences, Ciencia, Física y matemáticas
Share Embed Donate


Short Description

Download Viscosidad Labos 3 Fico...

Description

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

INDICE

1. Intr oducción……………………………………………………… oducción………………………………………………………

2

2.

3

Objetivos………………………………………………………....

3. Fundamento Teórico

4.

……………………………………………

4

3.1

Viscosidad de

los Líquidos………………………… Líqui dos…………………………….. …..

4

3.2

Método del Viscosímetro de Ostwald…………………..

5

3.3

Viscosidad Cinemática………………………………… …………………………………..

7

Materiales y Reactivos……………………………… Reactivos…………………………………………… ……………

8

4.1

Materiales……………………………………………….

8

4.2

Reactivos………………………………………………..

9

5. Procedimiento

Experimental……………………………………...

10

6.

Cálculos y Resultados…………………………………………….

11

7.

Conclusiones………………………………………………………

19

8.

Anexos…………………………………………………………….

20

9.

Bibliografía………………………………………………………..

22

10. Cuestionario……………………………………………………….

23

VISCOSIDAD – VISCOSIDAD – FISICO QUIMICA

Página 1

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

1. INTRODUCCIÓN Viscosidad es la

propiedad de un fluido un fluido que tiende a oponerse a su flujo

cuando se le aplica una fuerza. Los fluidos de alta viscosidad presentan una cierta resistencia a fluir; los fluidos de baja viscosidad fluyen con facilidad. La fuerza con la que una capa de fluido en movimiento arrastra consigo a las capas adyacentes de fluido determina su viscosidad, que se mide con un recipiente (viscosímetro) que tiene un orificio de tamaño conocido en el fondo.

La práctica de viscosidad es una práctica muy importante en el sentido industrial debido a que esta se fundamenta mucho en leyes físicas y químicas que nos permite entender porque tal compuesto es más espeso que otro, o porque un compuesto es utilizado como lubricante, etc.

El saber cuan viscoso es una solución nos permite saber por ejemplo su peso molecular, es decir podemos determinar el peso molecular de una solución desconocida gracias al método de viscosidad. El  El  poder estudiar la viscosidad de una sustancia nos ayuda a concluir cuanto varia con respecto a la temperatura, si es más viscoso o menos viscoso, etc.

El conocimiento de la viscosidad de un líquido nos ayuda en el área de mecánica de fluidos ya que podemos saber qué tipo de líquido es importante y porque usarlo en tal máquina para que esta funcione en óptimas condiciones. O porque usar tal lubricante para carro a tal temperatura y porque no usar otro. O tal vez en las bebidas como las cervezas, ya que la viscosidad influye mucho en el gusto de la persona,  persona,  etc. En fin el conocimiento de la viscosidad trae consigo muchas conclusiones que pueden llevar al éxito al  éxito de una empresa. una empresa.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

2. OBJETIVOS Determinación de la viscosidad de líquidos por el método del flujo capilar

Determinación de la energía del flujo y la entropía del flujo a partir de las mediciones de viscosidad a diferentes temperaturas

Calcular la viscosidad del temperaturas.

tolueno y la glicerina a diferentes

Determinar una ecuación para expresar la variación de la viscosidad con respecto a la temperatura de un líquido.

Calculo de ΔH para el tolueno y la glicerina.

Calculo de ΔS para el tolueno y la glicerina a diferentes temperaturas.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

3.FUNDAMENT 3. FUNDAMENTO O TEORICO La viscosidad es lo contrario de la fluidez, generalmente se define como resistencia al flujo. Los líquidos (y también los gases) pueden fluir, es decir desplazarse una porción respecto a otra .Las fuerzas de cohesión entre moléculas originan una resistencia interna a este desplazamiento relativo denominado viscosidad.

Se llama viscosidad o frotamiento interno a la resistencia experimentada por una porción de un líquido cuando se desliza sobre otra como consecuencia del rozamiento molecular. El agua fluye más fácilmente que la melaza y esta con más facilidad q una pasta de caucho. Los aceites de motor están clasificados en una escala que corresponde a su viscosidad .Como la viscosidad normalmente aumenta cuando disminuye la temperatura tenemos que reemplazar el aceite para motor “pero de verano” (alta viscosidad) con uno de viscosidad más baja para el tiempo frió.

En base al modelo cinético molecular. La viscosidad de los gases aumenta al aumentar la temperatura. La viscosidad de los líquidos disminuye al aumentar a la temperatura.

Las viscosidades de los líquidos se miden comúnmente con el viscosímetro de Ostwald, o para líquidos más viscosos con el viscosímetro de esfera .La unidad de viscosidad es el poise (1g.cm-1.s  –1),  –1), es el más favorable para determinar la viscosidad de un líquido por comparación con otro liquido cuya viscosidad ya es conocida y en condiciones experimentales idénticas .

3.1 VISCOSIDAD DE LOS LIQUIDOS La viscosidad de un líquido puede ser determinado su velocidad de flujo a través de un bulbo capilar.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Para el volumen (v) de un líquido que fluye a través de un tubo capilar de radio r, longitud L, en un tiempo t, bajo una diferencia de presión P; su viscosidad N es expresada mediante la ecuación de Poiseville

Si las dimensiones del capilar y el volumen del líquido que fluye son constantes, entonces para dos líquidos, uno de ellos el de referencia, se tiene:

Ni, 1/ Ni,2= Di,1x ti,1 / Di,2x ti,2

Donde las presiones son proporcionales a la densidad. Esta ecuación es la base del viscosímetro de Ostwald.

Ni, 1: Viscosidad del líquido de referencia Ni, 2: Viscosidad la que vamos a hallar Di, 1: Densidad del líquido de referencia. Di, 2: Densidad del que vamos a hallar su viscosidad Ti, 1: Tiempo en que escurre el líquido de referencia Ti, 2: Tiempo en que escurre el segundo liquido

3.2 METODO DEL VISCOSÍMETRO DE OSTWALD Este método consiste en medir el tiempo que tarda en fluir por el capilar C, el líquido contenido entre las marcas “a” y “b”. La viscosidad relativa de una sustancia medida en el viscosímetro de Ostwald es con respecto al agua a la temperatura del experimento. Para determinar la viscosidad relativa de un líquido a una cierta temperatura, se debe determinar el tiempo de flujo de un volumen dado de líquido y el tiempo que tarda en fluir el mismo volumen de agua a igual temperatura, en el mismo viscosímetro. La presión P no es la misma, depende de la presión hidrostática del líquido, la cual para alturas idénticas depende únicamente de sus densidades. Conocida la viscosidad relativa se debe multiplicar por la viscosidad del líquido de

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

La dependencia entre la viscosidad y ciertos límites de temperatura, obedece a una ecuación del tipo:

LOG N = A/T + B

Donde A y B son constantes para el líquido dado

3.3 VISCOSIDAD CINEMATICA. En hidrodinámica intervienen junto con las fuerzas debidas a la viscosidad las fuerzas de inercia, que dependen de la densidad. Por esto es de importancia la viscosidad dinámica referida a la densidad, conocida como viscosidad cinemática y se define como: V = n/ρ Y tiene como unidades = m²/s 1cST = ( 1/10²)St = 1/10 m²/ s Donde: St = Stoke.

La viscosidad se mide con la ayuda de viscosímetros de varios tipos (por ejemplo de Ostwald, Engler, Saybolt, etc).

Experimentalmente la viscosidad de un líquido puede determinarse midiendo su velocidad de flujo por un tubo laminar. El volumen V de un líquido que fluye a través de un tubo capilar de radio r durante un tiempo t bajo un presión ▲P constante, está dado por la ecuación de Poiseuille como:

n = Π▲Pr t/8lV

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Si las dimensiones del capilar y el volumen de líquido son constantes:

n = K▲Pt

▲P = γh = ρgh

n = Kρght

Dónde:

h = diferencia de altura. ρ = densidad del líquido.

La relación de viscosidades de líquidos pude determinarse fácilmente empleando la ecuación inmediatamente anterior, así para los líquidos 1 y 2: N1/n2= kgh ρ1 t1 / kgh ρ 2t2 n1/n2 = ρ1 t1 / p2t2)

En donde t1 y t2 representan los tiempos de flujo. Como sustancia de referencia se emplea el agua para el cual son conocidos l viscosidad y la

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

4. MATERIALES Y RECATIVOS 4.1 MATERIALES: 1. Viscosímetro de Ostwald

4. Termostato

5. Tubo de goma y bombilla

2. Cronometro

6. Soporte y pinzas

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

4.2 REACTIVOS: 1.  Aceite lubricante

2. Tolueno

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

5. PROCEDIMIENTO EXPERIMENTAL 1º.

Lavar debidamente el viscosímetro con mezcla sulfocromica caliente.

2º.

Luego enjuagar con agua destilada seguido por acetona y seguidamente aseado por aspiraciones del aire seco a través de él.

3º.

El viscosímetro es colocado verticalmente en el baño termostático a la temperatura de 250C con ayuda de la pipeta, se introduce un volumen de agua destilada, dejando que luego alcance la temperatura de equilibrio del baño.

4º.

Por succión a través de un tubo de goma, acoplado al viscosímetro, se eleva el líquido en la rama capilar hasta que el menisco rebase la marea hasta la marca A. Dejando entonces fluir el líquido, se anota el tiempo que tarda el menisco en atravesar sucesivamente las señales “A” y “B”.

5º.

La experiencia debe repetirse empleando el mismo volumen de benceno, luego aceite lubricante. La experiencia con cada uno de los líquidos debe realizarse a la temperatura 250C, 300C, 350C y 400C.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

6. CALCULOS Y RESULTADOS 1. TOLUENO

0

N

Masa del

T0

pacómetro

C

vacío

Masa (pico

Vol.

ɵ H2O

ɵ tolueno

metro + tolueno)

(ml)

(seg.)

(seg)

1

25

30.922

73.00814

50

3.86

4.166

2

30

30.922

73.90385

50

3.66

3.80

3

35

30.922

73.62080

50

3.40

3.40

 ρ Tolueno (g/ml)

T0K

1/T0K

n (H2O) cp

 ρ H2O (g/ml)

0.8417

298.15

3.3540 x 10-3

0.895

0.9971

0.8596

303.15

3.2987 x 10-3

0.8007

0.995678

0.8539

308.15

3.2452 x 10-

0.7225

0.994061

n Tolueno

Ln (n Tolueno)

 ρ  n/ ρ

 ρ) Ln(n/ ρ

 ΔS (kcal/mol)

0.81540 cp

-0.2040 cp

0.9687

-0.0318

-1.0649x10-3

0.7177 cp

-0.3017 cp

0.8349

-0.1804

-1.0471x10-3

0.6206 cp

-0.4771 cp

0.7268

-0.3191

-1.0103x10-3

1.1.

Densidad:



 

  

+

 





  



Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

1.2.

Viscosidad a diferentes temperaturas:

                                    

1.3.

      

Hallar energía “E” y A:

     + +   

  



 



     

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

                                  

Entonces:

 Ahora despejando A de de la ecuación original se tiene tiene que:



1.4.



 

      

    

               

Entalpia ΔH:

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

∑  Usando el Método de mínimos:

                           ∆          ∆  ∆ 

Entonces:

1.5.

Entropía ΔS:

 















Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

2. GLICERINA:

N0

T0C

Masa del

Masa (pico metro

Vol.

ɵ H2O

pacómetro vacío

+ glicerina)

(ml)

(seg)

ɵ

Glicerina (seg)

1

25

30.922

92.2418

50

3.86

180.10

2

30

30.922

92.2108

50

3.66

137.533

3

35

30.922

91.965

50

3.2285

96.73

 ρ Glicerina (g/ml)

TK

1/T K

n (H2O) cp

 ρ H2O (g/ml)

1.2264

298.15

3.3540 x 10-

0.895

0.9971

1.2258

303.15

3.2987 x 10-

0.8007

0.995678

1.2205

308.15

3.2452 x 10-

0.7225

0.994061

n Glicerina

Ln (n Glicerina)

 ρ  n/ ρ

 ρ) Ln(n/ ρ

 ΔS (kcal/mol)

51.3621 cp

3.9389 cp

41.88048

3.7348

-1.0649x10-3

37.04216 cp

3.6120 cp

30.2187

3.4084

-1.0473x10-3

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

2.2.

Viscosidad a diferentes temperaturas:

                                     



2.3.

FIIS-UNAC

      

Hallar energía “E” y A:

     + +   

  



 



Usando el Método de mínimos:

     

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

                                  

Entonces:

 Ahora despejando A de de la ecuación original se tiene tiene que:





Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

∑ 



Usando el Método de mínimos:

                         

Entonces:

FIIS-UNAC

 















Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

7. CONCLUSIONES 

A medida que aumenta aumenta la temperatura, disminuye el valor de la viscosidad en ambos casos, mostrándonos una relación inversa entre sus magnitudes.





Este fenómeno se repite al analizar S y la temperatura, encontramos una relación inversa, y a la vez una relación proporcional con respecto al valor de la viscosidad.



La viscosidad viscosidad de un líquido es es afectada por la variación de la temperatura y

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL 8. ANEXOS Wilhelm Ostwald Nació el 2 de septiembre de 1853 de 1853 en la ciudad de Riga, de Riga,   que en aquellos momentos formaba parte del Imperio del Imperio ruso, y ruso, y hoy en día es la capital de Letonia, de Letonia,   en una familia dealemanes dealemanes del Báltico. Cursó

estudios

en

la

de Dorpat de Dorpat (hoy Universidad graduándose profesor

en

en1875. en1875.   dicho

Universidad de

Trabajó

centro

hasta

Tartu), como 1881.

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Obtuvo el premio el premio Nobel de Química en 1909 en 1909 por su trabajo en la catálisis la catálisis y por sus investigaciones sobre los principios fundamentales que rigen los equilibrios químicos y las velocidades de reacción.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

9. BIBLIOGRAFIA 

DILLARD, Clyde R. Química: reacciones, Estructuras, Propiedades.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

10.

FIIS-UNAC

CUESTIONARIO

1. Demuestre a partir de la mecánica de fluido que la relación de las

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

viscoso (también denominado fluido newtoniano)  newtoniano)  a través de un tubo cilíndrico de sección circular constante

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Esta fuerza es dirigido debido a la viscosidad, las fuerzas que actúan sobre

∆ +        ∆ +   

el centro de masa del líquido es

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

  ∆∆    ∆          

Entonces se demuestra que:





     

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL Para el Petróleo

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

la estructura molecular ya que esta intervienen en la transición de cantidad

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

UNIVERSIDAD NACIONAL DEL

FIIS-UNAC

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

View more...

Comments

Copyright ©2017 KUPDF Inc.
SUPPORT KUPDF