E5 Equilibrium of gases
Piston air pump (von Guericke ~1650)
The mercury air pump is a special type of air pump. The first model of the air pump - and of the pumps used in industry for handling large masses of air - is the piston air pump. Its essential part is a cylinder S, in which the tightly fitted piston K can displace air. The cylinder takes the place of the barometer tube of the mercury pump and the piston that of the mercury. Fig. 211 explains the principle of a piston air pump: Like in the mercury pump (Fig. 209) the vessel A, in the piston pump you separate and link intermittently the cylinder S and the vessel to be pumped out either through a three ways tap, as the tap o in Geissler's pump and H in Fig. 198, or by a valve or slide. Correspondingly, such pumps are called tap, valve or slider air pump.
The tap air pump (Fig. 211) operates as follows: You set the tap so that the piston is linked to the outside air and push the piston to Position I; you press thereby the air out of the cylinder. You then close the tap and take the piston to Position II; this creates an almost empty ( we will discuss this further on) space between the piston and the cylinder bottom. Now you link the vessel to be emptied through the tap to the cylinder; thereby spreading the limited amount of air into the empty cylinder - it becomes rarefied. You then shut off the vessel by means of the tap from the cylinder, link the cylinder to the atmosphere and return the piston to the position I and repeat this cyle of actions. The already thin air of the vessel becomes thinner.
It depends on the care with which the different parts of the pump (piston wall, piston, taps, valves, piston rings, etc.) have been manufactured how close the vacuum is perfected. However, a dry air pump cannot do better than a mercury pump. The reason is that in both of them the vessel to be emptied temporarily empties into a supposed to be empty space. In the mercury pump, it is really empty (apart from traces of mercury vapour), in the piston pump, it is not. In fact, the mercury pump fills the space into which it is driven (like the piston of a piston pump, and indeed like a piston, which is congruent with the cylinder space) completely and therefore, on its return, leaves behind a completely empty space; the piston does not. When it returns, the cylinder fills again with air which previously was limited to the useless space. The smaller this is compared with the entire cylindrical space, the better a vacuum is the thereby caused rarefaction of the air of the useless space.
The smallness of the useless space effectively determines the performance of the air pump. The best dry slide air pumps achieve rarefaction to 1/2 mm mercury (measured by a air tight sucking socket). The uselss space is smallest in oil pumps, piston pumps (most with valves), in which the piston carries with it a non-evaporating oil layer, so that the piston is surounded by an oil layer and adjusts very perfectly to the wall and bottom of the cylinder. For them, rarefactions of 0.01 mm mercury are quite normal. The rarefaction which can be achieved with a mercury pump is 1/105 mm or less.
Piston air pumps can also condense gas. However, these pumps are built differently from the vacuum pumps, because they must deal with high pressures (often several hunderts of atmospheres). Their action can be seen from Fig. 211. In order to compress the air in the vessel, when the piston is in the Position II, you turn the valve, so that the connection to the outside is closed and that leading into the vessel open; if you then take the piston to the Position I, it will press the air from the cylinder into the vessel. You then turn the tap so that the cylinder is separated from the vessel and communicates with the atmosphere. If you then return the piston to the Position II, the air passes through the tap into the cylinder, etc. The possibility of reducing or increasing the pressure in a closed space arbitrarily (in face of the pressure acting on the walls) allows it to perform well.
You operate as follows: In a cylindrical tube RR (Fig. 212), an airtight piston K can be moved along the wall. If you rarify the air in B, let the space A be connected to the atmosphere, then K experiences from the side of A an additional pressure and moves as the arrow shows. In contrast, if you condense in the air B , while A remains connected to the atmosphere, K experiences from B a higher pressure and moves in the opposite direction. In the first case, the normal atmospheric pressure becomes an excess pressure and you speak of suction (due to rarefaction), in the second case of pressure action (due to the condensation); these actions are frequently combined.
For example (one of many), condensed air drives tube-mail: In a cylindrical tube with a diameter of several cm are cylindrical pistons, air tight gliding capsules with the letters. At the one end of the tube, you condense the air, so that the letter capsule experieneces an excess pressure and slides along the tube. - The gas which a railway train must carry with it in containers for illumination is condensed so that it occupies as little space as possible. Condensed carbonic acid is used for the operation of beer pressure aparatus, compressed oxygen , hydrogen, nitrogen serve many technical purposes.
Compression and rarefaction of gases (especially of air) is measured relative to the pressure of the atmosphere, that is, you measure by how much the pressure in the compressed or rarefied gas is above or below that in the atmosphere. However, the pressure in the atmophere (barometer level) changes. Hence one has to fix a certain atmospheric pressure as reference level. You use for this purpose the atmospheric pressure at a barometer reading of 760 mm mercury and 0º C (1.033 kg*/cm). This reference pressure is simply called one atmosphere; for example, one says: The gas in the container has the pressure of two atmospheres and means thereby that each 1 cm² of the container's wall experiences the pressure of two atmopsheres.
The fact that a steam boiler has been tested for 15 atmospheres means: Its wall has been tested whether it can stand up to a pressure equal to the weight of a 15·76 cm high mercury column with a 1 cm² cross-section, that is, 15·1,033 kg*/cm², etc. A pressure of 1/2, 1/ 4, 1/10, etc. atmosphere corresponds for rarefaction.
The instruments for such measurements are called manometers (Greek: manos = thin). You employ for compression and rarefaction different manometers. A manometer with which you can measure only in one direction starting from the normal pressure correspond to a thermometer, with which you can only measure above or below zero. An ordinary barometer indicates only changes of a few centimetres and shows therefore at one instant above and at another instant below 760 mm.
In its simplest form, a manometer for compression is a U-shaped, vertical, at both ends open glass tube which contains to a certain height mercury (or for very low pressures water or sulphuric acid or glycerin). The one end is connected to the vessel in which the pressure is to be measured, the other end to the atmosphere, so that there acts on the mercury in the one leg the gas, in the other leg the atmosphere. If the gas has the same pressure as the air, 1 Atm, the mercury in both legs has the same level; if the pressure in the gas is higher, it drives the mercury in its leg down and in the other leg up. The height of the column by which it eventually stands higher in the open leg than in the closed leg indicates by how much the gas pressure exceeds the atmospheric pressure.
If the mercury in the open leg is 1.76 cm or 2.76 cm, etc. higher than in the closed leg, it means that the gas pressure exceeds the air pressure by 1, 2, ··· atmospheres, that is, the pressure is 2, 3 atm. In both legs press 2, 3, ··· atmospheres on the mercury: In that linked to the gas container 2, 3, ··· atmospheres, in the open leg 1 atmospheric pressure in creased by the pressure of 1, 2, ··· mercury columns of 76 cm each. In order to cover just a few atmospheres, such a manometer must be very long. You avoid this by closing the leg to the atmosphere. Then you compress the air as the mercury rises and it encounters the pressure of the compressed air. Then you can manage with a tube which is about 60 - 80 cm long. These are only laboratory instruments, industry uses others: You let the gas pressure act, like in an aneroid barometer, on an elastic body and have a pointer indicate the pressure on a scale.
A measuring device for very hight pressures (thousands of atmospheres) is the pressure scale: You transfer the pressure F1 to be measured through a tube R into a cylinder and there to a slideable (carefully adjusted) piston of known cross-section (q) and load the piston by weights (p) until N1 indicates equlibrium. Fig. 213 shows this device connected to a bottle F1 filled with compressed gas. For a piston cross-section q, the pressure is then p/q.
Pressurs of rarefied gases are measured with manometers which are like barometers (mostly mercury, but also glycerin). Since you are then concerned with low pressures, the mercury column which balances the pressure, is much lower than corresponds to the atmospheric barometer height. In effect, such a devise is a shortened barometer (Fig. 214a). The shortening explained as follows: Imagine that you have closed the open end of a normal barometer at the pressure 760 mm just above the mercury by melting the glass, so that the mercury almost touches the top. Then the barometer cannot measure pressures over 760 mm, but all below 760 mm. However, if the largest pressure to be measured is 1/4 atmosphere, then 760 mm are not required and you connect the open leg of a barometer to a vessel, in which the pressure is 1/4 Atm. Then the mercury drops in the open leg to 19 cm above that in the other leg. You now close the leg just above the mercury. This barometer can now measure all pressures below 1/4 Atm, but none above that pressure. You read then the difference in the heights of the two legs and determine fractions of an a atmosphere on a millimeter scale. Such barometers are like fever thermometers which are shortened temperature measuring devices.
One of the most used vacuum manometers (McLeod 1841-1923 1874) employs directly Boyle's Law: It cuts off from the gas, the pressure px of which is to be measured, a known volume V, pressurizes it to a convenient volume v, thereby increases px to a readable pressure p and finds px = v·p/V. The vacuum meter only contains gas and mercury. Fig. 214 shows it at the moment of readings of v and p being taken: Lifting of the mercury container B separates the gas volume V from the other gas - it is the space D with the capillary E which runs off the device; its volume has been measured previously - and displaces it into the calibrated capillary E and compresses it into the volume q; the heigth difference of the mercury columns in C and E yields the pressure p in the volume v.
Water suction pump. Water pressure pump
The most familiar suction and pressure actions are those for which the surrounding atmosphere supplies the excess pressure. A suction action occurs when you pull a fluid through a tube (Fig. 215 below). The tube BC becomes the cylinder, the column of fluid AC inside it the piston of the scheme of Fig. 211. You close the end B with your lips and expand your chest as if to take a deep breath (without using your nose). The air, which until then occupied the section AB of the tube, expands through your mouth into your chest and thereby is rarefied. The end A of the column AC thus experiences a pressure, which is smaller than that of the atmopshere, the end C, in contrast, the atmospheric pressure, whence there is an excess in pressure which drives the fluid in the tube upwards.
The water suction pump acts similarly (Fig. 216). The ground water T takes the place of the fluid in the vessel of Fig. 215, the tube CB through which the water rises and the cylinder L, to which the tube leads (from which it is now and then separated by a vertical trap door S), that of the suction tube BC of Fig. 215 and of the chest; the expansion of the chest is replaced by lifting of the piston O.
The pump acts as follows: Initially, the ground water is at A in the tube CB and the piston at the bottom of the cylinder. If you lift the piston, the air below it becomes rarefied and reduces the pressure on the flap S. Therefore the trap opens, because the pressure from below exceeds that from above. The air, previously confined to AB, spreads now into the cylinder and becomes rarefied. Now the pressure acting from above on the water AC in the tube is lower than that from below and the water rises until the pressure of the rising column plus that of the air still in the tube and the cylinder equals the atmospheric pressure at T. You have then over the water column up to the piston the same pressure, the flap drops through its own weight and closes the tube. (However, the water need not yet have reached the piston) If you now press the piston downwards, the air between it and the (again closed ) flap S is compressed. This pressure opens the valve in the piston, which opens upwards and the air enters the atmosphere. Now the pump cycle restarts. The air which is still above the water column in the tube becomes more rarefied and the water is driven upwards by the excess pressure of the atmosphere until it reaches the cylinder. If now the piston is pressed downwards, the water opens S and reaches the upper side of the piston, is raised to the tube leading outside and runs away.
How high above the ground water level T can you raise the water? The pressure of the atmosphere balances a mercury column of 76 cm, that is, a water column of 13.6·76 cm - 10 m. Hence you can raise the water only by 10 m over the level of the ground water. However, as a rule, suction pumps are not built carefully enough, so that they reach 8 rather than 10 m. Wherever the ground water lies deeper, you lift the water as high as possible with a suction pump and direct the discharge tube upwards (Fig. 217). Into this tube you force more water by means of the piston until it reaches the discharge opening. It cannot fall back, because between the tube and the piston is a trap which opens in the direction of the tube and closes towards the cylinder.
Heron ball. Fire-engine
The air pressure does not yield here more than in ordinary suction pumps: The water reaches higher up, because the piston pushes it. In this case, the air pressure really drives the water much higher up than 8 m. But the air is at first compressed and given a pressure which lies far above that of the atnmosphere, whence the water can be thrown that high up.
The most important component of the fire engine is the air chamber. It relies on the same principle as the Heron ball (Fig. 218): You fill a bottle partly with fluid, then plug it tightly and stick through it air tight a tube below the level of the fluid. The level is thus subdivided into two layers, the larger one (EC) - in contact with the air in the bottle - and the smaller one a - which bounds the column of fluid in the tube and is in contact with the air outside. The device begins to act, that is, to fling like a water fountain the fluid through the tube, as soon as the air over EC presses considerably more strongly than the atmosphere on the fluid it touches in the tube ab. You generate this difference in air pressure by driving air from outside through the tube into the space over EC. In this way, you increase the pressure of the air already there. If you stop the forced supply of air and open the tube, the pressure over EC, because it now is larger than that in the atmosphere, drives the fluid upwards through the tube and as long out of the vessel until the air in the vessel occupies a space in which its pressure has sunk to atmospheric pressure, that is, to the same pressure which is acting from outside on the fluid in the tube.
For example, the siphon bottle is a Heron ball for effervescent drinks. The pressure of the escaping carbonic acid, which assembles over the fluid, is stronger than that in the atmosphere. If you open the tap of the tube, which reaches down into the fluid, it drives the fluid outside. Also, the spray bottle of the chemist (Fig. 219) is a Heron ball into which you drive the air through a special tube, which, however, ends above the fluid.
You also employ the Heron ball in the fire engine. However, you increase then the pressure in the air chamber by pumping water into it and thus compressing the air. The air chamber is served by two pumps, which work together in such a manner that while the one piston rises, the other drops, so that the water ejects continuously - not in jerks as in the case of an ordinary water pump during lifting and lowering of the piston.
The siphon (Fig. 220) is a unique suction pump without flaps, valves or similar components. It only has a tube which forms a U with unequal legs and can also employ a hose. You see from the figure that the shorter leg - it takes the place of the suction tube of the suction pump - sticks into into the vessel filled with the fluid, the level of which takes the place of the ground water level. However, the ordinary suction pump ejects the lifted water above the ground water level T, while the siphon only works when the opening a lies below the ground water level. In order to start the action of the siphon, you suck in the fluid at a - harmless fluid with your mouth, dangerous ones by a sidewards tube (poison siphon) - until the entire tube is filled as far as a. If you now stop action, the fluid ejects at a in a jet. We will see below, how long it does so.
This process is more readily understood by watching the construction of a siphon: The vessels A and B in Fig. 221 contain water to the levels a and b. It will be explained below why the one level (here a) must be higher than the other one. Above the levels stick out tubes closed on top by fluid supported by the atmospheric pressure, the water columns a and b are both shorter than the air pressure would allow, that is less than 10 m (in the case of mercury less than 76 cm). In order to install them free of air, you proceed as in Torricelli's experiment. Subsequently, the two tubes will become the legs of the siphon and must therefore be connected. For this purpose, we will later on make holes into them at c and d and link them by a water filled tube e which has no air in it. However, we ask first of all: How large is the pressure with which the fluid acts at c and d on the wall of the tubes?
The pressure which the columns of fluid exert at the level of the fluid on the wall of the tubes equals the atmospheric pressure. At a point above it, it is smaller, in fact, by the pressure of the fluid column between the height of this point and the fluid level. It is therefore at c equal to p minus the pressure of the column a, at d equal to p minus the larger pressure of the (higher) column b. Hence the pressure at c is larger than that at d and this difference starts the action of the siphon. If c and d are connected by the tube e filled with water, the water experiences the pressure from c to d, moves in this direction and pushes outside the water ahead in b: The siphon acts.
At the instant when the higher pressure pushes the water away from c, water enters at c from a, driven by the atmospheric pressure acting on a. The difference in pressure between c and d remains therefore and the siphon continues to work. While it works, it shifts water out of A into B. Hence the water level in A sinks and that in B rises, whence the difference in the pressures at c and d drops continuously. When the level drops below the level at a, air enters the suction leg and ejects all of the fluid. The output leg need not end in a vessel filled with fluid (B) (we have assumed this, in order to simplify the presentation), it can lead to the atmosphere; you only have to fill it (by suction from its end) until below the level of the vessel A, in order to start the siphon.
The pressure which drives the water out of the siphon depends on the difference in the lengths of the fluid columns a and b; however, this difference becomes smaller as the fluid level a sinks and the fluid level b rises. Thereby the pressure decreases and with it the discharge velocity of the siphon, while the fluid level sinks. Nevertheless, you can keep the discharge velocity constant by letting the siphon sink with the level, for example, by letting the device swim on the level (Fig. 222).
Mariotte's vessel. Pipette
Also Mariotte's vessel (Fig. 223) keeps the escape velocity constant (Laboratoty equipment). It is created by making a hole in the wall of a Heron Ball (Fig. 218), which lies below the lower end of the tube. If you open a, the fluid leaves, because there acts at a only the atmospheric pressure, but from the inside the pressure of the air above the fluid level, increased by the pressure of the fluid between S and a. As a result of the reduction of the fluid in the bottle, the air above it expands and its pressure drops. When it has dropped so far that it and the pressure of the water column from S to the level of b (the tube opening) together are bypassed by the atmospheric pressure of the air in the tube, then air enters all the time at b and rises through the fluid upwards above the level. Hence you have at b at all times the atmospheric pressure, that is, the same pressure as at a. The excess pressure, under which the fluid is ejected, is also the pressure of the fluid between the levels b and a. It remains constant until the fluid drops to the level of b, but also the escape velocity remains constant until then.
You can increase or decrease this pressure by sliding the tube up and down and thus lengthening or shortening the column. If you slide the tube down to the level of the escape opening, the flow stops, because then the height of the column becomes zero. - The outflow also stops, if you close the tube above and thus stop the entry of air; the internal pressure acting on a is then soon much smaller than the atmospheric pressure acting from outside on a, so that a discharge becomes impossible. The Mariotte bottle behaves at this stage like a pipette (Fig. 224) which you fill partly by sucking and then close. Also here the discharge is impeded in that the pressure acting from inside outwards of the (by suction) rarefied air and the fluid column does not exceed the atmospheric pressure.
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