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course Phy 232
Siphon a plug of water into the tube, seal the end of the tube to create an air column between the plug and the sealed end, and screw the cap back on. Give the bottle a moderate squeeze. Note that the tube should have come with a cap on the end, but the cap might have been left off; if so you can seal the end with your thumb; if the end is cut at a sharp angle you can easily cut it off square.Does the air column get longer or shorter? By what percent do you estimate the length of the column changes?
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After squeezing the bottle, the air column gets shorter by a little. The percent change is approximately 5%-10%.
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Does the volume of the air column increase or decrease? By what percent do you estimate the volume of the column changes?
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The volume of the air column decreases because the liquid takes up some of the space previously occupied by the air column. With less space, there is less volume.
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Does the number of molecules in the air column increase, decrease or remain the same? By what percent do you estimate the number of molecules changes?
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The number of molecules in the air column remains the same because at the end of the tube, a cap is placed to prevent air leakage. With less space, the air just gets closer together but the total molecules remain the same because there is nowhere else for the air to go.
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Does the mass of the air in the air column increase or decrease? By what percent do you estimate the mass of the air in the column changes?
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The mass of the air also remains the same as a total weight. No air is lost or gained by squeezing the bottle because there is no place for the air to be released and no new air is added into the system. Therefore the mass of the air as a whole is constant. However the mass of the air per unit of space/distance does increase because the same amount of air at the beginning must fit into a smaller region.
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Does the pressure in the air column increase, decrease or remain the same? By what percent do you conjecture the pressure in the column changes?
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The pressure in the air column increases because the volume decreases, which causes there to be less room for the same amount of air that initially took up more space before the air column shortened.
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Does the pressure in the bottle increase, decrease or remain the same? By what percent do you conjecture the pressure in the bottle changes?
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The pressure in the bottle remains the same because the pressure created by squeezing the bottle is transferred into the air column, causing the bottle to remain at the same pressure as it started with.
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When you hold the bottle in the squeezed position, with the water plug stationary, the pressure in the bottle results in a force on the plug which pushes it toward the capped end, while the pressure in the air column results in a force that pushes the plug away from that end. Which force do you think is the greater, or are they equal?
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The force that is pushing towards the capped end is the greater force. This is because the pressure generated by squeezing the bottle moves down the tube towards the capped end. The air column gets shorter and also builds up more pressure in it. But the pressure from the bottle is greater than the pressure generated from the air column in the opposite direction causing the plug to move towards the capped end a little ways.
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Once the plug is stationary the pressures have equalized, since net force in this state is zero and the ends have equal areas.
This isn't quite true, though, if one end of the water 'plug' is at a different height than the other. For a small 'plug' this difference is pretty much negligible.
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Which do you think is greater, the pressure in the bottle or the pressure in the air column?
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The pressure in the air column and the pressure in the bottle are equal. This is shown by the air column remaining at a constant length when the bottle is held down squeezed.
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Measure the length of the air column.
What is the length of the air column?
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9 and one fourth inches.
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How far would the water plug have to move to make the air column 10% shorter?
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.925 inches
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Squeeze the bottle so the air column becomes 10% shorter. It's up to you to figure out how to tell when it's 10% shorter. If you can't squeeze hard enough to achieve the 10% difference, then figure out what percent you can manage and note the percent in your answer.
On a 1-10 scale, with 10 the hardest squeeze of which you are capable without risking injury, how hard did you have to squeeze the bottle and what percent change did you achieve in the length of the air column?
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8 and I achieved the 10 % difference.
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Now, using the same 1-10 scale, give the bottle squeezes of 2, 5 and 8. Estimate the percent changes in the length of the air column.
What were your percent changes in air column length?
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2 - 2.7%
5 - 5.4%
8 - 10%
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Now by heating and/or cooling the bottle, what extremes in air column length can you achieve? Careful not to melt the bottle. It won't handle boiling water, and you shouldn't mess with water hot enough to scald you or cold enough to injure you (e.g., don't use dry ice, which in any case is too cold for the bottle, and certainly don't use liquid nitrogen).
Report your results:
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Using the hot and cold water alternatives, the air column changes in length by +- .9 inches from the original recorded length.
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Very good, but check my one note.
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