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Phy 232
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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2Quest
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You have given me insight on several questions recently and it has been very helpful. However, i still can not figure out the two different questions with the tube that forms a U. Is there anyway you could quickly do these problems. The hints for these seemed to get me more confused and I feel like I could grasp the concept better if you did two quick examples. These problems come up so often that I want to make sure I %100 understand how to do them properly. Thanks for the help.
A tube 4.1 mm in diameter is run through the stopper of a sealed 7-liter container. The tube outside the container forms a U, then runs in a straight line with slope .02 with respect to horizontal. Alcohol is introduced into the tube, and fills the U, extending into the linear section of the tube. The end outside the container is sealed, and the air column in the linear section is originally .78 meters long. The container is slightly heated, and the alcohol column is observed to move 7 mm along the linear section of the tube. If the temperature of the air in the container was originally 30 Celsius, what is the new temperature?
A tube 3.6 mm in diameter is run through the stopper of a sealed 1.5-liter container. The tube outside the container forms a U, then runs in a straight line with slope .027 with respect to horizontal. Alcohol is introduced 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 .76 meters along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion `alpha = 86 * 10^6 / C. If the temperature of the air in the container was originally 15 Celsius, what is the new temperature?
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For various reasons I'm not going to provide a solution to this problem.
The questions I provided previously were as follows:
What is the volume of the container before and after being heated?
What additional volume of tubing has become available to the air in the container?
How much higher is the alcohol column as a result of the heating, and by how much did the pressure inside the container therefore increase?
This gives you the new volume and pressure of the system. Air can't escape so n stays constant. What therefore is the new temperature?
Given your best answers to these questions, or good questions about them, I would be glad to give hints as to how to put them together.
Having given these questions enough thought, you would probably be able to make a good attempt at a solution.
Be sure you understand the situation. It is just as if you heated the air in the bottle, observing just an open 'pressure tube'.
The bottle expands, which increases the volume of the enclosed air.
The liquid moves in the tube, which also increases the volume of the enclosed air.
As the liquid moves it goes a little higher as well, which increases the pressure of the enclosed air.
This gives you all the information you need about P and V in order to determine the change in T.
You aren't given the density of alcohol, but that's something the type of alcohol isn't specified, and you should know that alcohol is somewhat less dense than water. A reasonable estimate would be around .8 or .9 the density of water (which you should definitely know).
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