Problem understanding solution of a question about a hydrogen-filled balloon

[TahirMaqbool]

Homework Statement

Problem 5.1
A balloon is filled with hydrogen at room
temperature. It will burst if pressure
exceeds 0.2 bar. If at 1 bar pressure the
gas occupies 2.27 L volume, upto what
volume can the balloon be expanded ?

My doubt is that in the answer it states(solution attached below) that volume of gas should be less than 11.35 liter , wouldn't a lesser volume lead to a pressure more than .2 bar and hence bursting of baloon.

Relevant Equations

Boyle's law

View attachment 337516

 

[PeroK]

The question makes no sense to me. A balloon only inflates if you force more gas into it. At 1 bar, isn't the pressure balanced by the air outside? Doesn't the gas in the balloon need to be at a pressure of 1.2 bar for it to burst? And, isn't the size of the balloon important?

 

[PeroK]

Imagine we had a large but flimsy balloon. That balloon might require a small pressure to burst, but it must be stretched first. So, it would require a significant amount of gas to inflate it and burst it. Meanwhile, a small but equally flimsy balloon would require must less gas to inflate it to bursting point.

The question makes no sense to me!

 

[Steve4Physics]

It sounds like both the question and answer are incorrect. I'd guess the intended question should state:

The balloon will burst if the internal pressure exceeds the external pressure by 0.2 bar.

(That would mean the ‘bursting pressure’ is 1.2bar.)

Strictly speaking,, the question should ask for the maximum balloon volume at room temperature, though I suppose this is implied.

 

[hutchphd]

This is a very badly worded question. The author has committed conflation of inflation with pressurization.
It makes sense only if the balloon is not stretchy at all hence the volume is fixed as the air is introduced, causing an overpressure

View attachment 337516

The $V_2$ in the solution is the total gas volume (if at STP) that the ballooon will contain at bursting.

 

[kuruman]

I agree that the problem is not very well worded. Here is how to rephrase it in order to get the given answer without confusion.

A balloon is filled with gas at room temperature and at pressure 0.2 bar. This same amount of gas, if placed in a 2.27 L rigid container at room temperature, would be at pressure 1 bar. Find the volume of the balloon.

 

[TahirMaqbool]

I agree that the problem is not very well worded. Here is how to rephrase it in order to get the given answer without confusion.

A balloon is filled with gas at room temperature and at pressure 0.2 bar. This same amount of gas, if placed in a 2.27 L rigid container at room temperature, would be at pressure 1 bar. Find the volume of the balloon.

That's all fine , how will you explain this
"Since balloon bursts at 0.2 bar pressure,
the volume of balloon should be less than
11.35 L."
A lesser volume will lead to a Higher pressure, isn't it wrong?

 

[hutchphd]

I believe this confusion arises from the 0.2 bar being a gauge pressure which means 1.2 bar absolute pressure (at STP in lab)

 

[PeroK]

That's all fine , how will you explain this

My explanation is that many physics questions these days are written by people with little or no understanding of physics. They construct questions which make no sense, and where you are expected to plug the numbers into the most seemingly appropriate equation.

I suggest you try to ignore and forget such questions. Students often lack the confidence to do this and, wrongly, assume that there is an obligation to do their best and there is something to be gained from analysing such questions.

If I find something that I suspect is garbage, my inclination is to throw it in the bin, and move on.

 

[nasu]

From the solution it would seem that the balloon is expanded at constant temperature and it has a constant amount of gas (it uses Boyle's law). How would you do that to a ballon? How do you increase/decrease pressure in a ballon without adding/removing gas or changing the temperature? If it is a soft ballon the pressure is equal to the atmospheric pressure. You can't increase its volume. Jus, maybe, squeeze the gas in a restricted portion of the balloon. But this can only increase pressure.
If it's a ballon with rigid walls, you can change volume even less.

Possibly the author just wanted a problem with Boyle's law and threw some random words into it thinking it would look better.

 

[kuruman]

That's all fine , how will you explain this
"Since balloon bursts at 0.2 bar pressure,
the volume of balloon should be less than
11.35 L."
A lesser volume will lead to a Higher pressure, isn't it wrong?

I don't have to explain anything. I just reworded the problem so that it makes sense. Note that there is no mention of bursting in my version.

If I find something that I suspect is garbage, my inclination is to throw it in the bin, and move on.

If I find something that I suspect is garbage, I see if there is a way to recycle it.

 

[TahirMaqbool]

My explanation is that many physics questions these days are written by people with little or no understanding of physics. They construct questions which make no sense, and where you are expected to plug the numbers into the most seemingly appropriate equation.

I suggest you try to ignore and forget such questions. Students often lack the confidence to do this and, wrongly, assume that there is an obligation to do their best and there is something to be gained from analysing such questions.

If I find something that I suspect is garbage, my inclination is to throw it in the bin, and move on.

While I reserve a possibility of error, dont assume it is written by random nobodies.
The book is standard textbook of chemistry across India, authored by numerous scientists.
I could show you the cover page .any ways thankyou for your time

 

[TahirMaqbool]

I believe this confusion arises from the 0.2 bar being a gauge pressure which means 1.2 bar absolute pressure (at STP in lab)

The application of Boyle's law in that case wouldn't be done in a manner it is done

 

[hutchphd]

I have no idea what they think they have done. But Boyle's is linear in both P and V so who knows what they are doing. Can you provide the citation for the problem? I think it is probably a well conceived but badly stated problem and advise @PeroK solution. Why recycle it?

 

[haruspex]

I believe this confusion arises from the 0.2 bar being a gauge pressure which means 1.2 bar absolute pressure (at STP in lab)

Except, the solution treats it as absolute.

The question can be found at https://byjus.com/question-answer/a...-temperature-it-will-burst-if-the-pressure-1/
I have seen arrant nonsense at that website before. Can't find a way to give feedback without joining up (if then).

 

[nasu]

If I find something that I suspect is garbage, I see if there is a way to recycle it.

This is not recyclin. It more like the drunk looking for the lost key under the lamp post because it is too dark in the area where he lost it. It's an easier job but he won't find the key.

 

[nasu]

While I reserve a possibility of error, dont assume it is written by random nobodies.
The book is standard textbook of chemistry across India, authored by numerous scientists.
I could show you the cover page .any ways thankyou for your time

If it is nonsense, the number of authors is irrelevant.
If it is not, then explain what do you think happens there: what is the initial state, the final state an especially by what process does it go between these two states.

 

[gleem]

One possibility is that the question was originally written in Hindi and mistranslated into English.

 

[kuruman]

If it is not, then explain what do you think happens there: what is the initial state, the final state an especially by what process does it go between these two states.

The solution treats the 0.2 bar as absolute pressure. Assuming that the solution is correct as written by the author(s), then we have to accept that the balloon was filled in a vacuum chamber from a reservoir containing gas at room temperature and absolute pressure of 1 bar. The gas transfer was done quasi-statically, maintaining the pressure and temperature of the gas in the reservoir constant. This was accomplished (sounds like a lab report, doesn't it?) by reducing the volume of the reservoir accordingly. At the moment just before the balloon burst, the amount of gas transferred was 2.7 L.

I think something like the above will do it. It's a lot to leave unsaid.

 

[haruspex]

The solution treats the 0.2 bar as absolute pressure. Assuming that the solution is correct as written by the author(s), then we have to accept that the balloon was filled in a vacuum chamber from a reservoir containing gas at room temperature and absolute pressure of 1 bar. The gas transfer was done quasi-statically, maintaining the pressure and temperature of the gas in the reservoir constant. This was accomplished (sounds like a lab report, doesn't it?) by reducing the volume of the reservoir accordingly. At the moment just before the balloon burst, the amount of gas transferred was 2.7 L.

I think something like the above will do it. It's a lot to leave unsaid.

You give the BYJU crew way too much credit. Some of them may be good, but there seems to be inadequate peer review.

 

[kuruman]

You give the BYJU crew way too much credit. Some of them may be good, but there seems to be inadequate peer review.

I admit I did not follow the BYJU link until now. Looking at the "Similar questions" was an eye opener. The "similar questions" differ mostly in the input numerical values except for when the authors decide to get creative with the laws of Nature as in the one below.

 

[neilparker62]

If it is nonsense, the number of authors is irrelevant.

“Why 100? If I were wrong, one would have been enough. [In response to the book "Hundred Authors Against Einstein"]”​

 

[PhDeezNutz]

I’m guessing at this stage (presumably 1000 level chem) they just want you to get comfortable using math as a tool for science.

Nuance comes later. I think the thing to remember is that most students at the 1000 level do not have a good mathematical grasp and questions like these are a way to drill them and prep them for later when they are ready for nuance.

 

[jbriggs444]

I’m guessing at this stage (presumably 1000 level chem) they just want you to get comfortable using math as a tool for science.

Nuance comes later. I think the thing to remember is that most students at the 1000 level do not have a good mathematical grasp and questions like these are a way to drill them and prep them for later when they are ready for nuance.

The question was written by an someone who was educated using just such questions. By someone who managed to obtain a credential without having first obtained an understanding.

If one wants to get students comfortable with mathematics in physics, better to do so with problems that make sense rather than with problems that do not.

 

[nasu]

There may be a confusion regarding the initial state of the balloon. They say "a ballon is filled with hydrogen".
This can mean either that the balloon is already filled in the initial state (this is what I assumed at the first reading) or that is in the process of being filled (as proposed by @kuruman) and the initial state would be an empty ballon, I suppose.

If the second case is assumed, the initial state is an empty ballon (vacuum) plus some gas at normal pressure in a tank. The gas expands and reduces its pressure as it enters the empty balloon. The pressure in the ballon increases from zero (ballon in vacuum) until it reaches 0.2 bar. Somehow we know from the begining that the amount of gas that will satisfy this condition will have a volume of 22.7 L at room temperature and 1 bar. The question is what will be the volume of the same at 0.2 bar. Nothing to do with the ballon, really. A specific (and specified) amount of gas expanding isothermally between two given pressures. Find the new volume.

But then there is no "maximum volume". This is a confusing remark. The amount of gas is established by the pressure, volume and tempreature given already so its volume at 0.2 bar is uniquely determined. You cannot increase the volume of the ballon with this amount of gas unless you heat it up. And you cannot decerase it unless you cool it down.