Introduction
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- Bu səhifədəki naviqasiya:
- Dynamic gas model and the universal gas law
- PV diagrams, non-ideal gases, condensation
- Laplace law
- Solubility, partial pressure
Gas physicsWater has a very low compressibility because of the strong polar bonds between the molecules. The molecular bonds in oil are somewhat weaker, and oil is therefore slightly compressible. Air at room temperature and 1 bar has a density of about 1,25 kg/m3, about thousand times lower than that of water, and the distance between the molecules is accordingly roughly 10 times larger than in water. A gas is very compressible, but if a gas is at a temperature higher than its critical temperature, it is impossible to press the molecules together into a liquid phase. The amount of gas substance in a closed compartment can be characterised according to two traditions: either by volume and pressure or by the number of mol. Flow rate can accordingly be given by mass: kg/s; or volume: m3/s; or substance: mol/s. The metabolism of the body is based upon the chemical reactions between molecules, so the number of molecules (mol) is perhaps the most basic unit for medical gases used by the body. Dynamic gas model and the universal gas lawGas molecules (or atoms or small particles) at room temperature are not at rest. It was the British botanist Robert Brown who in 1827 discovered in his microscope that small grains of pollen in water moved and collided, he thought it was a life process. The average effect of gas molecule collisions with the walls constitutes the pressure of the gas. It was Avogadros2 great discovery that the pressure is proportional to the number, not the mass, of the particles. With reference to Avogadro the number of particles therefore has got its own numbering system: the mol which is ≈6·1023 particles and corresponds to the molecular weight [gram] of a gas, e.g. 1 mol of oxygen is 32 g oxygen. The type of particles should be specified, but often we mean both atoms (e.g. Ar) and molecules (e.g. O2). The reason for the number dependence is that smaller particles move faster so that their contribution to pressure statistically is the same. Accordingly, usually for a certain amount of substance the pressure will be dominated by the smallest particles because they are usually more numerous (the mass of spheres is proportional to the radius r3, so with equal mass it is 106 as many 0,1 μm spheres as 10 μm spheres). The thermal movement of gas molecules has an important consequence: in a mixture of particles such as air, the particles do not necessarily sediment in layers according to their weight. It is the mass of a particle at a certain temperature which determines whether the molecule settle under gravitational forces or thermal movements are forceful enough to overcome gravity. At room temperature light particles such as N2 (molecular weight 28), O2 (32), CO2 (44), Ar (40) and H2O (18) will not settle with the heaviest molecules at the lowest levels. Larger molecules like sevoflurane (200) however do settle to the floor to a noticeable degree. According to the gas law a certain gas pressure is obtained by fewer molecules the higher the temperature. Accordingly, warm gas is lighter and ascends into the air (warm air balloons). The universal gas law is based upon Avogadros discoveries. It is given in a variety of forms; here by the Boyle&Mariotte / Gay-Lussac3 version using the amount of substance n [mol] as a parameter: Equation 3 Universal gas law PV = nRT n is the number of all particles in the enclosed gas volume, that was Avogadro's great discovery, The particles may be atoms (noble gas), molecules (e.g. O2 or CO2) or any small particle from electrons to droplets. The contribution to pressure is from each particle, it is the number that contributes and not the size. P is the pressure [Pascal], V is the volume [m3], R the universal gas constant (8,3 [Joule/ºKmol]) and T the temperature [ºK]. Validity
Other versions
There are two different pressure scales in common use: absolute pressure (AP) or relative to atmospheric pressure (RP). Often it is not defined but determined by convention. Most pressures are relative pressures. Bottle filling is RP, an oxygen bottle is “empty” when it has atmospheric pressure, and negative pressure is not good as ambient gas may be aspired into the bottle. Absolute negative pressures do not exist, so if negative pressure is given it must be RP. Also with suction devices relative (negative) pressures are often used. Higher negative pressure then means higher vacuum and lower absolute pressure. PV diagrams, non-ideal gases, condensationFig.5 shows a pressure-volume (PV) diagram of a gas in a closed volume. At high temperatures the gas is more ideal following the Boyle-Mariottes law, Eq.3. In this region the gas can not be compressed into a liquid, irrespectively of how high the pressure is. At lower temperatures the curves loose their hyperbolic form, and at the critical temperature Tc a point is reached where it is possible to compress the gas into a liquid. At temperatures below Tc there is a constant pressure range where the substance is more or less liquefied. A liquid is not very compressible and when completely liquefied the pressure rise is very rapid at a further lowering of volume. Tissue (except lungs and guts) does not normally contain gas, so tissue is like a liquid, highly incompressible, but may easily change its form. 
Figure 5 PV-diagram for a closed volume Above the critical temperature it is not possible to compress a gas into the liquid state, the vibrational thermal energy is high enough to break the tight bonds between the molecules. Below the critical temperature the gas may be compressed to a liquid, the gas in this range is called a vapor. In daily talk we do not make the precise division, for room temperatures we should say water vapor, nitrous oxide vapor and oxygen gas. This would clarify the important fact that a bottle of carbon dioxide at room temperature may contain gas in the liquid phase. Then the bottle filling must be determined by weighing and not by pressure measurement. The oxygen bottle can not contain liquefied oxygen at room temperature, and the degree of filling can therefore directly be determined from reading the manometer pressure. Examples: a) Calculate how many liter of gas you have left in a 10L oxygen bottle at 120 bar. Solution: Tc for oxygen is -119 oC, so the oxygen must be in the gas phase. We use the Boyle-Mariotte gas law in the form P1V1=P2V2 so that 120.10=1.V2 and V2=1200 [L]. b) Calculate how many liter of gas you have left in a bottle of N2O having weighed it and subtracted the empty bottle weight (tared) and found the N2O content to be 2.2 kg. Solution: Tc for N2O is 36.5 oC and the N2O may be in the liquid phase. We need not know the ratio of liquid to gas, our weighing takes care of all the N2O molecules. The molecular weight of N2O is 44 and 1 mol is therefore 44 gram. The amount of substance in the bottle is 2200/44=50 [mol]. We use Eq.3: PV=nRT and put P=100kPa and T=300 K, then V=1245.3 [L]. Table 2 Critical temperature Tc, pressure Pc ; boiling point (1 bar) Tb.
T
ransport and storage of liquefied gas is practical because of the reduced volume, a large hospital is a big consumer of e.g. oxygen and nitrogen. According to Table 2 the storage of liquid oxygen must be done in large thermos bottles at temperatures lower than the Tc. Oxygen can e.g. stored at -119 oC and 50 bar, or -160 oC and 6 bar. To reduce the storage pressure to atmospheric pressure the temperature must be lowered, for oxygen in an open bottle (1 bar) down to the boiling point -183 oC. Nitrogen is used for cooling in the laboratories, for tissue long term storage and for cryospray. It is often practical to transport small volumes of liquefied gases in open thermos bottles at 1 bar and boiling temperature. Water is an important substance in medicine. Air can absorb water in the gas phase, such water vapour is invisible to the human eye, just as oxygen and nitrogen. The warmer the air, the more water molecules can be absorbed. Air saturated with water vapour corresponds to a relative humidity (RH) of 100%. At 37oC the partial pressure of the H2O molecules is then 6kPa. If the gas is saturated with water vapour and the temperature is lowered, water condensates in small droplets. This is mist or fog and is visible to the human eye, it is particles (droplets) and not single molecules. Laplace lawIn a blood vessel the blood pressure exercises a force against the walls which is counteracted by three different force components in the wall: 1) elastic tissue tension, 2) surface tension, and 3) active muscle tension (tonus). Tension T is measured as force pr meter length perpendicular to the force [N/m], Fig.6. Laplace4 found the following formula for the pressure P [Pa] in a cylinder of radius r [m] and the total wall tension T [N/m]: Equation 4 Laplace P = T/r (cylinder) Some peculiarities of this equation are linked with the fact that it does not contain pi, that pressure increases beyond limits as r 0, and that the pressure and the tension components are orthogonal, ref. Problem 10. T may itself be a function of r, so that the increase in pressure with small values of r may be modified. A tube has one dimension of curvature, and since the sphere has two such dimensions, the pressure for a sphere is doubled: P = 2T/r . 
Figure 6 Laplace cylinder model These equations are applicable in many medical situations also with active muscles in the walls, e.g. blood vessel, spherical pathological enlargement of blood vessels (aneurisms), pressure in the ventricles of the heart during systole, pressure in the urine bladder, pressure in the airways of the lungs. In the lungs the alveoli are prismatic or polygonal in shape, i.e., their walls are flat, and the Laplace law applies only to curved regions. Alveoli do not readily collapse into one another because they are suspended in a matrix of connective tissue "cables" and share common, often perforated walls, so there can be no pressure difference across them. Surfactants have important functions along planar surfaces of the alveolar wall and in mitigating the forces that tend to close the small airways. Laplace’s law as it applies to cylinders is an important feature of the mechanics of airway collapse, but the law as it applies to spheres is not relevant to the individual alveoli. Solubility, partial pressureGases do dissolve in liquids like oil, water and blood. This process is called physical solubility if there are no chemical reactions between the gas and the liquid. The gas molecules find their positions between the liquid molecules, and if the gas molecules fit well in the space between them the solubility is high. The gas becomes a part of the liquid phase, and is not to be regarded as small gas bubbles. There is a transport of gas across a gas/liquid interphase as long as there is a concentration difference. The concept of partial pressure is essential in this respect as a practical measure of gas concentration in a liquid. Henry’s law states that the amount of gas dissolved in a liquid is proportional to the partial pressure of the gas in equilibrium with the liquid. Partial pressure in a liquid may be measured with a sensor covered by a membrane permeable to the gas but not to the liquid. 
Figure 7 Left: dry gas mixture, right: after insertion of a water filled dish On Fig.7 a closed chamber at 37 oC is filled with dry nitrogen gas up to a pressure of 80 kPa and then with dry oxygen gas so that the total pressure is 100 kPa (1 bar). At 37 oC no chemical reactions between the two gases occur, we have a mechanical mixture. According to Daltons law the partial pressure of each gas contributes to the total pressure as if it were alone. The partial pressure of oxygen (Fig.7) is therefore 20 kPa. On Fig. 7 (right) we then introduce a small dish of water into the chamber. The water has already been in prolonged contact with room air so that the water is in equilibrium with the oxygen and nitrogen of the air. With the dish inside no net transport of oxygen and nitrogen occurs across the gas/water interphase, but as the gas was dry a transport of water molecules into the gas starts (evaporation). This goes on until the chamber gas is saturated with water vapour. The relative humidity (RH) is then 100%, at 37oC corresponding to a water vapour partial pressure of about 6 kPa. The total pressure in the chamber has increased to 106 kPa. The slightest temperature fall somewhere in the chamber will then start water vapour condensation. Table 3 shows the solubility coefficient of different gases in blood and oil. It is practical to give the amount of a dissolved gas as shown: litre gas per litre liquid [L/L=1], the Ostwald solubility coefficient which is temperature, but not pressure dependent. If the gas pressure is doubled the amount of dissolved gas is also doubled according to Henry’s law. But that is as amount of substance [mol], not as volume [L], because the doubled pressure has also halved the volume. The number of dissolved molecules pr litre liquid [mol/L] may therefore be more physiological relevant, but less practical because it is pressure dependent. Table 3 Solubility of gases in blood and oil at 37 oC
If nitrogen is to be replaced by nitrous oxide in an anaesthesia, the transport of nitrous oxide in the blood stream is more rapid than the wash out of nitrogen (why?), therefore gas volumes filled with nitrogen e.g. in the guts can increase dramatically but transiently when large amounts of nitrous oxide suddenly arrives. Oil may seem to be a curious choice of liquid, but it equals fat sufficiently and body fat may store large amounts of gas and so influence gas kinetics strongly. After a prolonged anaesthesia it may take a long time to wash out the anaesthetic gases from the fat during wakening. Oil data is also used because oil is more stable and give more reproducible data than fat. Yüklə 1,16 Mb. Dostları ilə paylaş:
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