Do Different Volumes of Helium Affect Molecular Speed in Balloons?

[Vibhor]

Homework Statement

[/B]
Two balloons with Helium gas are filled, first with 10 liters of He and second with 20 liters. Molecules of which balloon will be moving faster as compared to the other?

Homework Equations

The Attempt at a Solution

Speed of molecules is directly proportional to temperature . Consider the fact that pressure inside balloon is same as ambient pressure i.e pressure is constant ( Atm. pressure) . Applying Ideal gas law PV = nRT ,temperature depends on 'n' and V . Volume is given but , 'n' is not given .

Is the question incomplete or am I missing something ?

Many Thanks

 

[Bystander]

10 liters

20 liters

'n' is not given

or am I missing something ?

You "am" missing something.

 

[Vibhor]

Are you suggesting that 'n' i.e number of moles can be calculated from the volume given ? Should n₁ = 10/22.4 and n₂ = 20/22.4 ?

 

[Bystander]

Preference would be some unspecified constant, but otherwise, yes.

 

[Vibhor]

But what I did (division by 22.4) was under the assumption that 1 mole of an ideal gas occupies 22.4 liters at "STP" i.e at 273K . Why should we assume that gas is filled at a constant temperature of 273K ?

 

[Bystander]

Why should we assume that gas is filled at 273K ?

Hence, the UN-specified constant.

 

[Vibhor]

Sorry . I do not understand . Could you please explain ?

 

[Bystander]

please explain

You multiply by a constant; you then divide by that same constant; what do you get? Rid of the constant.

 

[haruspex]

There is not enough information in the problem statement. I assume the balloons are initially identical, but are we considering them immediately after filling or on return to ambient temperature?
In the attempted solution it says the balloon contents are at atmospheric pressure, which seems unlikely. Is this a given or just part of the attempted solution?

 

[Vibhor]

There is not enough information in the problem statement. I assume the balloons are initially identical, but are we considering them immediately after filling or on return to ambient temperature?

I interpret this as immediately after filling .

In the attempted solution it says the balloon contents are at atmospheric pressure, which seems unlikely. Is this a given or just part of the attempted solution?

I think the gas inside the rubber party balloons are always at a pressure just above the ambient pressure (approx. equal to ambient pressure ) . It is part of the attempted solution.

 

[haruspex]

I interpret this as immediately after filling .

Well, that is rather a critical question, no? But if so, what would that say about the temperatures?

I think the gas inside the rubber party balloons are always at a pressure just above the ambient pressure (approx. equal to ambient pressure ) . It is part of the attempted solution.

Either the volumes are quite different or the pressures are. Or both. Without knowing the relaxed volumes of the balloons it is impossible to say how the two volumes and pressures will change. But as I hinted above, I don't think you need to investigate that beyond some basic assumptions.

 

[Vibhor]

Well, that is rather a critical question, no? But if so, what would that say about the temperatures?

This is what we need to find . Translational speed of molecules is directly proportional to temperature . Higher the temperature higher the speed.

Either the volumes are quite different or the pressures are.

Volume of one is double that of the other . Pressures are same . This is my thinking .

 

[haruspex]

This is what we need to find . Translational speed of molecules is directly proportional to temperature . Higher the temperature higher the speed.

Sure, but you are only assuming the question relates to just after filling the balloons. That assumption affects the answer.
How far do you think 'adiabatic' would apply here?

Volume of one is double that of the other . Pressures are same . This is my thinking .

It would be somewhat strange for a balloon to be filled to double the size without some increase in pressure. It need not be much to affect the answer.

 

[ehild]

They are not party balloons I am sure. Can be meteorologic ones - of the same volume when filled, which means when they are taut. That also means about the same pressure, a bit higher than atmospheric. But then the temperature must be different

 

[Vibhor]

They are not party balloons I am sure. Can be meteorologic ones - of the same volume when filled, which means when they are taut. That also means about the same pressure, a bit higher than atmospheric. But then the temperature must be different

In that case the 20L would have double the number of moles and half the temperature as compared to 10L one ??

 

[ehild]

In that case the 20L would have double the number of moles and half the temperature as compared to 10L one ??

I think so.

 

[Vibhor]

I think so.

Fine . And molecules in 20L balloon would be moving at slower(half) average speed than the 10L balloon ??

What if we change the question a bit and take two party balloons and we put in 1L and 2L of air ( i.e volume of air inside =volume of balloon) . Do you think we would consider temperatures to be same (ambient temperatures) ??

Since Pressure and temperatures would be same in this case , the Volume would be directly proportional to the no of moles of air put in . The number of moles in 2L balloon would be double that of 1L balloon .But since temperatures are equal , in this case molecules in 2L balloon would be moving at same average speeds as that in 1L balloon

Does that seem correct ??

 

[ehild]

Since Pressure and temperatures would be same in this case , the Volume would be directly proportional to the no of moles of air put in . The number of moles in 2L balloon would be double that of 1L balloon .But since temperatures are equal , in this case molecules in 2L balloon would be moving at same average speeds as that in 1L balloon

Does that seem correct ??

Yes, in case of ideal gas.
But how can you fill one party balloon with twice as much gas so as the pressure is the same in both? The pressure should balance the tension of the rubber wall, which must be higher if the volume is greater.

 

[Vibhor]

Ok. How would two meteorological balloons as we interpret in the OP have equal gas pressures i.e same as ambient pressure ? Are they closed or do they have an opening ?

 

[haruspex]

In that case the 20L would have double the number of moles and half the temperature as compared to 10L one ??

How can it have half the temperature?!
You put 10L in each balloon, so far they're the same. Now you put another 10L in one of them. Why should the temperature go down dramatically? Half the temperature (K) would be extremely cold.

 

[ehild]

Pretend you blow the content of your lung in one party balloon. It is not flat any more, but It is small and easy to press. .
You blow air twice in the other balloon. It becomes round and hard to press. What you need to do with the first one to make it as big and taut as the second balloon?

 

[haruspex]

Pretend you blow the content of your lung in one party balloon. It is not flat any more, but It is small and easy to press. .
You blow air twice in the other balloon. It becomes round and hard to press. What you need to do with the first one to make it as big and taut as the second balloon?

I started off down that line, but unfortunately we do not know whether that model applies. At 10L plus, they do sound more like meteorological balloons, which don't become taut. So now I'm thinking they could be, as originally suggested, both at pretty much atmospheric pressure. Several ways in which the information is inadequate.

 

[ehild]

I agree that the information is inadequate.

 

[Vibhor]

@ehild could you please reply to post19

 

[ehild]

Ok. How would two meteorological balloons as we interpret in the OP have equal gas pressures i.e same as ambient pressure ? Are they closed or do they have an opening ?

The weather balloons are closed. The hot-air balloons are open.
The pressure in the balloon should balance the ambient pressure + the tension of the wall. The weather balloons are blown up to a certain size.
I do not really know what was in the mind of the problem writer.