Assume that you have a cylinder with a movable piston.
What woul...

Question

Assume that you have a cylinder with a movable piston. 
What would happen to the gas volume of the cylinder if you 
were to do the following? 
(b) Increase the amount of gas by one-fourth while holding 
the temperature and pressure constant

Accepted Answer

Hi everyone. This problem reads consider a cylinder with a movable piston. If you were to do the following, what would happen to the cylinders? Gas volume while maintaining the same temperature and pressure, increase the volume of the gas by 1/5. Okay, so the question that we want to answer is what would happen to the cylinders? Gas volume. Okay, so what we want to reference here, because we're dealing with gasses is we're going to reference the ideal gas law, which is pressure, times volume is equal to the number of moles, times gas constant, r times temperature. Okay, so we see here that we are maintaining the same temperature and pressure. Alright, so what we're going to do is we're going to rewrite this ideal gas law to reflect our times t overpressure and what this equals is the initial volume over the initial moles is equal to final volume over final moles. And what we want to solve for here is the final volume. Okay, so let's rearrange this so that we're solving for final volume. And when we rewrite this, we get the final volume is going to equal the initial volume, times the final moles over the initial moles. Okay, And we're going to assume an initial amount of volume is equal to one leader. So let's go ahead and write our assumptions here, we're going to assume that we have a volume equal to one leader and we're going to assume that we have most equal to one leader for easier comparison to the final amounts. Okay, so let's go ahead and plug in what we have. So our initial volume is going to so let's right here, this is initial volume and our moles here is initial Okay, so let's go ahead and plug those in. So our initial volume is one leader and our final moles is 6/5. So what we're going to do is we're going to see here that Our final moles is going to equal one plus one times 1/5. Okay, so that means our final moles is going to be 6/5. So that's the value we're going to put here for our final molds. So we have 6/5 moles and this is over our initial moles which we said is one mole. Okay, so once we do this calculation we'll see that our final volume is going to equal 1.2 leaders. Alright, so now that we know what our final volume is, we're gonna take our final volume And we're going to subtract our initial volume from that. So we have a final volume is 1.2 leaders and we assumed an initial volume of one leader, so this is going to be - leader. So we get 0.2 or 1/5. So what this means is the volume increases by 1/5. That is what's going to happen to the cylinders. Gas volume. So let's go ahead and highlight this as our final answer volume increases by 1/5. That's it for this problem. I hope this was helpful.

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