Finding out the mass of gas transferred outside of a room

[Taylan]

Homework Statement

The volume of a room is 60m^3. Temperature=25degrees and pressure=101300Pa. Due to the wind, there will be a pressure drop outside the room to 99000Pa. What is the mass of air that will be transferred outside through the window? M=28,96g/mol

Relevant Equations

PV=nRT

I thought I should use the ideal gas law to find out moles of air that would be transferred out through the window but the temperature and volume outside is not known. Can you help me further? thanks

 

[DaveE]

I suppose the outside volume is essentially infinite. So I think your headed on the wrong track there. What do you know about the pressure at the window (inside vs. outside)? Why would gas move from inside to outside? When would gas stop moving outside?

 

[bonbon22]

Problem Statement: The volume of a room is 60m^3. Temperature=25degrees and pressure=101300Pa. Due to the wind, there will be a pressure drop outside the room to 99000Pa. What is the mass of air that will be transferred outside through the window? M=28,96g/mol
Relevant Equations: PV=nRT

I thought I should use the ideal gas law to find out moles of air that would be transferred out through the window but the temperature and volume outside is not known. Can you help me further? thanks

i think you should assume that temperature is constant, and the question phrases it differently but it may be referring to the pressure inside the room changing to 99000 or 2300 what is the answer?

 

[Taylan]

I suppose the outside volume is essentially infinite. So I think your headed on the wrong track there. What do you know about the pressure at the window (inside vs. outside)? Why would gas move from inside to outside? When would gas stop moving outside?

inside = 101300Pa and outside=99000Pa. The gas would move from higher to lower pressure and the movement would stop when the pressures are equal.

 

[Taylan]

i think you should assume that temperature is constant, and the question phrases it differently but it may be referring to the pressure inside the room changing to 99000 or 2300 what is the answer?

No, the pressure inside is 101300Pa and outside it is 99000Pa so some air will move outside due to the pressure difference. I don't think I am supposed to assume the temperature is constant in this specific question though

 

[DaveE]

OK, so let's look at the gas law inside the room, PV=nRT. V and R are constant. You now know the initial and final pressures, let's call the Pi (initial) and Pf (final). So let's rearrange things nT=PV/R. Then you could compare the initial conditions to the final conditions.
We know n will change because of the way the question was asked. I would have assumed that T is constant, but you are correct, theoretically it could change. In the real world, assuming normal sized rooms and windows, it won't change much at all (as long as the air is still all moving out). Plus, I don't think solving for the change of temperature as air is leaving is an introductory physics question. That answer would require a bunch of information that isn't provided (like how big is the window).

 

[Taylan]

OK, so let's look at the gas law inside the room, PV=nRT. V and R are constant. You now know the initial and final pressures, let's call the Pi (initial) and Pf (final). So let's rearrange things nT=PV/R. Then you could compare the initial conditions to the final conditions.
We know n will change because of the way the question was asked. I would have assumed that T is constant, but you are correct, theoretically it could change. In the real world, assuming normal sized rooms and windows, it won't change much at all (as long as the air is still all moving out). Plus, I don't think solving for the change of temperature as air is leaving is an introductory physics question. That answer would require a bunch of information that isn't provided (like how big is the window).

oh ı see. okay thanks! so ı guess since V and R are constant I am going to further rearrange it and say V/R = nT/P ? and then (nT/P)before= (nT/P)after ?

 

[DaveE]

oh ı see. okay thanks! so ı guess since V and R are constant I am going to further rearrange it and say V/R = nT/P ? and then (nT/P)before= (nT/P)after ?

Something like that. I would name the variables that are changing as before and after values. Then write the equations that describe the before state and the after state. You can use these two equations to determine how much things changed. Since they are asking how the mass changes, you should know that the answer will be found by finding how much n changed.

 

[Taylan]

Something like that. I would name the variables that are changing as before and after values. Then write the equations that describe the before state and the after state. You can use these two equations to determine how much things changed. Since they are asking how the mass changes, you should know that the answer will be found by finding how much n changed.

Thank you!
alright so:

n1.T1./P1 = n2.T2./P2

n2= (n1.T1.P2)/(P1.T2)

since T is constant:

n2=(n1.P2)/P1

I know P1 (101300Pa)
n1 can be found out from ideal gas law equation since P1, V1, T1 and R is known.

about P2.. I know that the air will keep getting out until the pressure outside and inside will be equal. But which pressure is this? The middle value of 99000Pa and 101300Pa is what comes to my mind but not sure if that makes sense because can't think of an explanation about why it should be that way