Ideal gas: two tanks connected by a cylinder

[A13235378]

Homework Statement

Two tanks A and B, are connected with a cylinder of negligible volume. Tank A has a temperature of 200k and tank B has a temperature of 300k, both have the same volume. Eventually, 1 mol is inserted into the cylinder. What is the final amount of moles in tank B?

Relevant Equations

PV = nRT

I ASSUME THAT THE PRESSES OF THE TWO CONTAINERS WILL BE EQUAL IN THE FINAL (STATIONARY REGIME). SO

Pa = Pb

naRTa/V = nbRTb/V

naTa = nbTb

Than , I just need to set up a system

My question is , so, will the two pressures at the end be the same? And as for the temperatures, can I also say they will be the same?

 

[kuruman]

If you assume that the gas in the 300 K tank is at 300 K and the gas in the 200 K tank is at 200 K, can the pressures be the same?

 

[haruspex]

The set up is not entirely clear. I assume the tanks start at the same pressure. Are they the same volume? Maybe we don't need to know.
"Eventually" suggests temperature equalises, and we can take pressure to be almost equal throughout.
1mol "inserted" into a cylinder of negligible volume is an odd way to describe it. I assume they mean 1 mol moves through the cylinder from A to B.

If so, what will the final temperature be?

 

[kuruman]

"Eventually" suggests temperature equalises, and we can take pressure to be almost equal throughout.
1mol "inserted" into a cylinder of negligible volume is an odd way to describe it. I assume they mean 1 mol moves through the cylinder from A to B.

I interpreted the statement of the problem as saying that 1 mole of gas is inserted in the cylinder between the two tanks and it then redistributes itself between the tanks. The negligible volume has to do with ignoring any gas that might occupy it compared with the amount of gas in either cylinder. I believe the tanks are each held at constant temperature as the redistribution occurs. OP has the right equation but it seems that he does not understand it completely hence the question whether the pressures are equal.

 

[haruspex]

I interpreted the statement of the problem as saying that 1 mole of gas is inserted in the cylinder between the two tanks and it then redistributes itself between the tanks. The negligible volume has to do with ignoring any gas that might occupy it compared with the amount of gas in either cylinder. I believe the tanks are each held at constant temperature as the redistribution occurs. OP has the right equation but it seems that he does not understand it completely hence the question whether the pressures are equal.

Yes, that all makes sense, except for "eventually".
So presumably the question is, what fraction of the 1 mol goes into B?

 

[ehild]

I ASSUME THAT THE PRESSES OF THE TWO CONTAINERS WILL BE EQUAL IN THE FINAL (STATIONARY REGIME). SO

Pa = Pb

naRTa/V = nbRTb/V

naTa = nbTb

Than , I just need to set up a system

My question is , so, will the two pressures at the end be the same? And as for the temperatures, can I also say they will be the same?

I undersrand the problem that both tanks are in heat baths, A at 200 k, B at 300 K. The tanks are empty at the beginning.One moll gas is inserted into the connecting cílinder, and it will ne distributed among the tanks. As the gas moves freely through the cylinder, the pressure will be the same in both tanks at the end. The temperetures are determined by the heat baths, they stay the same 200 K in A and 300 K in B. You need to fnd nA and nB, knowing that nA+nB=1