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course PHY 232
2/15 2:38 pm
Brief Bottle Experiment 2aRaising Water using Thermal Energy
This experiment requires the bottlecap with the single tube, a bottle, a sink with hot and cold running water, a cup or shallow container, a ruler, and a teaspoon.
You have previously squeezed the bottle and measured the height to which the water column was raised in the tube as a function of the perceived intensity of your squeeze of the bottle. Now you're going to raise water by heating the gas in the bottle.
The procedure is very simple. Just do as follows:
• Fill the bottle about 1/4 of the way full of room-temperature water.
• Make sure when the cap is tightened that the tube will extend to within a centimeter or so of the bottom of the bottle.
• Nearly tighten the cap, but leave it loose enough that you could easily squeeze air out of it if you wished.
• Run cold tap water over the bottle for about 15 seconds and, keeping the bottle under the stream, tighten the cap, being careful not to squeeze the bottle.
• Holding the tube at about the height of the bottlecap, run hot tap water over the bottle and watch the water flow out of the tube.
Describe what happens:
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Just like it says: the water runs out of the tube as T increases creating a change in P since V is very nearly constant.
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@& P changes until water reaches the top of the tube. Then V increases, displacing water.*@
If you were to sketch a graph of pressure vs. volume, from the instant the hot water was turned on until the flow slowed to a drip, what would the graph look like?
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P would increase while V would increase negligibly compared to how much P changes. This would change would slow to a near stop as T_bottle --> T_H2O. So a nearly vertical line is what the graph would look like so it's an isochoric process.
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@& The process isn't isochoric after water starts flowing out of the tube.
It's pretty much isochoric until the tube fills; since the thin tube doesn't have much volume there is very little water displaced.
While the tube is filling the graph is vertical.*@
Now repeat but this time hold the tube right at the level of the top of the bottlecap, and catch the outflowing water in a cup or a shallow container. Once the flow has decreased to a slow drip, place the end of the tube in the collected water and turn off the tap. The water will return to the container. Note approximately how long this takes.
Describe what you observed.
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The whole process took about 110 seconds with the second stage lasting 70 seconds and it reclaimed very nearly all of the water albeit slowly, much slower than how fast the water flowed out.
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Repeat once again, exactly as before, but this time instead of just turning the tap off, turn the hot water off and the cold water on. Compare what happens with what happened in the preceding:
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This was markedly quicker than before though the same amount of water was pushed out. The intake took only 30 seconds this time.
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Repeat once again, but this time leave the water in the container and measure how much you have, in level teaspoonfuls. If you had an 'official' teaspoon from a measuring set, use it. Otherwise use a teaspoon from a set of eating utensils. Assume that a teaspoon holds 4.7 milliliters of water (this is so for an accurate teaspoon; the teaspoons in a typical set of eating utensils are usually pretty close to this).
How high above the water level in the bottle was the end of the tube?
How many teaspoonfuls of water did you get, and how many milliliters? How accurately do you think you were able to determine the number of milliliters?
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My tsp said 4.93 mL on it. The tube was 24 cm above water level and I collected 10.5 tsps or 51.45 mL. I think this is accurate to about ±0.5 mL as I was able to get very level spoonfuls.
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@& Let's see, a pound is 454 grams, an ounce is 1/16 of a pound, a tablespoon is half a fluid ounce, a teaspoon is a third of a tablespoon. So a teaspoon is 1/3 * 1/2 * 1/16 * 454 grams = 1/96 * 454 grams = 4.73 grams, implying 4.73 milliliters.
More precisely a pound is 453.59237 grams, but that wouldn't make any difference at the level of three significant figures.
There is some sort of discrepancy in the definition of the fluid ounce. The weight of a fluid ounce of water is a little greater than the weight of 1/16 of a pound.
Never knew that. I'll have to look further into it.*@
@& For the purposes of this experiement, of course, it makes no difference.*@
Repeat again, this time with the tube as high as possible.
How high above the water level in the bottle was the end of the tube?
How many teaspoonfuls of water did you get, and how many milliliters? How accurately do you think you were able to determine the number of milliliters?
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The tube was 81.5 cm above the water level and I got 5 tsp full so 24.5 mL and that is again about ±0.5 mL.
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Repeat once more, this time with the end of the tube only a couple of centimeters higher than the water level in the container.
How high above the water level in the bottle was the end of the tube?
How many teaspoonfuls of water did you get, and how many milliliters? How accurately do you think you were able to determine the number of milliliters?
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The tube was 2 cm above water level and I collected 16.5 tsp so 80.85 mL ±0.5 mL.
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At this point you have all your data, and while you're set up you might want to take data for brief_bottle_experiment_2b, where you turn the tube into a pressure tube and observe pressure differences due to heating and cooling the bottle. That experiment is pretty quick.
Make a table of the number of milliliters of water displaced, vs. the height to which it was raised. Add a third column for the PE change of the displaced water.
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mL, height cm, `d PE J
24.5, 81.5, 0.2
51.45, 24, 0.12
80.85, 2, 0.029
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How high do you think it would be possible to raise water in the tube, using your hot and cold water, if the tube was long enough?
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Well over 1 m but not more than 1.5 m. I did a little figuring and if it loses x mL / y cm then in 53 cm 24.5 will be zero so by that I get about 1.4 m. That doesn't seem to quite hold but gives an idea about it anyway.
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@& Not bad for an estimate, but as I'm sure you suspect the relationship isn't linear.*@
If the tube was long enough, and you were to raise the water to the greatest possible height, how much water would be displaced to this height, and what would be the PE change of this water?
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Well based on what I just responded my height would mean that 0 mL could be collected and so PE would be 0.
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@& Right. Whatever the max height is, no mass raise means `dPE = 0.*@
At what height do you estimate the PE change of the displaced water would be maximized?
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Based on above I would say it would be not very far away from 24 cm so about 36 cm.
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Based on your observations and the volume of the bottle, what do you think is the difference in temperature between your hot and cold water?
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Just feeling it I know it was least 40º F since my source had both very cold water and very hot water and the data seems to support this as well.
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@& If your maximum volume change was 15% of the original, then your temperature change would be 15% of the original temperature.
15% of 300 Kelvin would be 45 Kelvin.*@
Brief Bottle Experiment 2b
Raising Pressure using Thermal Energy
You have previously created a 'pressure tube' and measured the length of the air column as a function of the perceived intensity of your squeeze of the bottle.
You will now measure the effect on the air column in a pressure tube, due to heating the bottle.
As before, create a 'water plug' in the tube, positioned so that you have an air column of length 30 cm or so, and cap the end of the tube.
Put the cap on the empty bottle and screw it down most of the way, but don't quite tighten it, so that air can still flow into or out of the bottle. Before tightening the cap, run cold water over the bottle for about 15 seconds. Then, with cold water still running over the bottle, tighten the cap (being careful not to squeeze the bottle hard enough to reduce its volume).
Measure the length of the air column in the tube.
Run hot water over the bottle for about 15 seconds, and with hot water still running over the bottle, mark the position of the water column so you can measure its length (you could, for example, place your thumbnail at the appropriate end of the air column and hold it there until you can measure the length). Turn off the water and take your measurement.
What were the lengths of the air columns?
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30.5 cm to begin with and then it shrank by 2.5 cm so 28 cm after heating.
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If the pressure in the tube was initially 1 atmosphere, what was the pressure after heating?
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P1V1=P2V2 so P2 = 1.09 atm.
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On the 1-10 'squeeze' scale you used previously, according to your data on previous experiments how high do you expect it would be possible to raise water in the tube using your hot and cold water, provided the tube was long enough?
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The 9% I got above which would be a squeeze of about 6 and that had a 45 cm column length. I would say the temperature squeeze would be at most 9 and that had 62 cm column.
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Brief Bottle Experiment 2c
Bottle Thermometer
You have seen how warming air in a sealed bottle can affect the water level in the bottle. Now you will use the water level in the tube to observe temperature changes.
Fill the bottle 1/4 of the way full, and before tightening the cap cool it the bottle using cold tap water. Tighten the cap while the cold water it still running over the bottle.
Remove the bottle from the tap water, dry it and allow it to sit at room temperature. Watch the water in the tube. Within a few minutes, provided there is enough temperature difference between the cold water and the room, the level should rise above the level of the bottlecap (a 20 degree difference in temperatures should do it). If not, you can place the bottle in a refrigerator for 5-10 minutes, with the cap on the bottle but not tight. Then quickly tighten the cap before the temperature in the bottle has had an opportunity to rise. If you now bring the bottle into a room the water level should rise above the cap.
After the water level has ceased to change, warm your hands with warm water and gently, without squeezing, place them around the bottle (if you need a free hand to hold the tube up, you can use one hand to warm the bottle, the other to support the tube). By how much does the vertical level of the water in the tube change due to the warming from your hand?
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I had 9.5 cm increase.
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Now position the tube to that when the water level increases, it does so into a nearly horizontal tube. Again warm your hand(s) and use them to warm (but not squeeze) the bottle. Does the water in the tube move further, or less far, than when the tube was vertical? How far did the water appear to move along the tube?
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It moved out of the tube but I got mine so cold to begin with it was already 50 cm high. It would definitely be more than vertical though.
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Carry the bottle to a few places (different parts of the house, near a heating or cooling vent, outside, in your car, etc.) where the temperature differs and observe how the water level fluctuates with temperature.
After moving to a new location, how quickly does the water level change?
What temperature difference do you estimate corresponds to what change in the water level? By how much does the water change per degree of temperature change, based on your rough estimate of temperature change?
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The level changed at a noticeable but not rapid speed. My two rooms were easily 15º F apart in temp and that had about 14 cm difference so 14 cm /15 º= 0.93 cm/º F.
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Brief Bottle Experiment 2d
Expansion of water and plastic
You will use the bottle system to observe volume changes of the bottle and the water in it, as temperature changes. You will need to be able to immerse the bottle in cold water. A large pot or pitcher would suffice, as would a larger plastic bottle with the upper part cut off. You will be siphoning water into the bottle so you'll need a cup or some sort of a container to hold the water to be siphoned.
First fill the larger container with cold tap water, and position it so you can easily move it beneath the faucet using one hand (e.g., have it resting in the sink so you only have to slide it under the faucet).
Fill the bottle with hot water from the faucet. Then:
• With the cap loose but ready to tighten, siphon more water into the bottle so that the bottle begins to overflow and, with the siphon still working and water overflowing the bottle, tighten the cap. (This doesn't take long but it does require some coordination and maybe a little practice; your instructor managed on the second try (on the first try the tube flopped out of the container from which it was siphoning).
• The tube will still be full, 'trying' to siphon but with the bottle full, there won't be any flow.
• Without letting much water out of the tube, raise the tube to a vertical position.
You should end up with a bottle full of water, with the water extending upward into the tube to a point near the top. There should be no air in the bottle or in the tube, up to the level of the water.
Squeeze the bottle until just a little water comes out of the tube, and release the squeeze. This will reduce the level of the water in the tube. Do so again, repeating if necessary until the water in the tube is about 10 cm below the top of the tube.
Hold the tube in a vertical position, with your thumbnail marking the water level. Rest the bottle on the counter and see what, if anything, happens to the water level in the tube. Lift the bottle off of the countertop by the cap and see what, if anything, happens to the water level.
Note what you observe:
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The start was about 11 cm and on the countertop it was 13 cm and then off was 14.5 cm
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Now, keeping your thumbnail in place on the tube, immerse the bottle into the cold water. Keep your eye on the water level.
The water level in the tube will undergo some clear changes.
Note what happens to the water level during the first 30 seconds or so, then what happens over the next few minutes. You don't have to record times, but you should glance at a clock every once in awhile so you are aware of the approximate time frame in which different things happen.
Report what you observe. Estimate the changes in water level, in centimeters.
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Change after 30 s of 3 cm and then 7, 11, and 17 cm at 1, 2, 3 min respectively.
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Assume that any noticeable changes in water level in the tube were due to changes in the volume of the bottle and/or to the volume of the water in the system. The cross-sectional are of the tube didn't change significantly, nor did the density of the water in the tube.
There are several ways in which we could describe the reasons for the behavior of the water in the tube, in terms of the volume of the bottle and the volume of the water present in the system. Give at least a couple of possible explanations:
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For one I would say the the bottle is contracting which in turn contracts the water. Also, when the bottle is in the air as opposed to the counter heat is lost to the air since more of the bottle is exposed to the air. The speed of these changes of course depends on the thermal conductivity of the plastic since that's what determines the rate of temp exchange between the air/water and the water in the bottle.
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Now give the explanation you think makes the most sense, in terms of physical properties of water and plastic.
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I think the above seems to work and I have a hard time fabricating another possibility. So the plastic 'transmits' heat to the water and that rate is the thermal conductivity of the the plastic and the plastic itself contracts which contracts the water in addition to what the water would contract on it's own.
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Self-critique (if necessary):
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Self-critique rating:
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@& Very good. Check out my notes.*@