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Phy 232
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Test1Problem
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I am having a difficult time determining how to go about this problem. Could you help me through the process of finding the new temperature? I know the formula to find a change in volume that equals, (`alpha)*(original volume)*(change in temperature). Would I incorporate this equation into the problem to solve for the temperature change? If so, I am unsure on how to account for the change(expansion) of the container.
A tube 3.6 mm in diameter is run through the stopper of a sealed 7.5-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 .71 meters along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion `alpha = 76 * 10^6 / C. If the temperature of the air in the container was originally 29 Celsius, what is the new temperature?
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The coefficient of volume expansion is three times the coefficient of linear expansion.
The volume enclosed by the bottle expands exactly as it would if the bottle was made of solid plastic with the given coefficient of linear expansion.
You need to find the volume of the air originally enclosed in the bottle, and the volume enclosed after heating.
As a first approximation, for reference, you can assume that that tube is horizontal, so the pressure remains constant. In this approximation the ratio of pressure to temperature remains constant.
However to properly answer the question you need to account also for the increase in the vertical level of the water in the tube, which results in a change of pressure.
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