Question

Two soap bubbles coalese to form a single bubble . If V is the subsequent change in volume of contained air and S the change in total surface area , T is the surface tension and P is the atmospheric pressure . Find a relation between P,V,S,T

Answer 1

@ParthKohli @ganeshie8

Answer 2

but how to bring in Patm ?

Answer 3

@whpalmer4 @imqwerty @rvc

Answer 4

@chmvijay can u help?

Answer 5

@Awolflover1

Answer 6

If 2 bubbles make a single bubble, then the total surface area will b decrease. Right?

Answer 7

And energy will b released

Answer 8

If u break a single bubble into many bubbles , then the surface area will b increase nd energy needed to do so

Answer 9

In this case
Energy release=TS

Answer 10

Here
S=increase of surface area

Answer 11

T=surface tension

Answer 12

yes u r right...

Answer 13

i have calculated S=2r1r2

Answer 14

* S=-2r1r2 right?

Answer 15

I dont know how S=2r1r2

Answer 16

wait i will check again..now i think its wrong..

Answer 17

r1^3+ r2^3 =R^3

Answer 18

but if i go by this method and find V and S its very time consuming and lengthy...is there any short method?

Answer 19

hey wont V be zero?

Answer 20

the volume of two bubbles will be equal to the volume of the bigger bubble right?

Answer 21

Yes u r right!
Volume of 2 bubbles = volume of bigger bubble

Answer 22

Nd volume of a sphere=(4/3)πr^3

Answer 23

so how can we find the relation? Subsequent change in volume is zero..??

Answer 24

So we can write
(4/3)πr1^3+(4/3)πr2^3=(4/3)πR^3
Right?

Answer 25

this what i used to find the relation..(i have written it above..did u see?)

Answer 26

U wrote
r1^3+r2^3=R^3
Which wrong

Answer 27

why?

Answer 28

why is it wrong?

Answer 29

Sorry

Answer 30

U r also correct !!

Answer 31

its ok!

Answer 32

Anyway i dont know that relation berween those

Answer 33

but u didn't my previous doubt.....

Answer 34

V=0 right?

Answer 35

@shamim ?

Answer 36

Yes change of volume = 0

Answer 37

then how can we find a relation bet V,T,S,P?? if one is zero?

Answer 38

@ganeshie8 @samigupta8 @tkhunny @agent0smith

Answer 39

Okk @priyar i found a way...

Answer 40

great what is it?

Answer 41

Luk it's not the volume addition in any way

Answer 42

What u have to do is conserve the moles

Answer 43

isn't the volume same?

Answer 44

n1+n2=N
N1 ,N2 r the moles of air in 1 n 2nd soap bubble
N is that of bigger bubble

Answer 45

oh ok..

Answer 46

U got whati want to say priyar

Answer 47

ya..u r conserving the moles right?
but i have a doubt..why won't the volume be same?

Answer 48

U myt have done gaseous state ....what do u do over there do u add up the volumes..of gas no naa...den here also d same thing rules

Answer 49

Is d ans 3PV+ 4ST=0

Answer 50

but in fluids we do that always..

Answer 51

Where do we use dis thing in fluids

Answer 52

usually to find the radius of the bigger bubble formed by two smaller bubbles we use the fact that the volume remains the same..right?

Answer 53

btw the answer is correct! how did u get it?

Answer 54

The same way i told u ...u need to work upon it...there will be like
P1V1 + P2V2 =PV

Answer 55

From conservation of moles....

Answer 56

Now put in the value of P1 as Po+4T/R1 n same put in the value of P2 n P also

Answer 57

Plug in the value of volumes also as they r spheres only....4/3πr^3

Answer 58

Po+4T/R1 ?

Answer 59

Excess pressure

Answer 60

what is ur Po and R1? first tell me the notations

Answer 61

Po is atmospheric pressure n R1 is radius of frst bubble

Answer 62

R u in 11th grade?

Answer 63

@priay did u get it?

Answer 64

sorry.. @samigupta8 was seeing my math doubt..
(P+aT/R1)V1+(P+4T/R2)V2=(P+4T/R)V is this correct?

Answer 65

how to proceed?

Answer 66

(P+4T/R1)V1+(P+4T/R2)V2=(P+4T/R)V how to proceed further how to eliminate V1, V2..
@samigupta8..

Answer 67

V1 is 4/3πr1^3

Answer 68

but won't it be lengthy..wait i'll do..

Answer 69

Same u cn find out V2

Answer 70

It is definitely not lengthy i solved it jst calculation based...

Answer 71

N pls dpn't cut 4/3 π on both lhs n rhs sides

Answer 72

Don't*

Answer 73

oh...i just did that!

Answer 74

(P+4T/R1)4/3 pi R1^3+(P+4T/R2)4/3 pi R2^3=(P+4T/R)4/3piR^3

Answer 75

Okk now open the brackets n solve it

Answer 76

PoV1 + 16/3πTR1^2 types trms will form

Answer 77

oh then se substitute 4piR1^2 as S1 right?

Answer 78

Correct u made it

Answer 79

yay got it!

Answer 80

Thanks..!

Answer 81

@ParthKohli

Answer 82

here won't V be zero??

Answer 83

Hey again u r having d same doubt...okk...luk in d question itself it says that V is volume change then why r u noy considering it....

Answer 84

no..that was for parthkohli.. regarding another Q that was related with equating volume..