Video Experiments 8

Video Experiments 8-9: Pressure, Volume, Temperature, Work for a Confined Gas

Experiment 8

The 'bottle engine' consists of a soft drink bottle containing some water. Water volume is about 20% of container volume, and the rest of the container is full of air. The container is sealed with a stopper in its opening. Through the stopper are three plastic and/or glass tubes. One extends down into the water at the bottom of the bottle and up to a considerable height above the bottle, and its ends are uncapped; when pressure in the bottle rises water tends to rise in this tube. Another extends only a short way into the bottle and a short way above it, and is capped outside the bottle; this tube is used to release pressure, which happens when the cap is removed. A third tube extends only a short way into the bottle and a considerable distance out of the bottle, and contains colored alcohol extending about 1/3 of its length; when this tube is formed into a U shape it can be used to measure pressure in the bottle.

Observe the clip Bottle Pressure 1, on the EPS01 CD (run EPS01, click on Volume, Temperature, Pressure Experiments (bottle engine) ) in order to understand the setup of the system. In this clip you see the overall system, and how increasing pressure by squeezing the bottle forces water up the vertical tube.

Observe the clip Bottle Pressure 2, taking relevant data. Assume that the bottle contains 1600 cm^3 of air, originally at room temperature.

Note the height of the water column in the vertical tube and for each height calculate the additional system pressure needed to raise water to this height (i.e., calculate the pressure of a column of water of this height).
Note the initial length of the air column, and from observing the change in the length of the air column in the pressure-measuring tube determine the length of this column for each water column height.
Determine the ratio of the air volume in each compressed column to the air volume in the original column, assuming that the cross-sectional area of the tube remains unchanged (the inner cross-sectional diameter of this tube is 1/8 inch, and can be used to calculate volumes if necessary; however the ratios can be calculated without knowing this diameter).
From these ratios and from the inverse proportionality between pressure and volume (which occurs when the temperature of the gas in a sealed container remains constant), determine for each water column height the pressure in the air column. Give each pressure as a multiple of the initial pressure (e.g., 1.037 times the original pressure, 1.192 times the original pressure, etc.--the numbers will be closely related to the volume ratios in a way you should understand from the gas laws).
Sketch a graph of the pressure difference (this is the difference in pressure between the top of the the water column and the water level in the container, as determined by Bernoulli's Equation, in N/m^2) vs. the pressure in the air column (the latter again expressed as a multiple of the original pressure).
Determine the slope of this graph and explain why this slope should equal atmospheric pressure.

Bottle Pressure 3: Determine the temperature change in the bottle as a result of the warmth from the instructor's hands:

From the change in the position of the alcohol column determine the change in the maximum volume of the gas in the bottle.
From this change in position and the slope of the meter stick determine the change in the altitude of the alcohol column, and thereby determine the pressure change in the bottle. (You may need to make an observation at the beginning of this clip, or perhaps in a previous clip, in order to determine the slope of the meter stick; you may assume that the table is level and that the beaker is 14 cm high. You may also assume that the density of the alcohol solution in the container is 860 kg/m^3).
From your results and the gas law determine the temperature of the gas in the bottle, assuming that the initial temperature was 23 Celsius.
How significant was the pressure change as opposed to the volume change in your determination of the temperature?
How significantly do you therefore think that the change in slope in the second part of the video clip will affect the motion of the alcohol column?

Experiment 9

The clips listed here won't work from the homepage. See the CD EPS01 EPS01 CD (run EPS01, click on Volume, Temperature, Pressure Experiments (bottle engine) ) for these clips.

Bottle Engine #1, Bottle Engine #2 We see here how the bottle engine is operated as a heat engine. We cool the air in the bottle by immersing the bottle in ice water, cooling the sides of the bottle and hence the air in the bottle; we keep the short tube uncapped during the cooling process, so that the process takes place at atmospheric pressure. We then cap the short tube and immerse the bottle in warm water, which causes the pressure inside the bottle to increase. Since pressure in the open end of the tube remains at atmospheric pressure, the water must rise in the tube to equalize pressures within the bottle. We note that until the water reaches the top of the tube there is very little expansion of the air inside the bottle--since the tube has very little volume very little fluid must be displaced to fill the tube. After the tube is filled, pressure ceases to rise and water flows out the top to accomodate the resulting expansion of the gas. This increases the potential energy of the system (the water can be caught as it flows out and therefore has more PE than before), thereby performing mechanical work. In the second of these two clips we measure the amount of water 'pumped' upward by the system to a given height. We note that in this clip the ice water should be at 0 Celsius and the hot water is at about 50 Celsius; however the gas temperatures probably ranged from about 7 Celsius to about 46 Celsius.

Video Clip 20 cm In this and the following clips water is 'pumped' using ice water and 53 Celsius water; the gas temperatures range from about 7 Celsius to about 48 Celsius. In this clip water is raised to an average height of about 20 cm. You should observe the amount of water collected, and in this and the following clips you should make any other observations which might be pertinent to analysis of the system.

Video Clip 53 cm In this clip water is raised to an average height of about 53 cm.

Video Clip 80 cm In this clip water is raised to an average height of about 20 cm.

Video Clip 100 cm In this clip water is raised to an average height of about 100 cm.

Video Clip 120 cm In this clip water is raised to an average height of about 120 cm.

In each clip you saw a certain amount of water raised to some average height above its original level. For each clip:

Determine the amount of work done by the system (the amount of work done is equal to the increase in the potential energy of the water).
Determine the pressure in the bottle as water is flowing out the top of the tube (Bernoulli's Equation applies--the pressure of the water flowing out of the tube is atmospheric pressure, about 100 kPa; the altitude of the water is less at the water surface in the bottle than at the top of the tube)
Determine the temperature in the bottle, assuming that the inside temperature was 7 Celsius when the bottle was sealed off from the atmosphere.
If the air in the bottle requires 5/2 * 8.31 J / mole to raise its temperature by 1 degree Kelvin, then how much thermal energy did it take to heat the air?
What is the efficiency of the process, defined as the work don divided by the thermal energy supplied to the system?
How much thermal energy would be taken from the system as it cools and returns it to its original state?

Why does the system not do as much work when the height to which water is raised is too small?

Why does the system not do as much work when the height to which water is raised is too great?

At what height do you think this system, working at the given temperatures, will attain maximum efficiency?