ideal gas and engine cylinder

[fullcircle69]

I am trying to understand what would happen in a certain scenario regarding an internal combustion engine. I am trying to determine why might a cylinder fill with more atmosphere when comparing two atmosphere's that have the same density, but one has higher pressure.

Lets say we have two cylinders that are the same volume and are both sealed under vacuum with a valve. Cylinder A is placed in an atmosphere of an ideal gas that is at 70F and 29inHg. Cylinder B is placed in another atmosphere that is 80F and 29.5inHg. So both atmosphere have the same gas DENSITY.

So now if you open both valves for the same amount of time, do both containers fill with the same amount of air?

 

[MintJulep]

PV=nRT

 

[fullcircle69]

PV=nRT Ideal gas law

Can you please explain in more detail how to apply the ideal gas law to this example?

Don't both atmosphere weigh the same per volume and doesn't that weight cause the atmosphere to fill the cylinders?

 

[MintJulep]

One equation. One unknown. Solve for the unknown.

 

[fullcircle69]

Cyl A:

70F -> 294.26111K
29inHg -> 98205.2565PA

Density 1.16272

Volume=2.99638e-3 x R


Cyl B:

80F -> 299.816666K
29.5475-> 100059.304Pa

Density 1.162721

Volume=2.99638e-3 x R


Based on these calc's the volume of air in each cyl is the same....

I was told that the air with the higher pressure would yield more volume in the cylinder. But my reasoning could not verify this and it appears that these calculations agree with me.

Do my calc's appear corrent?

 

[IRstuff]

You're confused. Volume of a cylinder is a mechanical construct given by bore and stroke. Not sure what you're giving as fact and what you're giving as supposition, but the two gases must be at differing densities if the volume is the same, but T/P is different. That's the whole point of the ideal gas law.

TTFN

FAQ731-376

 

[fullcircle69]

Your right I am confused, but you see my calculations, so what am I doing wrong?

How is t/p different?

 

[fullcircle69]

If my original post is not clear, let me try to restate my question. Which cylinder A or B will have more molecules of gas after the valve is opened?

 

[IRstuff]

Is this for school?

TTFN

FAQ731-376

 

[fullcircle69]

I wish I was still in school! Why do you ask?

 

[MintJulep]

Perhaps my original answer was unclear. So I'll write it again.

PV=nRT

 

[IRstuff]

You've been given the ideal gas law, so why can't you solve for the amount of gas

TTFN

FAQ731-376

 

[fullcircle69]

Thanks.

40 moles vs 34 moles.

I forgot what the definition of a mole was!!!

 

[zekeman]

Look, if the density is the same then how do you get a difference in the number of moles.
The gas law stated should prove this, so you have a math error or your original statement about the equality of densities does not square with your P,T values.

 

[zekeman]

On second blush, you might have a more interesting problem, since in each case the atmosphere pushes the ideal gas into the cylinder with an amount of work=PV, so the internal energy in the cylinder is increased by PV; thus the new internal energy is equal to the enthalpy of an equal weight of atmospheric gas.

Now you will end up with a new T in each case to which you can apply the ideal gas law.

 

[fullcircle69]

I thought about this some more last night and got confused again because I didn't understand how i could have a different number of moles if the density was the same?

Zekeman comments may be more relevant to this problem.

So I assume now i have to base it on a new T that is created after the "work' has been done through the gas transfered to each cylinder. (Zekeman is this what you mean?)

 

[zekeman]

Yes

 

[IRstuff]

There should be no confusion about your P and T values. If they are correct, then n = PV/RT. Again, you are still unclear about what is fact/measurement, and what is supposition.

Your original statement:

"Lets say we have two cylinders that are the same volume and are both sealed under vacuum with a valve. Cylinder A is placed in an atmosphere of an ideal gas that is at 70F and 29inHg. Cylinder B is placed in another atmosphere that is 80F and 29.5inHg. So both atmosphere have the same gas DENSITY."

Your last sentence is incorrect, based on the first two sentences. Density, as measured by n/V is equal to P/RT, so doing the math shows that condition A has a higher gas density than condition B.

TTFN

FAQ731-376

 

[fullcircle69]

If I use

https://www.brisbanehotairballooning.com.au/faqs/education/116-calculate-air-density.html

to calculate teh air density of both atmopheres
Cyl A:

70F -> 294.26111K
29inHg -> 98205.2565PA
Cyl B:
80F -> 299.816666K
29.5475-> 100059.304Pa

I get the same density 1.163kg.m^3 for each.

IRSTUFF - Please explain how this is wrong?

 

[IRstuff]

That was based on your original 29.5 inHg. With your new value of 29.5475, the densities are the same.

TTFN

FAQ731-376