EK question with rooms and stuff

[chiddler]

Two rooms connected by closed door. A scientist finds the mass, density, energy, and pressure of the gas in each rooms to be identical. The door is opened. The scientist measures mass, density, energy and pressure in the two rooms combined. What values changed in the second measurement?

NOTHING should change, right? They are 100% identical!

I. Mass
II. Density
III. Energy
IV. Pressure

I and III will change, according to the book.

so. what's going on?

A second shorter question: what happens to a gas if there is no gravity?

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[MedPR]

That's interesting. Was there any further explanation? I can't see why anything would change either.

Edit:

I was thinking pressure would decrease since the number of collisions on the walls might decrease. Obviously that's not true though, so I have no clue.

 

[milski]

The scientist measures mass, density, energy and pressure in the two rooms combined.

In the first case the measurement is in each room. In the second the measurement is of both rooms together. Mass and energy will increase, since you're measuring the two rooms together. Density and pressure will not, since they don't depend on the amount of gas measured.

 

[MedPR]

The scientist measures mass, density, energy and pressure in the two rooms combined.

In the first case the measurement is in each room. In the second the measurement is of both rooms together. Mass and energy will increase, since you're measuring the two rooms together. Density and pressure will not, since they don't depend on the amount of gas measured.

So this is more of a VR question than anything else...

If the mass in each room is x, then the mass in the combined room will be 2x. And 2x counts as a change from x? That's lame.

Can you elaborate on how/why energy would increase? Also, by the same reason that you increased mass, you increased moles and T (since you increased energy). By PV=nRT, if you increase moles, temperature, and volume, you must also increase pressure, correct? Doubled volume and doubled moles cancels out, but there is still the matter of increased energy (temperature), which must be counterbalanced by increased pressure.

 

[milski]

Yes, it seems rather obvious. He's most likely in a chapter on thermodynamics and they are about to discuss internal vs external variables - things that depend on how much of substance you're working with vs things that don't. (mass vs density in this problem would be a good example).

 

[milski]

So this is more of a VR question than anything else...

If the mass in each room is x, then the mass in the combined room will be 2x. And 2x counts as a change from x? That's lame.

Can you elaborate on how/why energy would increase? Also, by the same reason that you increased mass, you increased moles and T (since you increased energy). By PV=nRT, if you increase moles, temperature, and volume, you must also increase pressure, correct? Doubled volume and doubled moles cancels out, but there is still the matter of increased energy (temperature), which must be counterbalanced by increased pressure.

Temperature stays the same - you can get that from PV=nRT (double n, double V) or from zeroth law of thermodynamics, which says that the heat will flow until the temperatures equalize.

One way to think about why energy will increase is purely mechanical. The air particles continue to have the same (average) energy but since you have twice as many of them, you will double the total energy in the system.

You should not try to equate T with the total energy of the system, at least when you change the amount of matter in the system. It's not an accident that temperature is not measure in Joules. Temperature describes something which is closer to 'energy density' - how much of energy you have in a unit of matter, not the total energy of that matter.

 

[chiddler]

wow what a lame question...

 

[milski]

wow what a lame question...

So you got it right on the first try?

 

[chiddler]

So you got it right on the first try?

lol



no

 

[chiddler]

oh hey what about my gas question.

what happens to a gas in 0 gravity?

 

[milski]

lol



no

Don't beat yourself, it could have been phrased better. It does introduce an important distinction between things like mass and pressure.

 

[MedPR]

This is a dumb question. I have 5 beans in my left hand and 5 beans in my right hand. Now I count how many beans I have in both hands combined. Does the number of beans increase?

Normal people answer: No
EK answer: Yes, because now you have 10, as opposed to having 5 and 5 before.

Dumb.

 

[MedPR]

oh hey what about my gas question.

what happens to a gas in 0 gravity?

P=F/A. 0gravity = 0acceleration = 0force= 0pressure? idk.

 

[milski]

oh hey what about my gas question.

what happens to a gas in 0 gravity?

Right, sorry, forgot about that one. It has a uniform distribution of the pressure. Under gravity you get slightly higher pressure at the bottom of the container. For all typical containers that you would encounter, the difference is insignificant and you need not worry about it.

 

[chiddler]

P=F/A. 0gravity = 0acceleration = 0force= 0pressure? idk.

sounds plausible.

so if we put the slightest pressure on the gas, it becomes liquid?

 

[chiddler]

Right, sorry, forgot about that one. It has a uniform distribution of the pressure. Under gravity you get slightly higher pressure at the bottom of the container. For all typical containers that you would encounter, the difference is insignificant and you need not worry about it.

this makes sense because the molecules are small enough and fast enough for gravity to be insignificant.

but why is what medpr said incorrect?

 

[milski]

sounds plausible.

so if we put the slightest pressure on the gas, it becomes liquid?

No, no Virtually none of the movement of the molecules in a container happens due to gravity. All of the pressure comes from KE of the particles which was transferred to them whenever the gas was heated above the absolute zero.

 

[MedPR]

this makes sense because the molecules are small enough and fast enough for gravity to be insignificant.

but why is what medpr said incorrect?

I guess there could be horizontal acceleration, which makes a>0 even though g=0.

 

[milski]

this makes sense because the molecules are small enough and fast enough for gravity to be insignificant.

but why is what medpr said incorrect?

You've said it - the effect of gravity is insignificant. Consider the velocity of a typical particle, the distance that it travels and the acceleration due to gravity. It's a Saturday, so I'm not going to do the math, but you'll find the changes in velocity to be insignificant.

In presence of gravity you will have a slight bias for particles moving faster downward which will create a slightly higher pressure on the bottom of the container compared to the top of it. But then again that's so small that there's no point including it in any calculations.

 

[milski]

I guess there could be horizontal acceleration, which makes a>0 even though g=0.

Why do you need acceleration? The particles will be perfectly happy buzzing around at constant speed and engaging in occasional elastic collisions. With no changes from outside, that can go on forever.

 

[chiddler]

Why do you need acceleration? The particles will be perfectly happy buzzing around at constant speed and engaging in occasional elastic collisions. With no changes from outside, that can go on forever.

thanks very much for the helpful responses

 

[MedPR]

Why do you need acceleration? The particles will be perfectly happy buzzing around at constant speed and engaging in occasional elastic collisions. With no changes from outside, that can go on forever.

How can there be pressure if they aren't accelerating at all?

 

[milski]

How can there be pressure if they aren't accelerating at all?

Particles moving at constant speed?

 

[MedPR]

if P=F/A, and constant speed = 0 acceleration, and F=ma, then F=0, then P=0?

 

[milski]

if P=F/A, and constant speed = 0 acceleration, and F=ma, then F=0, then P=0?

You do get plenty of acceleration when the particle collides with the wall - it's velocity will end up more or less opposite to what it was. But that happens due to repulsion between the particle and the particles of the wall and has nothing to do with gravity.

 

[MedPR]

You do get plenty of acceleration when the particle collides with the wall - it's velocity will end up more or less opposite to what it was. But that happens due to repulsion between the particle and the particles of the wall and has nothing to do with gravity.

Right! That's why i was saying acceleration that was independent of gravity. Even if the particles are moving along with constant speed, once they collide with something they are going to either change direction, or slow down, thus they will be accelerating.

 

[milski]

Right! That's why i was saying acceleration that was independent of gravity. Even if the particles are moving along with constant speed, once they collide with something they are going to either change direction, or slow down, thus they will be accelerating.

Sure. For what it's worth, they won't slow down, particle collisions are a fairly unique example of real elastic collisions.

But how does that translate to 0 pressure at 0 gravity?? Or did I misunderstand what you were originally saying?

 

[MedPR]

Sure. For what it's worth, they won't slow down, particle collisions are a fairly unique example of real elastic collisions.

But how does that translate to 0 pressure at 0 gravity?? Or did I misunderstand what you were originally saying?

What I originally said was 0gravity=0acceleration=0force=0pressure. I forgot to account for the acceleration due to collisions. I corrected myself and said there could be acceleration other than gravity, so you could have some amount of pressure even in 0 gravity.

 

[dreamweaver1988]

So this is more of a VR question than anything else...

I think most of the MCAT is more VR than anything else.

If the mass in each room is x, then the mass in the combined room will be 2x. And 2x counts as a change from x? That's lame.

The question was written to see if you know what measurements can and cannot be added. You can add two masses together and get a total mass. You can add two energies together and get a total energy. However, you cannot add two pressures or two densities together (actually, you can...just not correctly).

A really easy example of density (pressure will be similar):

You have two spoons, each full of 1 mL (so, 1 gram) of water. You add these two in a mixing bowl, and now the mass of the water is 2 grams. The mass changed. The volume also changed, of course.

You have two spoons, each full of 1 mL of water. The density of water is 1 g/mL. When you mix the two spoonfuls of water together in the mixing bowl, what happens to the density? Well, now you have 2 grams of water, but you also have 2 mL of water. (2 grams)/(2 mL) = 1g/mL. Let me add that the numbers don't actually matter. If you're making jungle juice and you pour in rum, tequila, and vodka, and each has the same density, what is the density of the delicious concoction you consume? It's the same as the densities of the individual components of the drink. Hope that helps.

Can you elaborate on how/why energy would increase? Also, by the same reason that you increased mass, you increased moles and T (since you increased energy). By PV=nRT, if you increase moles, temperature, and volume, you must also increase pressure, correct? Doubled volume and doubled moles cancels out, but there is still the matter of increased energy (temperature), which must be counterbalanced by increased pressure.

Don't overthink it. Energy, mass, and other measurements are independent and thus can be added. Density and pressure depend on volume and area, respectively.

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[milski]

What I originally said was 0gravity=0acceleration=0force=0pressure. I forgot to account for the acceleration due to collisions. I corrected myself and said there could be acceleration other than gravity, so you could have some amount of pressure even in 0 gravity.

For reasonably sized containers, there is no amount of pressure generated by gravity. When there it, it demonstrates as difference between the top and the bottom of the container.