Can Temperature Alone Affect the Volume of Air in a Room?

[Serhiy]

Homework Statement

The air pressure in the room is 10 ^ 5 pascals, the temperature is 20 degrees Celsius. To what temperature should the air be heated so that 5% of the molecules leave the room?

Relevant Equations

p=nkT

maybe the temperature need to be changed from Celsius to Kelvin

 

[PeroK]

Well, yes, that formula applies to absolute temperature. Can you make an attempt to solve this yourself?

 

[valenumr]

Is this a well defined question? How does the air escape the room?

 

[PeroK]

Is this a well defined question? How does the air escape the room?

Through a pressure valve, of course!

 

[valenumr]

Through a pressure valve, of course!

I think the gist is what temperature is required to expand the volume by 1.05. it should be straight forward, but really terrible question.

 

[valenumr]

Anyway, I'd use the ideal gas law, pv=Nrt. Only temperature and volume change. I don't think temperature units much matter.

 

[Serhiy]

I think the gist is what temperature is required to expand the volume by 1.05. it should be straight forward, but really terrible question.

maybe your thoughts are correct, but this task looks in the same record that I described to you, but in my native language. but thank u

 

[Gordianus]

PV=NRT applies ONLY with T in Kelvin.

 

[Serhiy]

PV=NRT applies ONLY with T in Kelvin.

ok, thank you

 

[Serhiy]

Well, yes, that formula applies to absolute temperature. Can you make an attempt to solve this yourself?

yup, i try again. thank u

 

[PeroK]

Anyway, I'd use the ideal gas law, pv=Nrt. Only temperature and volume change. I don't think temperature units much matter.

Lord Kelvin would be turning in his grave!

 

[valenumr]

PV=NRT applies ONLY with T in Kelvin.

But why does it matter. If v scales by 1.05, so would t. I have to think about that for a minute,but I think it is linear.

 

[PeroK]

But why does it matter. If v scales by 1.05, so would t. I have to think about that for a minute,but I think it is linear.

Technically the scale itself doesn't matter as long as you adjust the relevant constant(s), but the scale must start from $0$.

 

[valenumr]

But why does it matter. If v scales by 1.05, so would t. I have to think about that for a minute,but I think it is linear.

Okay, I thought about it

 

[Orodruin]

PV=NRT applies ONLY with T in Kelvin.

No. It only applies when T is an absolute temperature. Whether Kelvin or some other absolute temperature scale is used is irrelevant.

I think the gist is what temperature is required to expand the volume by 1.05.

No, this is incorrect. (Although pretty close ...)

 

[valenumr]

No. It only applies when T is an absolute temperature. Whether Kelvin or some other absolute temperature scale is used is irrelevant.No, this is incorrect. (Although pretty close ...)

I would appreciate some clarification on that note, the second part..

 

[valenumr]

I would appreciate some clarification on that note, the second part..

Oh, do you mean 1/.95 vs 1.05?

 

[Orodruin]

I would appreciate some clarification on that note, the second part..

Keep in mind that these are the homework forums. The problem should not be solved by others before the OP has gotten it right.

 

[PeroK]

Oh, do you mean 1/.95 vs 1.05?

The problem tells you to fix $V$ and reduce $N$ to $0.95N$. Why would you want to redefine the problem as a change in volume? And, if you do, you better check you have the correct change in volume.

 

[valenumr]

The problem tells you to fix $V$ and reduce $N$ to $0.95N$. Why would you want to redefine the problem as a change in volume? And, if you do, you better check you have the correct change in volume.

Does it? I see how that is different from what I was thinking, but the question is a bit ambiguous. But I get what you are saying. It is t percent of the "molecules".

 

[valenumr]

Keep in mind that these are the homework forums. The problem should not be solved by others before the OP has gotten it right.

I apologize if I was being too direct.

 

[valenumr]

The problem tells you to fix $V$ and reduce $N$ to $0.95N$. Why would you want to redefine the problem as a change in volume? And, if you do, you better check you have the correct change in volume.

Oh shoot, it's late for me right now, or early if you like. I was thinking v and n were proportional, so it shouldn't matter.

 

[jbriggs444]

Oh shoot, it's late for me right now, or early if you like. I was thinking v and n were proportional, so it shouldn't matter.

It does matter.

Yes, $V$ and $n$ are proportional -- if all other things ($P$, $R$ and $T$) are held constant. But $T$ is not being held constant. We are varying it.

In this case it is $V$, $P$ and $R$ that are constants. Can you see why?

This means that the relevant relationship is between $n$ and $T$.

 

[valenumr]

It does matter.

Yes, $V$ and $n$ are proportional -- if all other things ($P$, $R$ and $T$) are held constant. But $T$ is not being held constant. We are varying it.

In this case it is $V$, $P$ and $R$ that are constants. Can you see why?

This means that the relevant relationship is between $n$ and $T$.

Yeah, it was late and I probably shouldn't have been answering homework topics. I got the answer roundabout, but I see that perok suggestion of a pressure valve, even in perhaps jest, is the right way to think about it.