Bubbling thoughts
Two soap bubbles of different sizes are joined by a tube.
What will happen next?
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6 solutions
Can we also say that since the volume of the smaller bubble is less, it's internal pressure will be more and vice versa for the other bubble? (Based on Boyle's law)
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Boyle's law is applicable only for constant temperature and number of moles. Since the bigger bubble has more number of moles of air, I don't think Boyle's law would be applicable here.
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Yes it's the different number of moles in both the bubbles, for inapplication of Boyles law.
No, and it's not because of the moles. If the bubbles were at the same P,T the moles would be in proportion to the volumes and Boyle's Law would hold if they were just in connected containers and a larger pressure was applied on both. The small bubble, in this case has a different pressure because of the surface tension adding to the atmospheric pressure. As a result, there is flow when the two are connected.
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I'm sorry, but I don't get what you're trying to say here. First you say that P and T were constant, then you add that Boyle's law would hold. I still don't get why the difference in the number of moles isn't the right reason for the failure of Boyle's law in this phenomenon.
As the others have mentioned, you cannot use Boyle's Law this way as the number of moles in the 2 bubbles is different. However, you can consider Boyle's Law when applying to the entire system, i.e. the total number of moles in the 2 bubbles is equal to the number of moles in the final single bubble. You will essentially use the law indirectly through the Ideal Gas Law/Equation.
If you create the bubble with the straw then the air will flow out as soon as you take the straw out of your mouth. but if you join two bubbles you will end up with a blocked straw. one of the bubbles is added to the end, which means that the surface of the bubble at where it meets the straw blocks it. ignoring that fact will make your answer correct.
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It is assumed that the two bubbles existed independently before they were joined by a tube. The tube's two ends are open to the air inside the bubbles.
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Why not add that bit of information to the question? As an engineer my first thought was to go get some bubbles and try it. As a numerical thinker, I thought well if the difference in the radius is .000000000000000000000000000000000000000000001, one is still bigger, but there would be no change, as the difference in pressure would be too small to have an effect.
The question should read: If two bubbles, that differ greatly in size, are connected to opposite sides of a straw. The straw is being pinched at the center, allowing no air to flow through the tube. What would happen if the center of the straw was released?
Now the question could be answered.
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@Matthew Radice – You, being an engineer, shouldn't make a fuss about the littlest of details. Even if the difference between radii was minuscule, in an ideal environment, the air would still flow from the smaller to larger bubble.
And if you think that the difference between the radii is too small to have an effect, I think that the difference between the radii is too small to even call one 'bigger' and the other 'smaller'.
(BTW when I originally made this problem I had included a valve in the tube which could be opened, but Brilliant re-edited the question to remove it.)
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@Parth Sankhe – Wait, I was trying to be funny... And being an engineer, I was taught to make a fuss about everything and will continue to do so!
The valve would have been a nice touch!
Sorry if you took my response the wrong way. It was a great question!
How is this different than if they were rubber balloons?
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No, this is not different than if they were rubber balloons. The same phenomenon will occur in rubber balloons as well.
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But it is clear that the pressure in a big balloon is greater than in a small balloon as you have stretched the rubber by blowing more air in, therefore the air would flow between the balloons from a big balloon to the small. Therefore the answer given is wrong. The pressure is proportional to the energy put in to stretching the skin of the buble or balloon. The wrong assumption made is that the surface tension is the same for both bubbles, however this is not always true. As you blow up a bubble (or balloon ) the surface tension increases until it bursts. Imagine a balloon that is big enough to make a 1m diameter balloon but is only blown up to 300mm and a much smaller balloon which is blown up hard to 300mm the pressures are very different, the surface tension is very different. This puzzle is indeterminate as stated. If the amount of matter in the skin is the same in both bubbles, they will equalise to the same size.
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@James Maybury – The amount of matter will not be the same in both the bubbles. It is assumed that the bubbles existed independently before joining them, thus the bigger bubble obviously had more air in it. If it had the same amount of air as the smaller bubble, that would cause it to compress till the surface tension force and the resistance to compression neutralise each other.
Stretching the rubber balloon more by putting more air in it doesn't mean that there is more pressure inside the balloon, it just means that there is more stress/pressure in the rubber layer of the balloon. The pressure of the air inside the balloon has nothing to do with how much stress the rubber is under.
The surface tension constant is same for both bubbles/balloon, since they are made of the same material. As long as two bubbles are made up of the same material and are of the same radius, the excess pressure inside both of them is same.
You can google the 'two balloon experiment' for more details.
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@Parth Sankhe – There is a lot of confusion here. 1.A mistake I have made is not realising that forcing 2 units of air into one balloon takes less energy than 1 unit each into 2 balloons as the increase in surface area ( therefore energy required) is less. Therefore it is dynamically unstable which is the point presumably being aimed at. 2. The mass I was talking about is the mass of the bubbles not the mass of the contents. The puzzle should stipulate this as the same. Identical quantities of soap is normally not true. Taking the two balloon experiment makes sense as the two balloons are presumably identical in their moulded size and thickness which is important. 3. Of course the pressure increases as the rubber/soap film is stretched.
Interesting principal. But be careful of assumptions.
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@James Maybury – I'm sorry, but I just don't get how energy has anything to do with this. And also, I don't get why pressure inside the balloon is proportional to the energy put into blowing the balloon.
The whole 'the pressure inside increases as the soap/rubber is stretched' thing is actually what confuses a lot of people into thinking that surely the bigger bubble would let it's air out, but as the solution explains, the opposite happens.
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@Parth Sankhe – One can always check or just remember blowing up balloons. It's always harder to start blowing it, and gets easier later, suggesting pressure is smaller later.
@Parth Sankhe – Firstly, I watched videos of it...Seeing is believing.
However, this part of your explanation is false: "The pressure of the air inside the balloon has nothing to do with how much stress the rubber is under."
Look at a force balance on the curved section of the balloon (assuming the material is very thin). θ is the angle between the tension force and tangent to the balloons surface.
p A − T sin θ − p o A = 0
p = p o + A T sin θ
The internal pressure p has a dependency on the tension T , and T has a dependency on stress/strain through Hooks Law in the elastic region (or a materials stress strain response in general).
What's most likely happening in the two cases (the bubble and the balloon) is sin θ is tending to 0 at a greater rate than T is increasing due to the very elastic nature of the materials, and as it expands p is tending to p o . until A T reaches the breaking strength of the material.
If you could imagine two identical spherical steel tanks and you tried to "blow one up", it should be obvious that the tank with the larger radius is going to be under significantly greater pressure, and the experiment would not play out in the same way.
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@Eric Roberts – The opposing force in balloons is tension, which does increase as you stretch the rubber, so your explanation is correct for balloons. However, in bubbles the opposing force is solely surface tension, which just depends on the material and the radius.
Pressure in rubber balloon. https://youtu.be/GiG0e1s6nV4
It's funny to see the actual reason because I thought it would be involving atmospheric pressure (which somehow we can know the Force exerted) and the pressure equation which is P=F/Area.
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Quite close.. since surface tension is the force in your equation, and the area is directly proportional to a function of the radius.
It’s not different from balloons at all
My first answer of this problem that they would pop (they are blowing bubbles; fragile), but yes it is correct
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The popping part is correct, but it was not what they meant to ask... The theme of the question was surface tension
Possessive form if 'it' is 'its'. If you're going to claim to be a site about education maybe you should learn grammar.
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Maybe if you're trying to learn a thing or two about science and math you shouldn't care about an apostrophe. This isn't a grammar improvement website, if a person even uses the most broken English to explain something, and it gets the point across, it doesn't matter. ( It's also pretty ironic that the first sentence of your comment was grammatically wrong)
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You don't handle criticism well.
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@Russell Yazbeck – You do not realize that you are a hypocrite. Just let him contribute to the site.
@Russell Yazbeck – You just pointed out an apostrophe mistake on an explanation to a science problem, you think that's criticism or just a bad attempt at grammar nazi'ing?
@Russell Yazbeck – This is a site for educating people. It is true that there was a mistake and I think that is great that you pointed it out, but there's simply no reason to create this unnecessary hostility. Like he said before, even if someone explains something in the most broken English ever, yet still manages to effectively convey their point, it doesn't matter how bad their grammar was. It works the same way for other things too; nobody discredits Shakespeare's work simply because he failed biology in 7th grade.
Just like this problem, there are many solutions and paths that may be taken to solve it. In this scenario, the end result is more important than the journey.
That's a typo, plus I think it's understandable that a better spelling would be expected from someone correcting the exercices...
Russell Yazbeck dont be a hater
Well I think you are the one that needs to learn grammar because you said “Possesive form IF ‘it’ is ‘its’” instead of OF.
Russell, the first sentence of your comment is grammatically incorrect.
You seem to have an idea that this content was produced by Brilliant; that is entirely incorrect. The post you read was made by a user like you, except much less rude.
Additionally, you should be aware that this application is used by people of all levels of education from many countries across the globe! Not all of these users come from English-speaking countries. They are here to study and enjoy math and science, and they use other resources to improve their English skills.
When you are salty you didn't know the answer be like
As long as the answer conveys the information correctly, the grammar should not matter.
In my opinion, it's reasonable to expect good English and correct it; just be nice!
You don't seem to realize this question is made by a user, not one of the Brilliant staffs.
Your first "sentence" in that comment is a sentence fragment. It has no verb. The second sentence is missing a comma and should be written: "...a site about education, maybe you..." instead. Fix your own problems before you criticize others.
Woah calm down dude.
Wait, there's no pipe that can penetrate inside a bubble..right?
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Yes it can
With the right condition(s), it can
Who knows...
If this app is brilliant it should know how to use the word “it’s” - this question alone misused it twice.
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This Answer! Which is written by a fellow user (i think), who does a great job explaining things.
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So ur only concern is the use of "it's" and not its...misplaced. Very funny.
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@Kingsley Mbaekwe – My exact thought. I've only passed Freshman High-school after it went out a few months ago, and I'm confused on these past questions. Even if I only did three, and I'm autistic and crap - this is above my grade level.
I was so confused at first. I kept thinking " The bubbles would pop, right?" Then I realized I was overthinking to much. This was a really fun question to think about.
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If the process is done very slowly, they won't
But the soap bubble is in equilibrium with the atmosphere is so its pressure should be the same as atmospheric pressure
Wait, doesn't every system tend toward equilibrium, so wouldn't the bubbles exchange air until they are the same size?
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That's how we see our everyday processes, that's how almost everything in our daily life happens. But wait, why is it so. Why do things tend to reach equilibrium. A better understanding to this is provided by the thermodynamic quantity, entropy, better say change in the entropy of universe. Although this can be used to determine the feasibility of a process but at constant temperature and pressure conditions, it is much easier if we use change in Gibbs free energy. Returning back to the question, why does every process tend to reach equilibrium, it is because the change in Gibbs free energy becomes zero, better say there is a minima at equilibrium if you draw the plot of Gibbs free energy of a process. Now, why not here? So, I'd like to know from you, reader, what would you say, is equilibrium the attainment of equal pressure, or equal volume or moles or something else?
Consider ideal gas equation: p V = n R T
Assume the soap bubbles are created under the same conditions, hence have the same temperature T . R is the molar gas constant. n is the amount of gas in moles. Let the smaller bubble be bubble 1 and the bigger bubble be bubble 2. Given that the density of gas always remain the same, n 1 + n 2 = n where n is the total amount of gas and V 1 + V 2 = V where V is the final volume of gas in a single bubble.
Manipulating the ideal gas equation, the following relationship can be obtained:
p 1 V 1 + p 2 V 2 = p V
Substituting V = V 1 + V 2 , the next relationship is:
V 2 V 1 = p 1 − p p − p 2
∵ V 1 < V 2 , and both volumes are positive,
p 1 − p > 0 and p − p 2 > 0 , and p − p 2 < p 1 − p
∴ p 2 < p 1
The bigger bubble has lower pressure than the smaller bubble initially, hence gas flows from the smaller bubble to the bigger bubble.
Thank you! I think this is the clearest and most rigorous answer.
I still don't understand how the larger bubble has a lower pressure... Wouldn't a lower pressure result in a smaller bubble? Does surface tension not play a role in this? So although the density is the same the pressure can be different... I am both fascinated and perplexed.
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Pressure of the gas can be understood as the force of the gas molecules hitting the inner surface area of the bubble (or whatever is holding the gas). When temperature goes up and the volume of the container remains fixed, the gas molecules move more quickly, hence the rate of change of momentum of the molecules are much higher, translating to a greater force and thus larger gas pressure. Since the mass and volume of gas is fixed, density remains the same. Hope this helps :)
Surface tension does play a role, and it is well-explained by Parth Sankhe too. Regardless, since gas will take up the entire volume of the container it is contained in, and surface tension will compress the gas into the ideal gas state, I believe that the ideal gas equation can explain this without considering the surface tension (for this case, using bubbles). If balloons were to be used, as the balloon stretches, the thickness of the balloon changes significantly and the surface tension constant of the 2 balloons will be significantly different, but I doubt the significance holds for bubbles.
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Thank you for taking time to explain this :)
Why not assume both bubbles have the same pressure? The initial condition for these bubbles should be stated clearly, otherwise, there are many possibilities for having different answers.
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They already have different size. Since the question did not specify the initial pressure, you can't assume that the 2 bubbles have the same initial pressure. Also, the question actually wants you to calculate the difference in initial pressure in the 2 bubbles to determine the net flow of air, which hints to you that you cannot assume the initial pressures.
Where does p2<p1 comes from? And why is p1-p>0 ?
A more intuitive approach: think of opening an inflated ballon, the ballon will slowly decrease in size while the air is flowing out of the small container (the ballon) into the big container (open space).
I think the reason this explanation works is because we know that the surrounding air is at a lower pressure than the balloon's air; we can't say the same about a bigger bubble though. In fact, the whole point of the problem is to prove that the bigger balloon/bubble will have its air at a lower pressure than the smaller one. But yes, your solution to some extent is a solid approach. Thanks!
Very intuitive, it's almost trivial. Thanks!
The gas have pxV =cost of V1<V2 then p1>P2
Application of Boyle's law has the constraint that number of moles should stay constant. Since both the bubbles obviously have different number of moles, Boyle's law ( P 1 V 1 = P 2 V 2 ) is not applicable.
O ar tende a deslocar-se de altas pressões para baixas pressões... Se ambas as bolhas tiverem o mesmo conteúdo, a bolha onde existirá maior pressão será na mais pequena visto que a área de superfície é menor. Assim o ar deslocar-se-à da bolha mais pequena para a bolha maior.
Você poderia explicar como a superfície sendo menor faz com que a bolha tenha maior pressão?
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Não sou capaz de explicar essa parte, até porque nem aprendi isto ainda, ahahahah Foi apenas intuição.
Nunca vi um br aqui, mt bom.
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Na verdade eu sou de Portugal, mas tamujunto ✌👍
Eh, no comprende, amigo. :-)
The smaller bubble exerts a greater force inward than the large one, so the air will flow from the small bubble to the large one.
Yeah so I was a professional clown and have done this trick. In THEORY this explanation works but in practice you get surface tension WITHIN each end of the straw and so nothing happens because each bubble seals each end of the straw. Otherwise one wouldn't be able to keep a bubble on the straw long enough to put a bubble on the other end. The explanation needs to be clearer and if yoh do y believe me just try it yourself ;-)
Exactly. There should have been an assumption the tube penetrates both bubbles. I did not see the assumption and I selected fourth answer.
We know as air always flows from high pressure region to low pressure region and excess pressure of air bubble is inversely proportional to radius so air flows from small bubble to large bubble.P=4S/R here P is excess pressure ; S is surface tension of liquid ; R is radius of curvature of bubble
The reason bubbles exist is because of surface tension. Surface tension causes the bubble to decrease it's surface area, till the point where it can't compress the air inside it anymore.
This causes some excess pressure to be developed inside the bubble, and it's value is equal to r 4 T , where T is the surface tension constant, and r is the radius of the bubble.
This means that the pressure inside the bubble is inversely proportional to it's radius, thus smaller bubbles will have greater pressure. As we all know, air flows from higher pressure to lower pressure, thus the smaller bubble further decreases in size and the larger bubble expands .