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course PHY 202
Brief Bottle Experiment 2aRaising Water using Thermal Energy
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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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When the cold water is poured over the bottle, it causes the pressure of the molecules to decrease. When the volume of air is sealed in and hot water is poured over the bottle, the molecules move faster and cause the air pressure in the bottle to increase. This pressure pushes the water out of the bottle through the tube until it pushes enough water out to equalize the pressure in the bottle.
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@& The heating occurs in two phases. First the pressure builds as water rises in the tube. Then the gas expands at constant volume. The gas continues to expand until the temperature of the air in the bottle stabilizes at the higher temperature.*@
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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Volume and Pressure would increase at the same rate until the point at which water stops flowing out of the bottle, because when the water stops, the pressure stops changing, as well as the volume.
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@& The pressure increases only while water is ascending in the tube. P stays the same, V changes, so this part of the process corresponds to a vertical line segment on the P vs. V graph.
Then the gas expands while pressure remains constant. On the graph V increases, P stays the same, so this part corresponds to a horizontal line segment.*@
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 same thing happened as before. I started with a cup of water. After running hot water over the bottle, 1/3 of the water came out at the cap. When removed from the heat, about half of the water removed returned back to the bottle in about five minutes.
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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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The same thing happened up until turning off the hot water. It only took a minute or two to collect 1/3 of the cup of water and then when cold water was turned back on over the bottle, it only took about 30 seconds to return all of the collected water back into the bottle. Wow!
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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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The end of the tube was at cap level, 7.5in above the water level in the bottle. I believe I was fairly accurate. I didn’t use a teaspoon, but a measuring cup and converted to ml. I started with 237ml of water in the bottle. Hot water forced about 79 ml out of the bottle.
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@& The important figure is how much air was in the bottle, not how much water. It's the air that's being heated, and that provides the increases in pressure and volume necessary to do the work.
If you know what kind of bottle you were using you can subtract the 237 ml from its capacity to determine the volume of air.*@
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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With the tube held strait up above the cap, about 60ml (12.75 teaspoonfuls) of water were collected. I believe I was fairly accurate.
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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 end of the tube was .5inch above the water level. Very quickly 100ml of the water were collected in the measuring cup, about 21.2 teaspoonfuls. I believe I was fairly accurate once again.
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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 oberve 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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Tube at cap level , 19cm 79ml displaced dPE=147mlm2/s2
Tube max height, 53cm 60ml displaced dPE=311mlm2/s2
Tube at min height, 2cm 100ml displaced dPE=19.6mlm2/s2
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@& Each mL of water has a mass of 1 gram. So you know how many grams of water are raised. You know the distance it was raised, so you can find the change in its PE.*@
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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I believe we could raise water to about 120cm using hot/cold water.
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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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Almost all the water used in the experiment would be displaced, 237ml. The change in PE would therefore be mgdy = 237g*9.8m/s2*1.2m = 2,787gm/s2
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@& If you raise water to the maximum height you only displace enough water to fill the tube.
No water would be collected, so there would be no change in PE.*@
At what height do you estimate the PE change of the displaced water would be maximized?
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At the highest possible height, about 100cm
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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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I’d say the cold water is about 50degrees F, and the hot water is about 120degrees F.
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@& You can draw conclusions about the relative change in water temperature from the changes in pressure and volume observed during this experiment.*@
Brief Bottle Experiment 2b
Raising Pressure using Thermal Energy
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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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Before cold water: 27cm air column
After cold water: 27cm air column
After hot water: 24cm air column
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If the pressure in the tube was initially 1 atmosphere, what was the pressure after heating?
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About 1.15atm The air column was compressed about 15%
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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? 120cm, maybe more.
Brief Bottle Experiment 2c
Bottle Thermometer
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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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After removing the bottle from the hot water, I placed the tube in a vertical position and watched as the water level rose about 54cm from the bottom of the tube. It then slowed down to almost a stop, so I put my hands around it and the water then rose quickly to about 60cm and slowed down.
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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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As soon as I removed the bottle from the hot water, I placed the tube outside the bottle in a horizontal direction. The water moved through and out the tube very quickly and I didn’t even have to put my hands around it.
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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?
I placed the bottle in the freezer, then removed it and held the tube in a vertical position. The water level increased by taking over 75% of the tube, then slowed to almost a stop. I then placed my hands around it and it rose to the tip of the tube and came out very quickly.
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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I’m estimating water level rises about one cm to every degree temperature rise.
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Brief Bottle Experiment 2d
Expansion of water and plastic
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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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I filled the bottle with hot water. I then tried my best to siphon cold water into it, but could never seem to get the tube completely full of cool water. I don’t know if this is because the cold water was causing the hot water to condense or not.
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@& You probably had the cap tightened before the siphon action began. Don't tighten the cap until water is flowing out of the end of the tube.*@
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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So then I placed the bottle in a cold bath and watched as the cold water in the tube, about 20cm above the cap of the bottle gradually and consistently decreased and made its way into the bottle.
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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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The cold water bath causes the warmer water molecules inside the bottle to slow down and condense, making room for the cooler water molecule to have room inside the bottle as well.
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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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By cooling the bottle, we decrease pressure. This decrease in pressure makes it possible to get more molecules into the bottle.
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@& Good data. See my notes to clarify what is likely going on in the system.*@
course Phy 202
2/16 10:30q001. If the air in a bottle builds pressure at constant volume from temperature 300 K to temperature 450 K, then expands at this constant pressure from 450 K to 900 K:
What is the ratio of highest pressure to the lowest?
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The Pressure ratio is 1.5
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What is the ratio of the highest volume to the lowest?
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The volume ratio is 2
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In terms of the initial gas volume and pressure V_0 and P_0:
What are the volume and pressure when the system reaches 450 K?
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V0=V0
P0=3/2P0
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What are the volume and pressure when the system reaches 900 K?
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P=P0(Ti/Tc)=3/2P0
V=V0(Tf/Ti)=2V0
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If the added pressure is used to raise water, how high will it be raised?
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y=P0/2`rho*g
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If the added gas volume displaces water to the preceding height, what volume of water will be raised?
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The `dV=2V0-V0=V0 so the displaced water is V0
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What do we get if we multiply the volume of water raised by the height to which it is raised?
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V0*P0/2`rho*g=P0*V0/2`rho*g
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Answer the same sequence of questions if the pressure builds at constant volume from 300 K to 600 K, then the gas is allowed to expand at this constant pressure until the temperature reaches 900 K.
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P ratio= 2, Volume ratio=1.5. At 600K, V0=V0 and P=2P0
At 900K, P=2P0 and V=3/2 V0
Water will be raised y=P0/`rho*g
Volume displaced is 1/2V0=V0*P0/2`rho*g
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Now we replace the specific temperatures by symbols.
If the temperature starts at T_c and is raised to T_i while the volume remains constant, what will be the new pressure?
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P=P0(Ti/Tc)
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If the temperature is then raised from T_i to T_h while the pressure remains constant, what will be the new volume?
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V=V0(Th/Ti)
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What is the expression for the change in the pressure?
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`dP=P0(Ti/Tc)-P0=P0(Ti/Tc-1)
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What is the expression for the change in the volume?
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`dV=V0(Th/Ti)-V0=V0(Th/Ti-1)
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What do we get when we multiply the change in pressure by the change in volume?
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P0V0(Ti/Tc-1)(Th/Ti-1)
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What does our product have to do with the PE gain of the system?
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It defines the PE gain of the system
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What would we have to do with our expression to get the actual PE gain?
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To get the actual PE gain, we would have to measure the initial volume and discover how high it moved.
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&#Good responses. Let me know if you have questions. &#