Sound Absorption in Liquids in Relation to Their Physical Properties2

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Sound Absorption in Liquids

In

Relation to Their Specific Heats. I I

B y

S .

P a r t h a s a r a t h y and D.

S .

G u r u s w a m i

With 1Figure

Abstract

I t has been shown in en earlier paper that the complete formula for observed

sound absorption is given by

2

' 5

3 3

hich contains the factor

(-/- - - Y ) ~

in addition

to

S t o k e s - K i r c h h o f f

term. While posit.ive and negative temperature coefficients of absorption

cannot be explained by any of the existing theories, the new formula well

explains both through such variation of

y

with temperature. In a similar

manner absorption with pressure is accounted for. It is noticed that at the

critical point in liquid-vapour systems the sound absorption is very great and

t,he

y

also is large which accounts for large sound absorption. Similar behaviour

is noticed in binary liquid mixtures also

a t

the critical temperature where

sound absorption has been found to be enormous.

1. Introduction

It

is now well-known that the observed absorption of sound in several

liquids is far in excess of tha t predicted by St o k e s -K i r c h h o f f formula.

There have been many attempts since then to account for this anomalous

absorption. The various approaches, thermal relaxation, structural relaxation

and second viscosity, have been developed by Herx fe ld and Rice1) and by

Kneser2 ) , by Hal l3) , and by Ec ka r t 4) and by L ie ber m an n5) respectively.

I t may be noted that the approach to the problem through relaxation and

second viscosity are essentially different. These methods are of very limited

application and it has been suggested th at everyone of them may play some

part in the contribution to the absorption of sound in the medium. But it is

essential to find out the specific conditions under which any one of them would

I

I


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288

nnalen

der Physik. 6 .Falge.

B a n d

16. 1955

be effective and if possible by experiments to critically differentiate between

them. These methods have been discussed in detail in the first part6) of our

paper.

In an earlier paper6), we have brought out the important bearing of the

ratio of specific heats on the phenomenon of absorption of sound and therein

we have given an empirical relationship connecting

y

(the ratio of specific

heats) and the ratio of observed sound absorption to classical absorption as

calculated on the basis of S t o k e s - K i r c h h o f f theory.

The observed absorption at 5

Mc.

is given by

a

is the absorption coefficient,

Y

is the frequency,

v

is the velocity of sound,

Q

is the density,

rj

is the coefficient of viscosity,

c ,

is the spccific heat a t

constant pressure,

k

is the coefficient of thermal conductivity.

From the above relation it is clear that a high value of the ratio of specific

heats is indicative of a high absorption coefficient. The contribution to ab-

sorption due to viscosity and due to thermal conduction are additive and

indcpcndcn t

.

In this paper we have examined whether the absorption changes with

temperature and pressure and also its variat.ion at critical solution tempera-

tures as recorded by earlier observers which have

so

far remained unaccounted

for on the basis of several theories proposed could be satisfactorily explained

by the new formula. Incidentally a few other consequences

of

the theory have

also been followed up.

2. Further

Examination of Excess

Absorption

a) y as

an

additive term

I t has been argued that the excess absorption of sound may be explained

on the basis of second viscosity and tha t this lat ter quanti ty may not bear

an y relation to the first viscosity. The above formula can be put in the form

OL 0:

i. e. it is the ratio

-

bs. to -- theory which is a function of

y ,

the ratio

of

specific heats. However since a high value of

y

is undoubtedly an indication

of high sound absorption

it

was thought that

y

may be a function

of

the

excess absorption only, thus yielding an equation

V2

V2

This again shows the importance of a study of the relationship, if any, of

sound absorption with other physical properties of the medium. In order to

6

S.

Parthasarathy and

D.

S. Guruswamy (under publication in this Journal)

This paper

forms

Part

I

of t,his series.


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S. Purthasarathy and D , S. Guruswami: Sound Absorption in Liquids. II

289

chech the above we have plotted the value of

y

against the difference

a a. - Th- .

VZ

The factor

A

has been included to make the equation dimensionally balanced.

In the following table are given the values of

y

and the absorption values,

both experimentally obtained and those calculated on the basis of S t o k e s

-

Kirchhoff formula. The y values of the liquids have been obtained

from

thermodynamic relationships as indicated in the previous paper.

The absorption values are mostly those of one of us

(S.P.), S. S.

C b a r i

and

D.

Sr in ivasan ' ) . In the third column is given the difference between

Table

1

Liquid

.

10-1

1. Carbon disulphide

2.

Chloroform

3.

Carbon tetrachloride

4. Benzene

6 . Ethyl acetate

6. Acetone

7.

Bromoform

8.

Chlorobenzene

9.

Toluene

10.

Cyclohexane

11

Methyl ethyl

ketone

12. Xylenc

(m)

13. Ethylene chloride

1 4 .

Nitrobenzene

15. Amyl alcohol (n)

16. Ethyl butyrate

17.

Amyl acetate

18.

Cyclohexanol

19.

Heptane

(b)

20. Acetophenone

21.

Hexyl alcohol

22.

Methyl alcohol

23.

Benzyl alcohol

24. Ethyl alcohol

25.

Butyl alcohol (n)

26.

Butyl alcohol

(iso)

27. Mercury

28. Water

5,05

10,o

19,l

8,25

7,7

6,3

8,5

7,6

15,3

7,6

7,6

9,o

23,9

13,2

66,67

12,4

15,3

119,2

10,o

12,8

61,O

14,3

38,5

24,6

44,7

43,2

8,5

5,05

7700

400

586

808

190

37

230

99

123

458

33

89

136

99

193

230

234

489

80

189

192

30,O

159

54

194

249

6,O

31,2

[ 3 0 b s .

~

7695

390

566,9

800

182

31,7

206,l

91 5

115,4

442,7

25,7

81,4

127

85,s

126

217,6

218,86

370

70

176,2

131,O

15,7

120,5

29,4

149,3

215,s

22,7

0,95

Y

~

1,566

1,491

1,455

1,447

1,436

1,416

1,386

1,366

1,350

1,335

1,325

1,319

1,315

1,299

1,298

1,287

1,281

1,255

1,237

1,225

1 218

1,214

1,205

1,204

1,183

1,159

1,147

1,007

The relationship between

y

and the excess absorption has been investi-

gated in the following graph.

A glance a t the graph shows th at there is no relationship between

y

and the

excess absorption. The spread

of

points is much greater and irregular for

those liquids which do not have very high absorption. This shows tha t the

factor A is not a constant and depends on the medium.

It

can possibly be a

7

S. Parthasarathy,

S. S.

Chari and

D.

Srinivasan,

J.

Physique Radium 14,

641 (1963).

Ann. Phrsik.

6.

E olge, Bd. 16

19


4/10

290

Annulen der

P h y s i k . 6 .

Folge. B u d

16. 1955

function of density, velocity, viscosity and/or frequency.

This

aspect is under

investigation. It is significant to note that though there are several liquids

with higher than 1,40, yet they do not appear lower than z = 400 1O-l';

for them the absorption must indeed exceed this value. Further one would

expect to show a maximum value for

y = 1 , 6 7

and be very small

N O ) for

a) y values and their deviation from the proposed formula

A

glance at the graph between

a bs./aTh.

and

y

given in the previous

paper6) (fig. 1)on the basis of formula 1 shows that a few liquids are off the

curve A )which was taken as the best fitting curve. It was originally thought

a

y

=

1.

150

I

Q

I I I 1

1

0 ?OO

zoo

300

400

500 600

bs -

OL

Th

VZ

Fig. 1

Table 2

Liquids

P o i n t s t o t he l e f t

of th e curv e

Acetone

. .

. . . .

Bromoform

. . . . . .

Choroform

. . . . . .

Carbon tetrachloride .

.

Ethyl acetate . . . .

Methyl ethyl ketone

.

Amyl alcohol . .

. . .

P oi n t s t o t he r i gh t

of

the curve

Cyclohexane . .

.

. .

Ethyl butyrate . . . .

Amyl acetate

.

. .

Acetophenone

. . . .

Y

1,42

1,385

1,49

1,45

1,435

1,325

1,30

1,335

1,29

1,28

1,22

Deviation

from

the curve

0,18

0,095

0,085

0,06

0,055

0,105

0,15

0,05

0 07

0,05

0,105


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8.

Purthasarathy and

D. S. Guruswami:

Sound

Absorption in Liquids. 11

291

that these deviations might be due to some other phenomena or property of

the molecule affecting sound absorption. A re-examination of the y values

obtained by different workers has suggested another plausible explanation

;

as for example

y

for benzene has been variously given as

1,45

and

1,33

giving

a difference of 0,12. Another example is that of cyclohexane for which we have

obtained

y = 1,335,

while Philip gives

1 ,47 .

While the former places the

point below the curve by a difference of 0,05 in y , the latter raises it far above

by 0,12. The fact is perhaps that the point lies half-way which

brings it

nearer

the curve. This emphasises the importance of an accurate knowledge of

y

especially where the gradient is medium and small i. e. in the second and

third portions of the curve.

The

following Table of such liquids showed that there was little in comm on

either among those left of the curve or among those right of it. However as

the deviations are small, they may be attributed to inaccuracies in the values

of

y . It may be pointed out that the deviations in the case of water, acetone

and acetophenone are however too much to be explained away. y values need

to be re-determined quite accurately for all liquids.

3. Variation of Sound Absorption with Temperatures

The classical theory of absorption due to S to k e s leads one to expect a

decrease in the absorption coefficient as the temperature is increased on

account of the decrease in the kinematical viscosity with increasing tempera-

ture. This should be true for all liquids but experiments by Pe l l a m and

Gal t8 )have shown tha t in certain liquids a decrease and in others an increase

of sound absorption occur with increasing temperature.

On the thermal relaxation theory an increase of temperature increases

the probalility of energy transfer i. e. the relaxation time t) ecomes smaller.

The effect of this on the observed absorption depends on both the relaxation

frequency and the frequency at which measurements are carried out. If

and v be these frequencies then v is increased on increasing the temperature

and in the case

> yo, v

shifts toward and an increased absorption results.

If however

Sound Absorption in Liquids in Relation to Their Physical Properties2

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