#$&*
Phy 242
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A tube 3.3mm is diameter is run through the stopper of a sealed 5L container. The tube outside the container forms a U, then runs in a straight line with slope 0.028 horizontal. Alcohol is gone into the tube and fills the U, extending into the linear section of the tube. Both ends of the tube are open. The container is slightly heated and the alcohol column is observed to move along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion 'alpha = 88*10^6 /C. If the temp of the air in the container was originally 24C then if the temp inc by 0.85C how far will the alcohol column move?
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You were going to help me out on this one and asked to submit it. I know we use PV=nRT, get P and convert the temp to K.
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@& There are several things going on at once in this problem.
The air in the container expands as the temperature increases.
The volume of the container increases as it is heated. The amount of the container's volume change is different than that of the air.
So the alcohol in the tube will move.
As the alcohol moves, its y coordinate increases, which causes an increase in pressure. The movement of the alcohol also opens up some volume in the tube, which is occupied by the air.
The easiest thing to analyze is the volume of the container. Your're given the coefficient of expansion. Can you use this, along with the given initial volume and the change in temperature, to find the new volume of the container?
To correctly analyze the rest is challenging, so we'll start out with a couple of simplifying assumptions.
First let's assume that the change in the y coordinate of the alcohol colums does not significantly increase the pressure. In this case the gas will be free to expand. So how much expansion would there be?
How much additional volume will the gas therefore occupy in the tube?
How far would the alcohol column have to more to make the required volume available?
If you can get this far in the analysis, you would be at the level of 7 out of 10 points.
Now, that would be the solution if the tube was level. However it isn't. Given the slope, how much higher would the top of the alcohol column be, assuming your previous answer? How much additional pressure would be required? If you wish you can assume that alcohol has the same density as water, but you would want to note this as an assumption. In fact it has about 70-80% the density of water.
Since the pressure of the gas would have to increase to move the alcohol to the new position, your previous assumption that the pressure is not significantly increased. The pressure in fact increases, which reduces the volume change.
Someone who gets this far in the analysis would have 8 points.
At this point you need represent the distance moved by the alcohol column by a variable, and set up expressions for the pressure and volume changes in terms of this variable. This would give you an equation, which could be solved for the variable. Any reasonable attempt at this, along with the rest of the analysis, would be worth 9 points.
This is generally the toughest problem on the test, and it's rare that anyone gets 10 points on this problem.
See how far you can get, in a reasonable time. It isn't that difficult to get to the 7-point level, but very difficult to get 10 points.
Note that there are many versions of this problem, each one with a different twist. But if you understand one, you can apply that understanding to the others.
*@
#$&*
Phy 242
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A tube 3.3mm is diameter is run through the stopper of a sealed 5L container. The tube outside the container forms a U, then runs in a straight line with slope 0.028 horizontal. Alcohol is gone into the tube and fills the U, extending into the linear section of the tube. Both ends of the tube are open. The container is slightly heated and the alcohol column is observed to move along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion 'alpha = 88*10^6 /C. If the temp of the air in the container was originally 24C then if the temp inc by 0.85C how far will the alcohol column move?
** **
You were going to help me out on this one and asked to submit it. I know we use PV=nRT, get P and convert the temp to K.
** **
@& There are several things going on at once in this problem.
The air in the container expands as the temperature increases.
The volume of the container increases as it is heated. The amount of the container's volume change is different than that of the air.
So the alcohol in the tube will move.
As the alcohol moves, its y coordinate increases, which causes an increase in pressure. The movement of the alcohol also opens up some volume in the tube, which is occupied by the air.
The easiest thing to analyze is the volume of the container. Your're given the coefficient of expansion. Can you use this, along with the given initial volume and the change in temperature, to find the new volume of the container?
To correctly analyze the rest is challenging, so we'll start out with a couple of simplifying assumptions.
First let's assume that the change in the y coordinate of the alcohol colums does not significantly increase the pressure. In this case the gas will be free to expand. So how much expansion would there be?
How much additional volume will the gas therefore occupy in the tube?
How far would the alcohol column have to more to make the required volume available?
If you can get this far in the analysis, you would be at the level of 7 out of 10 points.
Now, that would be the solution if the tube was level. However it isn't. Given the slope, how much higher would the top of the alcohol column be, assuming your previous answer? How much additional pressure would be required? If you wish you can assume that alcohol has the same density as water, but you would want to note this as an assumption. In fact it has about 70-80% the density of water.
Since the pressure of the gas would have to increase to move the alcohol to the new position, your previous assumption that the pressure is not significantly increased. The pressure in fact increases, which reduces the volume change.
Someone who gets this far in the analysis would have 8 points.
At this point you need represent the distance moved by the alcohol column by a variable, and set up expressions for the pressure and volume changes in terms of this variable. This would give you an equation, which could be solved for the variable. Any reasonable attempt at this, along with the rest of the analysis, would be worth 9 points.
This is generally the toughest problem on the test, and it's rare that anyone gets 10 points on this problem.
See how far you can get, in a reasonable time. It isn't that difficult to get to the 7-point level, but very difficult to get 10 points.
Note that there are many versions of this problem, each one with a different twist. But if you understand one, you can apply that understanding to the others.
*@