Egan's Fundamentals of Respiratory Care 12th Ed-Copy export (7).pdf

88 SECTION I Foundations of Respiratory Care Laplace’s law Poiseuille’s law sublimation latent heat of fusion pressure surface tension latent heat of...

88 SECTION I Foundations of Respiratory Care Laplace’s law Poiseuille’s law sublimation latent heat of fusion pressure surface tension latent heat of vaporization polycythemia tension law of continuity potential energy thermal conductivity laws of thermodynamics radiation thermodynamics melting point Raynold’s number relative humidity (RH) turbulent flow meniscus shear rate van der Waals forces molar volume solubility coefficient vaporization partial pressure specific gravity Venturi effect Pascal’s principle STPD viscosity percent body humidity strain-gauge pressure transducers water vapor pressure forces are much weaker in liquids than in solids, liquid molecules STATES OF MATTER can move about freely (see Fig. 6.1B). This freedom of motion There are three primary states and one secondary state of matter: explains why liquids take the shape of their containers and are solid, liquid, gas, and plasma. Fig. 6.1A–D depicts simplified capable of flow. However, similar to solids, liquids are dense and models of these states of matter. cannot be compressed easily. Solids have a fixed volume and shape. The molecules that In a gas, molecular attractive forces are very weak. Gas mol- make up the solid have the shortest distance to travel until they ecules, which lack restriction to their movement, exhibit rapid, collide with one another. This motion has been referred to as a random motion with frequent collisions (see Fig. 6.1C). Gases “jiggle.” Solids have a high degree of internal order; their atoms have no inherent boundaries and are easily compressed and or molecules are limited to back-and-forth motion about a central expanded. Similar to liquids, gases can flow. For this reason, position, as if held together by springs (see Fig. 6.1A). Solids both liquids and gases are considered fluids. Gases have no fixed maintain their shape because their atoms are kept in place by volume or shape. Both of these qualities depend on local condi- strong mutual attractive forces, called van der Waals forces.1 tions for the gas. Liquids have a fixed volume but adapt to the shape of their Plasma has been referred to as a fourth state of matter. Plasma container. If a liquid is not held within a container, the shape is is a combination of neutral atoms, free electrons, and atomic determined by numerous internal and external forces. Liquid nuclei. Plasmas can react to electromagnetic forces and flow molecules exhibit mutual attraction. However, because these freely, similar to a liquid or a gas (see Fig. 6.1D). Although A B            C D Fig. 6.1 Simplified Models of the Four States of Matter. (A) Solid (rigid network of interconnected springs). (B) Liquid (freely moving spheres with no space among them). (C) Gas (small rapidly moving particles with a lot of space among them). (D) Plasma (small rapidly moving charged particles with a lot of space among them).  CHAPTER 6 Physical Principles of Respiratory Care 89 mentioned here for the sake of completeness, plasmas are not TABLE 6.1 Thermal Conductivities in discussed further because at this time they are not known to be (cal/s)/(cm2 °C/cm) relevant to the practice of respiratory care. Material Thermal Conductivity (k) Internal Energy of Matter Silver 1.01 The atoms that make up all matter are in constant motion at Copper 0.99 normal temperatures.2 This motion results from internal energy. Aluminum 0.50 There are two major types of internal energy: (1) potential energy Iron 0.163 Lead 0.083 and (2) kinetic energy. Potential energy is referred to as the Ice 0.005 energy of position—that is, the energy possessed by an object Glass 0.0025 balanced on a shelf. Potential energy is a result of the strong Concrete 0.002 attractive forces between molecules. These intermolecular forces Water at 20°C 0.0014 are why solids are rigid and liquids have viscosity and cohesive- Asbestos 0.0004 ness. These same intermolecular forces are not as strong in gases. Hydrogen at 0°C 0.0004 Kinetic energy is the energy of motion, such as that of a falling Helium at 0°C 0.0003 object. Most internal energy in gases is in the form of kinetic Snow (dry) 0.00026 energy. Fiberglass 0.00015 Cork board 0.00011 Laws of Thermodynamics Wool felt 0.0001 Air at 0°C 0.000057 The term thermodynamics can refer to either the science of studying the properties of matter at various temperatures or the From Nave CR, Nave BC: Physics for the health sciences, ed 3, kinetics (speed) of reactions of matter at various temperatures. Philadelphia, 1985, WB Saunders. From the study of physics, we take special notice of the laws of thermodynamics. These laws describe how fundamental physical quantities (temperature, energy, and entropy) behave under the touch even when they are at room temperature. In this case, various circumstances and forbid certain phenomena (such as the high thermal conductivity of metal quickly draws heat away perpetual motion). A basic knowledge of these principles is helpful from the skin, creating a feeling of “cold.” In contrast, with fewer in understanding many aspects of respiratory care. Of particular molecular collisions than in solids and liquids, gases exhibit low interest is the first law of thermodynamics, one version of which thermal conductivity. states that an increase in the internal energy of a closed system can only be the result of work performed on the system. Work Convection can be viewed as the process of transferring energy to or from Heat transfer in both liquids and gases occurs mainly by convec- a system. The increase in internal energy of a system can be tion. Convection involves the mixing of fluid molecules at dif- observed as an increase in heat (as with a humidifier) or pressure ferent temperatures. Although air is a poor heat conductor (see (as during mechanical ventilation). Table 6.1), it can efficiently transfer heat by convection. To do so, the air is first warmed in one location and then circulated Heat Transfer to carry the heat elsewhere; this is the principle behind forced- When two objects exist at different temperatures, the first law air heating in houses and convection heating in infant incubators. of thermodynamics tells us that heat will move from the hotter Fluid movements carrying heat energy are called convection object to the cooler object until both objects’ temperatures are currents. equal. This is an example of transitioning from a higher state of energy to a lower state. Two objects with the same temperature Radiation exist in thermal equilibrium. Heat can be transferred in four Radiation is another mechanism for heat transfer. Conduction ways: (1) conduction, (2) convection, (3) radiation, and (4) evapo- and convection require direct contact between two substances, ration and condensation. whereas radiant heat transfer occurs without direct physical contact. Heat transfer by radiation occurs even in a vacuum, as Conduction when the sun warms the earth. Heat transfer in solids occurs mainly via conduction. Conduc- The concept of radiant energy is similar to that of light. Radiant tion is the transfer of energy by direct contact between hot and energy given off by objects at room temperature is mainly in cold molecules. How well heat transfers by conduction depends the infrared range, which is invisible to the human eye. Objects on both the number and the force of molecular collisions between such as an electrical stove burner or a kerosene heater radiate adjoining objects. some of their energy as visible light. In the clinical setting, radiant Heat transfer between objects is quantified by using a measure heat energy is commonly used to keep newborn infants warm. called thermal conductivity. Table 6.1 lists the thermal conduc- tivities of selected substances in centimeter-gram-second (cgs) Evaporation and Condensation system units. As is evident, solids (especially metals) tend to Vaporization is the change of state from liquid to gas. Vapor- have high thermal conductivity. This is why metals feel cold to ization requires heat energy. According to the first law of 90 SECTION I Foundations of Respiratory Care MINI CLINI to vibrate and the object has no heat that can be measured. This temperature is defined to be absolute zero. Although researchers Problem have come close to attaining absolute zero, no one has actually Bulk storage of oxygen in liquid form for hospitals consist of two basic com- achieved it; this is due to the third law of thermodynamics, ponents, a large tank to hold the liquefied gas and a vaporizer, which is a which states that absolute zero is impossible to achieve. tower containing radiator fins. The liquid oxygen flows from the bulk storage unit into the vaporizer, which allows ambient temperatures to heat the liquid, Temperature Scales converting it into gas. This is an efficient method to store a large quantity of oxygen in a relatively small space. For more information on the bulk storage Multiple scales can be used to measure temperature. The Fahr- of medical gases, see Chapter 41. enheit and Celsius scales are based on properties of water (freezing and boiling). A third scale, the Kelvin scale, is based on molecular Discussion motion. Absolute zero provides a logical zero point on which The liquefication of gases depends on two factors; a critical temperature and to build a temperature scale. In the International System of Units a critical pressure. Without one, the gas will not change to a liquid. The (SI), temperature is measured in Kelvin (K), with a zero point molecules of a liquid are closer together than those of a gas. The density of equal to absolute zero (0 K).3-7 Because the Kelvin scale has 100 liquid oxygen is about 1000 times greater than that of gaseous oxygen. degrees between the freezing and boiling points of water, it is a centigrade, or 100-step, temperature scale. The Kelvin scale has the unique quality of being based on the triple-point defini- thermodynamics, that energy must come from the surroundings. tion for water (the temperature at which all three phases of water This phenomenon is illustrated by the bulk storage of oxygen at exist). This temperature happens to be approximately 273 K hospitals and health care facilities. In such cases, large quantities (0.0°C).5-7 of compressed and liquefied oxygen is kept in tanks; it is then The cgs temperature system is based on Celsius (C) units. exposed to ambient temperatures and vaporized into its gaseous Similar to the Kelvin scale, the Celsius scale is a centigrade scale form in order to be made available for patient use (see Chapter (100° between the freezing and boiling points of water). However, 41). In one form of vaporization, called evaporation, heat is taken 0°C is not absolute zero but instead is the freezing point of water. from the air surrounding the liquid, cooling the air. In warm In Celsius units, kinetic molecular activity stops at approxi- weather or during strenuous exercise, the body takes advantage mately −273°C. Therefore 0 K equals −273°C, and 0°C equals of this principle of evaporative cooling by producing sweat. The 273 K. To convert degrees Celsius to degrees Kelvin, simply add liquid sweat evaporates and cools the skin. 273: Condensation is the opposite of evaporation. In condensa- K = °C + 273 tion, gases become liquids. Because vaporization takes heat from the air around a liquid (cooling), condensation must give heat For example: back to the surroundings (warming). A refrigerator (or air con- 25°C = 25 + 273 = 298 K ditioner) works on the principle of repeated vaporization cycles. The food cools as it passes energy through the walls of the refrig- Conversely, to convert degrees Kelvin to degrees Celsius, you erator into pipes containing condensed refrigerant. The refrigerant simply subtract 273. For example: warms, vaporizes, and expands. Then a compressor condenses 310 K = 310 − 273 = 37°C the refrigerant again, releasing heat that is carried away to the atmosphere by a radiator. The condensed refrigerant is then The Fahrenheit scale is the primary temperature scale in the passed by the food and the cycle repeats. The whole system is foot, pound, and second (fps) or British system of measurement. basically a heat pump transferring thermal energy from the food Absolute zero on the Fahrenheit scale equals −460°F. to the atmosphere. The next section expands on the concept of To convert degrees Fahrenheit to degrees Celsius, use the change of state and provides more detail on the processes of following formula: vaporization and condensation. °C = (°F − 32) 1.8 Temperature For example: Temperature and kinetic energy are closely related.2 Temperature °F = 98.6 is a measurement of heat. Heat is the result of molecules col- liding with one another. The temperature of a gas, with most °C = (98.6 − 32) 1.8 of its internal energy spent keeping molecules in motion, is °C = 37 directly proportional to its kinetic energy. In contrast, the tem- peratures of solids and liquids represent only part of their total To convert degrees Celsius to degrees Fahrenheit, simply reverse internal energy. this formula: Absolute Zero °F = (1.8 × °C) + 32 In concept, absolute zero is the lowest possible temperature that For example: can be achieved. That is the temperature at which there is no kinetic energy. Because there is no energy, the molecules cease °C = 100  CHAPTER 6 Physical Principles of Respiratory Care 91 Kinetic activity or pressure Celsius –273 –17.80 0 37 100 Kelvin 0 255.2 273 310 373 Fahrenheit –460 0 32 98.6 212 Fig. 6.2 Linear Relationship Between Gas Molecular Activity, or Pressure, and Temperature. The graph shows comparable readings on three scales for five temperature points. °F = (1.8 × 100) + 32 defined as the number of calories required to change 1 g of a solid into a liquid without changing its temperature. The latent °F = 212 heat of fusion of ice is 80 cal/g, whereas the latent heat of fusion Fig. 6.2 shows the relationship between the kinetic activity of oxygen is 3.3 cal/g. This change of state, compared with simply of matter and temperature on all three common temperature heating a solid, requires enormous energy. scales. For ease of reference, four key points are defined: (1) the zero point of each scale, (2) the freezing point of water (0°C), RULE OF THUMB The latent heat of fusion of ice is 80 cal/g, which is (3) body temperature (37°C), and (4) the boiling point of water about 24 times more than the latent heat of fusion of oxygen, which is why (100°C). oxygen is a gas at room temperature and ice becomes a liquid. CHANGE OF STATE Freezing All matter can change state. Because respiratory therapists work Freezing is the opposite of melting. Because melting requires extensively with both liquids and gases, they must have a good large amounts of externally applied energy, you would expect understanding of the key characteristics of these states and the freezing to return this energy to the surroundings, and this is basic processes underlying their phase changes. exactly what occurs. During freezing, heat energy is transferred from a liquid back to the environment, usually by exposure to Liquid-Solid Phase Changes (Melting and Freezing) cold. When a solid is heated, its molecular kinetic energy increases. As the kinetic energy of a substance decreases, its molecules This added internal energy increases molecular vibrations. If begin to regain the stable structure of a solid. According to the enough heat is applied, these vibrations eventually weaken the first law of thermodynamics,4 the energy required to freeze a intermolecular attractive forces. At some point molecules break substance must equal that needed to melt it. The freezing and free of their rigid structure and the solid changes into a liquid. melting points of a substance are the same. Sublimation is the term used for the phase transition from Melting a solid to a vapor without becoming a liquid as an intermediary The changeover from the solid to the liquid state is called melting. form. An example of sublimation is dry ice (frozen carbon The temperature at which this changeover occurs is the melting dioxide). Dry ice sublimates from its solid form into gaseous point.2 The range of melting points is considerable. For example, CO2 without first melting and becoming liquid CO2. This sub- water (ice) has a melting point of 0°C, carbon has a melting limation occurs because the vapor pressure is low enough for point of greater than 3500°C, and helium has a melting point the intermediate liquid not to appear. of less than −272°C. Fig. 6.3 depicts the phase change caused by heating water. At RULE OF THUMB The term vapor pressure refers to the tendency of a the left origin of −50°C, water is solid ice. As the ice is heated, its liquid to change to a gaseous state. In a closed system, the amount of liquid temperature increases. At its melting point of 0°C, ice begins to changing into vapor equals the amount of vapor condensing back into a liquid. change into liquid water. However, the full change to liquid water requires additional heat. This additional heat energy changes the state of water but does not immediately change its temperature. Properties of Liquids The extra heat needed to change a solid to a liquid is the Liquids exhibit flow and assume the shape of their container. latent heat of fusion. In cgs units, the latent heat of fusion is Liquids also exert pressure, which varies with depth and density. 92 SECTION I Foundations of Respiratory Care 100 Water to steam transition Temperature (°C) 50 0 Ice to water –50 0 100 200 300 400 500 600 700 800 Time in seconds (or calories added) Fig. 6.3 Temperature as a function of time for 1 g of water heated at the rate of 1 cal/s. (Modified from Nave CR, Nave BC: Physics for the health sciences, ed 3, Philadelphia, 1985, WB Saunders.) Variations in liquid pressure within a container produce an In this case, the total pressure is 2068 g/cm2, equal to 29.4 lb/ upward supporting force, called buoyancy. in2, or 2 atm. Although melting weakens intermolecular bonding forces, As shown in Fig. 6.4, the pressure of a given liquid is the same liquid molecules still attract one another. The persistence of at any specific depth (h), regardless of the container’s shape. these cohesive forces among liquid molecules helps explain the This is because the pressure of a liquid acts equally in all direc- physical properties of viscosity, capillary action, and surface tions. This concept is called the Pascal’s principle. tension. Buoyancy (Archimedes Principle) Thousands of years ago, Archimedes showed that an object sub- RULE OF THUMB Surface tension always forces a liquid have the small- est possible surface area. That is why aerosol droplets are round. A sphere merged in water appeared to weigh less than it did in air. This has the smallest surface area. effect, called buoyancy, explains why certain objects float in water. Liquids exert buoyant force because the pressure below a sub- merged object always exceeds the pressure above it. This differ- Pressure in Liquids ence in liquid pressure creates an upward or supporting force. Liquids exert pressure, which has the dimensions of force per According to the Archimedes principle, this buoyant force must unit area. The pressure exerted by a liquid depends on both its equal the weight of the fluid displaced by the object. The buoyant height (depth) and weight density (weight per unit volume), which force (B) may be calculated as follows: is shown in equation form as follows: B = dw × V PL = h × dw where dw is weight density (weight/unit volume) and V is volume where PL is the static pressure exerted by the liquid, h is the of displaced fluid. If the weight density of an object is less than height of the liquid column, and dw is the liquid’s weight density. that of water (1 g/cm3), it will displace a weight of water greater For example, to compute the pressure at the bottom of a than its own weight. In this case, the upward buoyant force will 33.9-feet (1034-cm)-high column of water (density = 1 g/cm3), overcome gravity and the object will float. Conversely, if an you would use this equation: object’s weight density exceeds the weight of water, the object will sink. PL = h × dw Clinically, this principle is used to measure the specific gravity = 1034 cm × (1 g cm3 ) of certain liquids. The term specific gravity refers to the ratio = 1034 g cm2 of the density of one fluid compared with the density of another reference substance, which is typically water. Fig. 6.5 shows the The answer (1034 g/cm2) also equals 1 atmosphere of pres- use of a hydrometer to measure the specific gravity of urine. sure (atm), or approximately 14.7 lb/in2. This figure does not The specific gravity of gases can also be measured. In this case, account for the additional atmospheric pressure (PB) acting on O2 or hydrogen is used as the standard instead of water. the top of the liquid. The total pressure at the bottom of the Gases also exert buoyant force, although much less than that column equals the sum of the atmospheric and liquid pressures. provided by liquids. Buoyancy helps keep solid particles suspended 94 SECTION I Foundations of Respiratory Care Gas Interface P Liquid molecules ∆v ∆v ∆v Fig. 6.6 Effects of shear stress or pressure (P) on shear rate (velocity gradient [v]) in a newtonian fluid. (Modified from Winters WL, Brest AN, editors: The microcirculation, Springfield, IL, 1969, Charles C Thomas.) Fig. 6.8 The Force of Surface Tension in a Drop of Liquid. Cohesive force (arrows) attracts molecules inside the drop to one another. Cohe- sion can pull the outermost molecules inward only, creating a centrally directed force that tends to contract the liquid into a sphere. TABLE 6.2 Examples of Surface Tension Temperature Surface Tension Substance (°C) (dynes/cm) Water 20 73 Water 37 70 Whole blood 37 58 Plasma 37 73 Ethyl alcohol 20 22 Mercury 17 547 A B Fig. 6.7 The Shape of the Meniscus Depends on the Relative Strengths of Adhesion and Cohesion. (A) Water: Adhesion stronger than cohe- Surface Tension sion. (B) Mercury: Cohesion stronger than adhesion. Surface tension is a force per unit length (equivalent to surface energy density) exerted by like molecules at the surface of a pumping water. The heart must perform even more work when liquid. A small drop of fluid provides a good illustration of this blood viscosity increases, as occurs in polycythemia (an increase force. As shown in Fig. 6.8, cohesive forces affect molecules inside in red blood cell concentration in the blood). the drop equally from all directions. However, only inward forces affect molecules on the surface. This imbalance in forces causes the surface film to contract into the smallest possible surface RULE OF THUMB Although an 80% helium/20% oxygen mixture (heliox) area, usually a sphere or curve (meniscus). This phenomenon is less dense than air, it actually has a slightly higher viscosity than air at explains why liquid droplets and bubbles retain a spherical shape. room temperature. This is because the molecular distance between helium and oxygen is less than that between nitrogen and oxygen. Surface tension is quantified by measurement of the force needed to produce a “tear” in a fluid surface layer. Table 6.2 lists the surface tensions of selected liquids in dynes per centimeter Cohesion and Adhesion (cgs). For a given liquid, surface tension varies inversely with The attractive force between like molecules is called cohesion. temperature: The higher the temperature, the lower is the surface The attractive force between unlike molecules is called adhesion. tension. Surface tension plays an important role in determining These forces can be observed at work by placing a liquid in a the relative sizes of connected alveoli (Fig. 6.9). To understand small-diameter tube. As shown in Fig. 6.7, the top of the liquid this, consider a spherical bubble of air in a liquid (analogous to forms a curved surface, or meniscus. When the liquid is water, an alveolus). According to the Laplace’s law, the pressure inside the meniscus is concave because the water molecules at the surface the bubble varies directly with the surface tension of the liquid adhere to the glass more strongly than they cohere to each other and inversely with its radius. Internal surface tension (T) will (see Fig. 6.7A). In contrast, a mercury meniscus is convex (see attempt to contract the bubble but is opposed by the resulting Fig. 6.7B). In this case, the cohesive forces pulling the mercury pressure inside the bubble (P). The law of Laplace defines the atoms together exceed the adhesive forces trying to attract the relationship between surface tension and the radius of a sphere mercury to the glass. (the “radius of curvature”):