EK Physics - Density

[ilovemcat]

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Okay, so I know this is a really stupid question, but it's something that's really annoying me as I sometimes miss problems because of it.

First, take into consideration these two questions:

Question 1: Two rooms are connected by a closed door. A scientist finds the mass, density, energy, and pressure of the gas in each room to be indentical. The door is opened. The scientist measures the mass, density, energy, and pressure in the two rooms combined. Which values changed in the second measurement?

Question 2: If the volume of a gas is decreased by a factor of 2, what is the change in its density?


The answer to question one is mass and energy because they're both extensive properties and change with quantity. The answer to question 2 is it increases by a factor of 2. Question 2 seems fairly obvious. But because of the logic associated with question 1, I sometimes miss easy questions like this.

Why is it that we assume for question 1 that the gas maintains its density even though the gas has a much larger room to occupy, whereas for question 2 - compressing the gas would result in a increase in density.

 

[Rabolisk]

Tricky questions that really won't help you much on the MCAT, but here goes.

For question 1, when the two rooms are connected, you have twice as much gas as you did from each room. If each room contained x moles of gas, the connected rooms as a whole now contain 2x moles of gas. Since you have twice as much, you have to have twice as much mass and energy. You also have twice the volume, so density remains the same. Pressure is a little harder to reason, but you have same velocity (temperature), twice the volume, and twice the number of particles. The rate at which particles are hitting the walls of the connected rooms, and the average kinetic energy of the particles as they do so remain the same.

For question 2, it's simply as you reasoned it. Hope that helps.

 

[ilovemcat]

Tricky questions that really won't help you much on the MCAT, but here goes.

For question 1, when the two rooms are connected, you have twice as much gas as you did from each room. If each room contained x moles of gas, the connected rooms as a whole now contain 2x moles of gas. Since you have twice as much, you have to have twice as much mass and energy. You also have twice the volume, so density remains the same. Pressure is a little harder to reason, but you have same velocity (temperature), twice the volume, and twice the number of particles. The rate at which particles are hitting the walls of the connected rooms, and the average kinetic energy of the particles as they do so remain the same.

For question 2, it's simply as you reasoned it. Hope that helps.

Ah, thank you! That makes so much more sense. I forgot to consider that the number of moles doubles which explains why density didn't change in that scenario. Silly me 😛