Conduction

Heat transfer in solids occurs mainly via conduction. Conduction is the transfer of heat by direct contact between hot and cold molecules. How well heat transfers by conduction depends on both the number and the force of molecular collisions between adjoining objects.

Heat transfer between objects is quantified by using a measure called thermal conductivity. Table 6-1 lists the thermal conductivities of selected substances in cgs (centimeter-gram-second) system units. As is evident, solids, in particular, metals, tend to have high thermal conductivity. This is why metals feel cold to the touch even when at room temperature. In this case, the high thermal conductivity of metal quickly draws heat away from the skin, creating a feeling of “cold.” In contrast, with fewer molecular collisions than in solids and liquids, gases exhibit low thermal conductivity.

Convection

Heat transfer in both liquids and gases occurs mainly by convection. Convection involves the mixing of fluid molecules at different temperatures. Although air is a poor heat conductor (see Table 6-1), it can efficiently transfer heat by convection. To do so, the air is first warmed in one location and then circulated to carry the heat elsewhere; this is the principle behind forced-air heating in houses and convection heating in infant incubators. Fluid movements carrying heat energy are called convection currents.

Radiation

Radiation is another mechanism for heat transfer. Conduction and convection require direct contact between two substances, whereas radiant heat transfer occurs without direct physical contact. Heat transfer by radiation occurs even in a vacuum, such as when the sun warms the earth.

The concept of radiant energy is similar to that of light. Radiant energy given off by objects at room temperature is mainly in the infrared range, which is invisible to the human eye. Objects such as an electrical stove burner or a kerosene heater radiate some of their energy as visible light. In the clinical setting, radiant heat energy is commonly used to keep newborn infants warm.

The following formula defines the rate at which an object gains or loses heat by radiation:

Et=ekA (T2−T1)

In this formula, E/t is the heat loss or gain per unit time. The symbol e is the emissivity of the object, or its relative effectiveness in radiating heat. The constant k is the Stefan-Boltzmann constant (based on mass and surface area). A is the area of the radiating object, and T₁ and T₂ are the temperatures of the environment and the object. In simple terms, for an object with a given emissivity, the larger the surface area (relative to mass) and the lower the surrounding temperature, the greater is the radiant heat loss per unit time.

Evaporation and Condensation

Vaporization is the change of state from liquid to gas. Vaporization requires heat energy. According to the first law of thermodynamics, this heat energy must come from the surroundings. In one form of vaporization, called evaporation, heat is taken from the air surrounding the liquid, cooling the air. In warm weather or during strenuous exercise, the body takes advantage of this principle of evaporation cooling by producing sweat. The liquid sweat evaporates and cools the skin.

Condensation is the opposite of evaporation. During condensation, a gas turns back into a liquid. Because vaporization takes heat from the air around a liquid (cooling), condensation must give heat back to the surroundings (warming). A refrigerator works on the principle of repeated vaporization cycles. As the food in the cooler passes its warmth to the cooler condensed refrigerant, it provides enough heat to cause it to vaporize. Sufficient energy is provided for the material to vaporize and expand, which cools the system, and the cycle repeats. The next section expands on the concept of change of state and provides more detail on the processes of vaporization and condensation.

Internal Energy and Temperature

Two interrelated terms are significant when discussing thermodynamics: entropy and enthalpy. Entropy is the amount of energy in a system that is unavailable for work. Entropy is the lowest amount of organization that a system can achieve (chaos). Enthalpy is the total measure of energy in the system. Enthalpy can be considered to be the order of a system. Temperature and kinetic energy are closely related.² Temperature is a measurement of heat. Heat is the result of molecules colliding with one another. The temperature of a gas, with most of its internal energy spent keeping molecules in motion, is directly proportional to its kinetic energy. In contrast, the temperatures of solids and liquids represent only part of their total internal energy.

Absolute Zero

In concept, absolute zero is the lowest possible temperature that can be achieved. That is the temperature at which there is no kinetic energy. Because there is no energy, the molecules cease to vibrate, and the object has no heat that can be measured. This temperature is defined to be absolute zero. Although researchers have come close to attaining absolute zero, no one has actually achieved it; this is due to the third law of thermodynamics, which states absolute zero is impossible to achieve.

Temperature Scales

Multiple scales can be used to measure temperature. The Fahrenheit and Celsius scales are based on a property of water. A third scale, the Kelvin scale, is based on molecular motion. Absolute zero provides a logical zero point on which to build a temperature scale. The SI (International System of Units) units for temperature are measured in kelvin (K) with a lower case “k,” with a zero point equal to absolute zero (0° K).5–7 Because the Kelvin scale has 100 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 definition for water (the temperature where all three phases of water exist). This temperature happens to be approximately 273° K (0.0° C).^5–7

The cgs temperature system is based on Celsius (C) units. Similar to the Kelvin scale, the Celsius scale is a centigrade scale (100 degrees between the freezing and boiling points of water). However, 0° C is not absolute zero but instead is the freezing point of water.

In Celsius units, kinetic molecular activity stops at approximately −273° C. Therefore 0° K equals −273° C, and 0° C equals 273° K. To convert degrees Celsius to degrees Kelvin, simply add 273:

°K=°C+273

For example:

25°C=25+273=298°K

Conversely, to convert degrees Kelvin to Celsius, you simply subtract 273. For example:

310°K=310−273=37°C

The Fahrenheit scale is the primary temperature scale in the fps (foot, pound, and second) or British system of measurement. Absolute zero on the Fahrenheit scale equals −460° F.

To convert degrees Fahrenheit to degrees Celsius, use the following formula:

°C=59(°F−32)

For example:

°F=98.6

°C=59×(98.6−32)

°C=37

To convert degrees Celsius to degrees Fahrenheit, simply reverse this formula:

°F=(95×°C)+32

For example:

°C=100

°F=(95×100)+32

°F=212

Figure 6-2 shows the relationship between the kinetic activity of matter and temperature on all three common temperature scales. For ease of reference, five key points are defined: the zero point of each scale, the freezing point of water (0° C), body temperature (37° C), and the boiling point of water (100° C).

Melting

The changeover from the solid to liquid state is called melting. The temperature at which this changeover occurs is the melting point.² The range of melting points is considerable. For example, water (ice) has a melting point of 0° C, carbon has a melting point of greater than 3500° C, and helium has a melting point of less than −272° C.

Figure 6-3 depicts the phase change caused by heating water. At the left origin of −50° C, water is solid ice. As the ice is heated, its temperature increases. At its melting point of 0° C, ice begins to 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.

The extra heat needed to change a solid to a liquid is the latent heat of fusion. In cgs units, the latent heat of fusion is defined as the number of calories required to change 1 g of a solid into a liquid without changing its temperature. The latent heat of fusion of ice is 80 cal/g, whereas the latent heat of fusion of oxygen is 3.3 cal/g. This change of state, compared with simply heating a solid, requires enormous energy.

Freezing

Freezing is the opposite of melting. Because melting requires large amounts of externally applied energy, you would expect freezing to return this energy to the surroundings, and this is exactly what occurs. During freezing, heat energy is transferred from a liquid back to the environment, usually by exposure to cold.

As the kinetic energy of a substance decreases, its molecules begin to regain the stable structure of a solid. According to the first law of thermodynamics, the energy required to freeze a substance must equal that needed to melt it. The freezing and melting points of a substance are the same.

Sublimation is the term used for the phase transition from a solid to a vapor without becoming a liquid as an intermediary form. An example of sublimation is dry ice (frozen carbon dioxide [CO₂]). Dry ice sublimates from its solid form into gaseous CO₂ without first melting and becoming liquid CO₂. This sublimation occurs because the vapor pressure is low enough for the intermediate liquid not to appear.

Pressure in Liquids

Liquids exert pressure. The pressure exerted by a liquid depends on both its height (depth) and weight density (weight per unit volume), which is shown in equation form:

PL=h×dw

P_L is the static pressure exerted by the liquid, h is the height of the liquid column, and d_w is the liquid’s weight density.

For example, to compute the pressure at the bottom of a 33.9-ft (1034-cm)-high column of water (density = 1 g/cm³), you would use this equation:

PL=h×dw

=1034 cm×(1g/cm3)

=1034g/cm2

The answer (1034 g/cm²) also equals 1 atmosphere of pressure (atm), or approximately 14.7 lb/in². This figure does not account for the additional atmospheric pressure (P_B) acting on the top of the liquid. The total pressure at the bottom of the column equals the sum of the atmospheric and liquid pressures. In this case, the total pressure is 2068 g/cm², equal to 29.4 lb/in², or 2 atm.

As shown in Figure 6-4, the pressure of a given liquid is the same at any specific depth (h), regardless of the container’s shape. This is because the pressure of a liquid acts equally in all directions. This concept is called Pascal’s principle.

Buoyancy (Archimedes’ Principle)

Thousands of years ago, Archimedes showed that an object submersed in water appeared to weigh less than in air. This effect, called buoyancy, explains why certain objects float in water. Liquids exert buoyant force because the pressure below a submerged object always exceeds the pressure above it. This difference in liquid pressure creates an upward or supporting force. According to Archimedes’ principle, this buoyant force must equal the weight of the fluid displaced by the object. Because the weight of fluid displaced by an object equals its weight density times its volume (d_w = V), the buoyant force (B) may be calculated as follows:

B=dw×V

If the weight density of an object is less than that of water (1 g/cm³), it will displace a weight of water greater than its own weight. In this case, the upward buoyant force will overcome gravity, and the object will float. Conversely, if an object’s weight density exceeds the weight of water, the object will sink.

Clinically, Archimedes’ principle is used to measure the specific gravity of certain liquids. The term specific gravity refers to the ratio of the density of one fluid compared with the density of another reference substance, which is typically water. Figure 6-5 shows the use of a hydrometer to measure the specific gravity of urine. The specific gravity of gases also can be measured. In this case, oxygen or hydrogen is used as the standard instead of water.

Gases also exert buoyant force, although much less than that provided by liquids. Buoyancy helps keep solid particles suspended in gases. These suspensions, called aerosols, play an important role in respiratory care. More detail on the characteristics and use of aerosols is provided in Chapter 35.

Viscosity

Viscosity is the force opposing a fluid’s flow. Viscosity in fluids is similar to friction in solids. The viscosity of a fluid is directly proportional to the cohesive forces between its molecules. The stronger these cohesive forces are, the greater the fluid’s viscosity. The greater a fluid’s viscosity, the greater its resistance to deformation, and the greater its opposition to flow.

Viscosity is most important when fluids move in discrete cylindrical layers, called streamlines. This pattern of motion is called laminar flow. As shown in Figure 6-6, frictional forces between the streamlines and the tube wall impede movement of the outer layers of a fluid. Each layer, moving toward the center of the tube, hinders the motion of the next inner layer less and less. Laminar flow consists of concentric layers of fluid flowing parallel to the tube wall at velocities that increase toward the center.

The difference in the velocity among these concentric layers is called the shear rate. The shear rate is simply a measure of how easily the layers separate. How easily the layers separate depends on two factors: (1) the pressure pushing or driving the fluid, called the shear stress; and (2) the viscosity of the fluid. Shear rate is directly proportional to shear stress and inversely proportional to viscosity.

In uniform fluids such as water or oil, viscosity varies with temperature. Because higher temperatures weaken the cohesive forces between molecules, heating a uniform fluid reduces its viscosity. Conversely, cooling a fluid increases its viscosity. This is why a car’s engine is so hard to start on a cold winter morning. The oil becomes so viscous that it impedes movement of the engine’s parts.

Blood, in contrast to water or oil, is a complex fluid that contains not only liquid (plasma, which is 90% water) but also cells in suspension. For this reason, blood has a viscosity approximately five times greater than the viscosity of water. The greater the viscosity of a fluid, the more energy is needed to make it flow. The heart works harder to pump blood than it would if it were pumping water. The heart must perform even more work when blood viscosity increases, as occurs in polycythemia (an increase in red blood cell concentration in the blood).

Cohesion and Adhesion

The attractive force between like molecules is called cohesion. The attractive force between unlike molecules is called adhesion. These forces can be observed at work by placing a liquid in a small-diameter tube. As shown in Figure 6-7, the top of the liquid forms a curved surface, or meniscus. When the liquid is water, the meniscus is concave because the water molecules at the surface adhere to the glass more strongly than they cohere to each other (see Figure 6-7A). In contrast, a mercury meniscus is convex (see Figure 6-7B). In this case, the cohesive forces pulling the mercury atoms together exceed the adhesive forces trying to attract the mercury to the glass.

Surface Tension

Surface tension is a force exerted by like molecules at the surface of a liquid. A small drop of fluid provides a good illustration of this force. As shown in Figure 6-8, cohesive forces affect molecules inside 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 area, usually a sphere or curve (meniscus). This phenomenon explains why liquid droplets and bubbles retain a spherical shape.

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/cm (cgs). For a given liquid, surface tension varies inversely with temperature: The higher the temperature, the lower is the surface tension.

Surface tension, similar to a fist compressing a ball, increases the pressure inside a liquid drop or bubble. According to Laplace’s law, this pressure varies directly with the surface tension of the liquid and inversely with its radius. The equation for a liquid bubble follows:

P=2STr

P is the pressure in the bubble, ST is the surface tension, and r is the bubble radius. Figure 6-9 shows this relationship for two bubbles of different sizes, each with the same surface tension.

Because the alveoli of the lungs resemble clumps of bubbles, it follows that surface tension plays a key role in the mechanics of ventilation (see Chapter 10). Abnormalities in alveolar surface tension occur in certain clinical conditions, such as acute respiratory distress syndrome. These abnormalities may result in collapse of alveoli secondary to high surface tension.

Capillary Action

Capillary action is a phenomenon in which a liquid in a small tube moves upward, against gravity. Capillary action involves both adhesive and surface tension forces. As shown in Figure 6-10, A, the adhesion of water molecules to the walls of a thin tube causes an upward force on the edges of the liquid and produces a concave meniscus.

Because surface tension acts to maintain the smallest possible liquid-gas interface, instead of just the edges of the liquid moving up, the whole surface is pulled upward. How strong this force is depends on the amount of liquid that contacts the tube’s surface. Because a small capillary tube creates a more concave meniscus and a greater area of contact, liquid rises higher in tubes with smaller cross-sectional areas (see Figure 6-10, B).

Capillary action is the basis for blood samples obtained by use of a capillary tube. The absorbent wicks used in some gas humidifiers are also an application of this principle, as are certain types of surgical dressings.

Boiling

Boiling occurs at the boiling point. The boiling point of a liquid is the temperature at which its vapor pressure exceeds atmospheric pressure. When a liquid boils, its molecules must have enough kinetic energy to force themselves into the atmosphere against the opposing pressure. Because the weight of the atmosphere retards the escape of vapor molecules, the greater the ambient pressure, the greater is the boiling point. Conversely, when atmospheric pressure is low, liquid molecules escape more easily, and boiling occurs at lower temperatures. This is why cooking times must be increased at higher altitudes.

Although boiling is associated with high temperatures, the boiling points of most liquefied gases are very low. At 1 atm, oxygen boils at −183° C.

Energy is also needed to vaporize liquids, as with other phase changes. The energy required to vaporize a liquid is the latent heat of vaporization. In cgs units, the latent heat of vaporization is the number of calories required to vaporize 1 g of a liquid at its normal boiling point.

Melting weakens attractive forces between molecules, whereas vaporization eliminates them. Elimination of these forces converts essentially all of the internal energy of a substance into kinetic energy. For this reason, vaporization requires substantially more energy than melting. As shown in Figure 6-3, almost seven times more energy is needed to convert water to steam (540 cal/g) than is needed to melt ice.

Evaporation, Vapor Pressure, and Humidity

Boiling is only one type of vaporization. A liquid also can change into a gas at temperatures lower than its boiling point through a process called evaporation. Water is a good example (Figure 6-11). When at a temperature lower than its boiling point, water enters the atmosphere via evaporation. The liquid molecules are in constant motion, as in the gas phase. Although this kinetic energy is less intense than in the gaseous state, it allows some molecules near the surface to escape into the surrounding air as water vapor (see Figure 6-11, A).

After water is converted to a vapor, it acts like any gas. To be distinguished from visible particulate water, such as mist or fog, this invisible gaseous form of water is called molecular water. Molecular water obeys the same physical principles as other gases and exerts a pressure called water vapor pressure.

Evaporation requires heat. The heat energy required for evaporation comes from the air next to the water surface. As the surrounding air loses heat energy, it cools. This is the principle of evaporative cooling, which was previously described.

If the container is covered, water vapor molecules continue to enter the air until it can hold no more water (see Figure 6-11, B). At this point, the air over the water is saturated with water vapor. However, vaporization does not stop when saturation occurs. Instead, for every molecule escaping into the air, another returns to the water reservoir. These conditions are referred to as a state of equilibrium.

Influence of Temperature

No other factor influences evaporation more than temperature. Temperature affects evaporation in two ways. First, the warmer the air, the more vapor it can hold. Specifically, the capacity of air to hold water vapor increases with temperature. The warmer the air contacting a water surface, the faster is the rate of evaporation.

Second, if water is heated, its kinetic energy is increased, and more molecules are helped to escape from its surface (see Figure 6-11, C). Last, if the container of heated water is covered, the air again becomes saturated (see Figure 6-11, D). However, the heated saturated air, compared with the unheated air (see Figure 6-11, B), now contains more vapor molecules and exerts a higher vapor pressure (as shown by the manometer in Figure 6-11, D). The temperature of a gas affects both its capacity to hold molecular water and the water vapor pressure.

The relationship between water vapor pressure and temperature is shown graphically in Figure 6-12. The left vertical axis plots water vapor pressure in both mm Hg and kPa (kilopascal). The horizontal axis plots temperatures between 0° C and 70° C. This graph shows that the greater the temperature, the greater the saturated water vapor pressure (bold red dots). Table 6-3 lists actual water vapor pressures in saturated air in the clinical range of temperatures (20° C to 37° C).

TABLE 6-3

Water Vapor Pressures and Contents at Selected Temperatures

Temperature (° C)	Vapor Pressure (mm Hg)	Water Vapor Content (mg/L)	ATPS to BTPS Correction Factor*
20	17.50	17.30	1.102
21	18.62	18.35	1.096
22	19.80	19.42	1.091
23	21.10	20.58	1.085
24	22.40	21.78	1.080
25	23.80	23.04	1.075
26	25.20	24.36	1.068
27	26.70	25.75	1.063
28	28.30	27.22	1.057
29	30.00	28.75	1.051
30	31.80	30.35	1.045
31	33.70	32.01	1.039
32	35.70	33.76	1.032
33	37.70	35.61	1.026
34	39.90	37.57	1.020
35	42.20	39.60	1.014
36	44.60	41.70	1.007
37	47.00	43.80	1.000

^*Correction factors are based on 760 mm Hg pressure.

Humidity

Water vapor pressure represents the kinetic activity of water molecules in air. For the actual amount or weight of water vapor in a gas to be found, the water vapor content or absolute humidity must be measured.

Absolute humidity (AH) can be measured by weighing the water vapor extracted from air using a drying agent. Alternatively, absolute humidity can be computed with meteorologic data according to the techniques of the U.S. Weather Bureau. The common unit of measure for absolute humidity is milligrams of water vapor per liter of gas (mg/L). Absolute humidity values for saturated air at various temperatures are plotted against the right vertical axis of Figure 6-12, using hash marks. The middle column of Table 6-3 lists these absolute humidity values for saturated air between 20° C and 37° C.

A gas does not need to be fully saturated with water vapor. If a gas is only half saturated with water vapor, its water vapor pressure and absolute humidity are only half that in the fully saturated state. Air that is fully saturated with water vapor at 37° C and 760 mm Hg has a water vapor pressure of 47 mm Hg and an absolute humidity of 43.8 mg/L (see Table 6-3). However, if the same volume of air were only 50% saturated with water vapor, its water vapor pressure would be 0.50 × 47 mm Hg, or 23.5 mm Hg, and its absolute humidity would be 0.50 × 43.8 mg/L, or 21.9 mg/L.

When a gas is not fully saturated, its water vapor content can be expressed in relative terms using a measure called relative humidity (RH). The RH of a gas is the ratio of its actual water vapor content to its saturated capacity at a given temperature. RH is expressed as a percentage and is derived with the following simple formula:

%RH=Content(absolute humidity)Saturated capacity×100

For example, saturated air at a room temperature of 20° C has the capacity to hold 17.3 mg/L of water vapor (see Table 6-3). If the absolute humidity is 12 mg/L, the RH is calculated as follows:

% RH=12mg/L17.3mg/L×100

%RH=0.69×100

%RH=69%

Actual water vapor content does not have to be measured for RH to be computed. Simple instruments called hygrometers allow direct measurement of RH without extracting and weighing the water in air.

When the water vapor content of a volume of gas equals its capacity, the RH is 100%. When the RH is 100%, a gas is fully saturated with water vapor. Under these conditions, even slight cooling of the gas causes its water vapor to turn back into the liquid state, a process called condensation.

Condensed moisture deposits on any available surface, such as on the walls of a container or delivery tubing or on particles suspended in the gas. Condensation returns heat to and warms the surrounding environment, whereas vaporization of water cools the adjacent air.

If air that is at an RH of 90% is cooled, its capacity to hold water vapor decreases. Although the water vapor capacity of the air decreases, its content remains constant. With a lower capacity but the same content, the RH of the air must increase. Continued cooling decreases the air’s water vapor capacity until it eventually equals the water vapor content (RH = 100%). When content equals capacity, the air is fully saturated and can hold no more water vapor.

Because RH never exceeds 100%, any further decrease in temperature causes condensation. The temperature at which condensation begins is called the dew point. Cooling a saturated gas below its dew point causes increasingly more water vapor to condense into liquid water droplets.

Figure 6-13 provides a useful analogy of the relationship between water vapor content, capacity, and RH. The various-sized glasses represent the capacity of a gas to hold water vapor. The larger the glass, the greater is its capacity. The water in the glasses represents the actual water vapor content. A glass that is half full is at 50% capacity, or 50% RH. A full glass represents the saturated state, which is equivalent to 100% RH.

Figure 6-13, A shows what happens when a saturated gas is heated. Warming a gas increases its capacity to hold water vapor but does not change its content. This is equivalent to pouring the contents of the full glass on the left in Figure 6-13, A into progressively larger glasses. The amount of water does not change, but as the glasses get larger, they become less full. We started with a full glass (100% RH) but end up with one that is only one-third full (33% RH).

A decrease in capacity would have the opposite effect. In Figure 6-13, B, we start with a large glass, which is half full (50% RH). The capacity of the glass is decreased by pouring the water into progressively smaller glasses (equivalent to decreasing the gas temperature). Eventually, the water volume is enough to fill a smaller glass (100% RH). What happens if we try to empty this full glass into an even smaller one? Because the smaller glass has less capacity, the excess content must spill over. This spillover is analogous to the condensation occurring when a saturated gas cools below its dew point. However, although condensation has removed the excess moisture from the air, the smaller glass is still full (100% RH).

Mini Clini

Condensation and Evaporation

A good clinical example of condensation and evaporation is the hygroscopic condenser humidifier, a form of artificial nose (Figure 6-14). These devices consist of layers of water-absorbent material encased in plastic. When a patient exhales into an artificial nose, the warm, saturated expired gas cools, causing condensation on the absorbent surfaces. As condensation occurs, heat is generated in the device. When the patient inhales through the device, the inspired gases are warmed, and the previously condensed water now evaporates, aiding in airway humidification. Chapter 35 provides more detail on humidification devices, including the artificial nose.

In clinical practice, two additional measures of humidity are used: percent body humidity (%BH) and humidity deficit. The %BH of a gas is the ratio of its actual water vapor content to the water vapor capacity in saturated gas at body temperature (37° C). The %BH is the same as RH except that the capacity (or denominator) is fixed at 43.8 mg/L:

%BH=AH43.8×100

The humidity deficit associated with a %BH less than 100% represents the amount of water vapor the body must add to the inspired gas to achieve saturation at body temperature (37° C). To compute the humidity deficit, simply subtract the actual water vapor content from its capacity at 37° C (43.8 mg/L).

Kinetic Activity of Gases

Because the intermolecular forces of attraction of a gas are so weak, most of the internal energy of a gas is kinetic energy. Kinetic theory says that gas molecules travel about randomly at very high speeds and with frequent collisions.

The velocity of gas molecules is directly proportional to temperature. As a gas is warmed, its kinetic activity increases, its molecular collisions increase, and its pressure increases. Conversely, when a gas is cooled, molecular activity decreases, particle velocity and collision frequency decrease, and the pressure decreases.

Molar Volume and Gas Density

A major principle governing chemistry is Avogadro’s law. This law states that the 1-g atomic weight of any substance contains exactly the same number of atoms, molecules, or ions. This number, 6.023 × 10²³, is Avogadro’s constant. In SI units, this quantity of matter equals 1 mole.

Density

Density is the ratio of the mass of a substance to its volume. A dense substance has heavy (high atomic weight) particles packed closely together. Uranium is a good example of a dense substance. Conversely, a low-density substance has a low concentration of light atomic particles per unit volume. Hydrogen gas is a good example of a low-density substance.

In clinical practice, weight is often substituted for mass, and weight density (weight per unit volume, or d_w) is actually measured. Solid or liquid weight density is commonly measured in grams per cubic centimeter (cgs). For gases, the most common unit is grams per liter. Because weight density equals weight divided by volume, the density of any gas at STPD can be computed easily by dividing its molecular weight (gmw) by the universal molar volume of 22.4 L (22.3 for CO₂). Box 6-1 provides examples of gas density calculations.

Box 6-1   Examples of Gas Densities d_w at STPD

dwO2=gmw22.4=3222.4=1.43g/L

dwN2=gmw22.4=2822.4=1.25g/L

dwHe=gmw22.4=422.4=0.179g/L

dwCO2=gmw22.4=4422.4=1.97g/L

For the density of a gas mixture to be calculated, the percentage or fraction of each gas in the mixture must be known. To calculate the density of air at STPD, the following equation is used:

dwair=(FN2×gmw N2)+(FO2×gmw O2)22.4L

dwair=(0.79×28)+(0.21×32)22.4

dwair=1.29g/L

FN₂ and FO₂ equal the fractional concentrations of nitrogen and oxygen in air.

Gaseous Diffusion

Diffusion is the process whereby molecules move from areas of high concentration to areas of lower concentration. Kinetic energy is the driving force behind diffusion. Because gases have high kinetic energy, they diffuse most rapidly. However, diffusion also occurs in liquids and can occur in solids. Gas diffusion rates are quantified using Graham’s law. Mathematically, the rate of diffusion of a gas (D) is inversely proportional to the square root of its gram molecular weight:

Dgas∝1gmw

According to this principle, light gases diffuse rapidly, whereas heavy gases diffuse more slowly. Because diffusion is based on kinetic activity, anything that increases molecular activity quickens diffusion. Heating and mechanical agitation speed diffusion.

Gas Pressure

Whether free in the atmosphere, enclosed in a container, or dissolved in a liquid such as blood, all gases exert pressure. In physiology, the term tension is often used to refer to the pressure exerted by gases when dissolved in liquids. The pressure or tension of a gas depends mainly on its kinetic activity. In addition, gravity affects gas pressure. Gravity increases gas density, increasing the rate of molecular collisions and gas tension; this explains why atmospheric pressure decreases with altitude.

Pressure is a measure of force per unit area. The SI unit of pressure is the N/m², or pascal (Pa). Pressure in the cgs system is measured in dynes/cm², whereas pounds per square inch (lb/in² or psi) is the British fps pressure unit. Pressure can also be measured indirectly as the height of a column of liquid, as is commonly done to determine atmospheric pressure.

Measuring Atmospheric Pressure

Atmospheric pressure is measured with a barometer. A barometer consists of an evacuated glass tube approximately 1 m long. This tube is closed at the top end, with its lower, open end immersed in a mercury reservoir (Figure 6-15). The pressure of the atmosphere on the mercury reservoir forces the mercury up the vacuum tube a distance equivalent to the force exerted. In this manner, the height of the mercury column (measured in either inches [British] or millimeters [cgs]) represents the downward force of atmospheric pressure. Barometer pressure is reported with readings such as 30.4 inches of mercury (Hg) or 772 mm Hg; this means that the atmospheric pressure is great enough to support a column of mercury 30.4 inches or 772 mm in height.

Alternatively, the term torr may be used in pressure readings. Torr is short for Torricelli, the seventeenth-century inventor of the mercury barometer. At sea level, 1 torr equals 1 mm Hg. A pressure reading of 772 torr is the same as 772 mm Hg.

The height of a column of mercury is not a true measure of pressure. Height is a linear measure, whereas pressure represents force per unit area. The pressure exerted by a liquid is directly proportional to its depth (or height) times its density:

Pressure=Height×density

At sea level, the average atmospheric pressure supports a column of mercury 76 cm (760 mm) or 29.9 inches in height. If we also know that mercury has a density of 13.6 g/cm³ (0.491 lb/in³), the average atmospheric pressure (P_B) is calculated as follows:

cgs units :PB=76 cm×13.6 g/cm3=1034 g/cm2

fps units :PB=29.9in×0.491lb/in3=14.7lb/in2

These two measures, 1034 g/cm² and 14.7 lb/in², are considered standards in the cgs and British fps systems, each being equivalent to 1 atm.

Similar to any solid material, a barometer’s housing reacts to temperature changes by expanding and contracting. In addition, the mercury column acts like a large thermometer. Both pressure and temperature affect the mercury level of a barometer. For accuracy, the reading must be corrected for temperature changes. The U.S. Weather Bureau provides temperature correction factors for barometric readings. To correct the reading, subtract the applicable table value from the observed reading. For pressures between those listed in the table, use simple linear interpolation.

Clinical Pressure Measurements

Mercury is the most common fluid used in pressure measurements both in barometers and at the bedside. Because of the high density (13.6 g/cm³) of mercury, it assumes a height that is easy to read for most pressures in the clinical range. Water columns can also be used to measure pressure (in cm H₂O) but only low pressures. Because water is 13.6 times less dense than mercury, 1 atm would support a water column 33.9 feet high, or about as tall as a two-story building.

Both mercury and water columns are still used in clinical practice, especially when vascular pressures are being measured. However, these traditional tools are rapidly being replaced by mechanical or electronic pressure-measuring devices. Even so, these new instruments must be calibrated against a mercury or water column before making measurements.

The simplest mechanical pressure gauge is the aneroid barometer, which is common in homes. An aneroid barometer consists of a sealed evacuated metal box with a flexible, spring-supported top that responds to external pressure changes (Figure 6-16). This motion activates a geared pointer, which provides a scale reading analogous to pressure.

This same concept underlies the simple mechanical manometers used to measure blood or airway pressure at the bedside (Figure 6-17). However, rather than the pressure acting externally on the sealed chamber, the inside is connected to the pressure source. In this manner, the flexible chamber wall expands and contracts as pressure increases or decreases.

A flexible chamber can also be used to measure pressure electronically. These devices are called strain-gauge pressure transducers. In these devices, pressure changes expand and contract a flexible metal diaphragm connected to electrical wires (Figure 6-18). The physical strain on the diaphragm changes the amount of electricity flowing through the wires. By measuring this change in electrical flow, we are indirectly measuring changes in pressure.

Although mm Hg and cm H₂O are still the most common pressure units used at the bedside, they do not represent the SI standard. The SI unit of pressure is the kPa; 1 kPa equals approximately 10.2 cm H₂O or 7.5 torr. To convert between these pressure units accurately, use the factors provided in the rear inside cover of this book.

 Rule of Thumb

One kilopascal equals approximately 10.2 cm H₂O. A pressure of 10 kPa equals approximately 100 cm H₂O. Conversely, a pressure of 60 cm H₂O equals approximately 6 kPa.

Partial Pressures (Dalton’s Law)

Many gases exist together as mixtures. Air is a good example of a gas mixture, consisting mainly of oxygen and nitrogen. A gas mixture, similar to a solitary gas, exerts pressure. The pressure exerted by a gas mixture must equal the sum of the kinetic activity of all its component gases. The pressure exerted by a single gas in a mixture is called its partial pressure.

Dalton’s law describes the relationship between the partial pressure and the total pressure in a gas mixture. According to this law, the total pressure of a mixture of gases must equal the sum of the partial pressures of all component gases. The principle states that the partial pressure of a component gas must be proportional to its percentage in the mixture.⁸

A gas making up 25% of a mixture would exert 25% of the total pressure. For consistency, the percentage of a gas in a mixture is usually expressed in decimal form, using the term fractional concentration. A gas that is 25% of a mixture has a fractional concentration of 0.25. For example, air consists of approximately 21% O₂ and 79% N₂. To compute the partial pressure of each component, simply multiply the fractional concentration of each component by the total pressure. Assuming a normal atmospheric pressure of 760 torr, the individual partial pressure is computed as follows:

Partial pressure=Fractional concentration×total pressure

PO2=0.21×760torr=160torr

PN2=0.79×760torr=600torr

As predicted by Dalton’s law, the sum of these partial pressures equals the total pressure of the gas mixture.

What if the total pressure changed? Barometric pressure changes, in addition to minor fluctuations caused by weather, are mainly a function of altitude. Considering only oxygen, we know that its fractional concentration, or fractional inspired oxygen (FiO₂), remains constant at approximately 0.21. At a P_B of 760 torr, the PO₂ is equal to 0.21 × 760, or 160 torr. At 25,000 feet, the FiO₂ of air is still 0.21. However, the P_B is only 282 torr, and the resulting PO₂ is 0.21 × 282, or 59 torr, just more than one-third of that available at sea level. Because the PO₂ (not its percentage) determines physiologic activity, high altitudes can impair oxygen uptake by the lungs. Mountain climbers must sometimes use supplemental oxygen at high altitudes for this reason. By increasing the amount of O₂ more than 0.21, we can raise its partial pressure and increase uptake by the lungs. For a practical application of this principle, see the accompanying Mini Clini.

Mini Clini

Why Are Oxygen Masks Needed on Airplanes?

 Problem

People who have traveled by air are familiar with the safety instructions given by the crew before flight. Instructions are included on how to use the oxygen masks. When and why are these masks needed?

Discussion

At a typical cruising altitude of 30,000 feet, the P_B outside the airplane cabin is approximately 226 torr. The inspired partial pressure of oxygen (PiO₂) is calculated as follows:

PiO2=0.21×226 torr=47 torr

If the cabin were to depressurize, travelers inside would be exposed to this low PiO₂. At this PiO₂, most people become unconscious within seconds and eventually die of lack of oxygen (anoxia).

To overcome this problem, emergency oxygen masks are available when the cabin depressurizes. These masks, assuming a tight fit, probably provide approximately 70% oxygen, or an FiO₂ of 0.70. The PiO₂ of a person wearing a mask under these conditions is calculated as follows:

PiO2=0.70×226 torr=158 torr

This PiO₂ (about the same as at sea level) is sufficient to keep the passengers alive until the crew can bring the plane down to a safe altitude.

In contrast, high atmospheric pressures increase the partial pressure of inspired oxygen (PiO₂) in an air mixture. Pressures above atmospheric are called hyperbaric pressures.⁹ Hyperbaric pressures commonly occur only in underwater diving and in special hyperbaric chambers.⁹ For example, at a depth of 66 feet under the sea, water exerts a pressure of 3 atm, or 2280 mm Hg (3 × 760). At this depth, the oxygen in an air mixture breathed by a diver exerts a PO₂ of 0.21 × 2280, or approximately 479 mm Hg. This is nearly three times the PO₂ at sea level.

The same conditions can be created on dry land in a hyperbaric chamber. The U.S. Navy uses hyperbaric chambers for controlled depressurization of deep-sea divers and to treat certain types of diving accidents. Clinically, hyperbaric chambers and oxygen are used together to treat various conditions, including carbon monoxide poisoning and gangrene. Chapter 38 provides more details on this use of high-pressure oxygen.

Solubility of Gases in Liquids (Henry’s Law)

Gases can dissolve in liquids. Carbonated water and soda are good examples of a gas (CO₂) dissolved in a liquid (water). Henry’s law predicts how much of a given gas will dissolve in a liquid. According to this principle, at a given temperature, the volume of a gas that dissolves in a liquid is equal to its solubility coefficient times its partial pressure:

V=α×Pgas

V is the volume of dissolved gas, α is the solubility coefficient of the gas in the given liquid, and P_gas is the partial pressure of the gas above the liquid. The solubility of gases in liquids is compared by using a measure called the solubility coefficient. The solubility coefficient equals the volume of a gas that will dissolve in 1 ml of a given liquid at standard pressure and specified temperature. The solubility coefficient of oxygen in plasma, at 37° C and 760 torr pressure, is 0.023 ml/ml. Under the same conditions, 0.510 ml of CO₂ can dissolve in 1 ml of plasma.

Temperature plays a major role in gas solubility. High temperatures decrease solubility, and low temperatures increase solubility. This is why an open can of soda may still fizz if left in the refrigerator but quickly goes flat when left out at room temperature.

The effect of temperature on solubility is a result of changes in kinetic activity. As a liquid is warmed, the kinetic activity of any dissolved gas molecules is increased. This increase in kinetic activity increases the escaping tendency of the molecules and partial pressure. As an increasing number of gas molecules escape, the amount left in a solution decreases rapidly. For a practical application of this principle, see the accompanying Mini Clini, which discusses blood gases and patient temperature.

Corrected Pressure Computations

To compute the new or corrected partial pressure of a gas after saturation with water vapor, the following formula is applied:

PC=Fgas×(PT−PH2O)

P_C is the corrected gas pressure, F_gas is the fractional concentration of the gas in the gas mixture, P_T is the total gas pressure of the mixture, and is the water vapor pressure at the given temperature (see Table 6-3). If only a single gas is present, F_gas equals 1, and the formula can be simplified:

PC=(PT−PH2O)

For example, in the presence of water vapor, Boyle’s law would have to be modified as follows:

V2=V1×(P1−PH2Oat T1)(P2−PH2Oat T2)

Correction Factors

Instead of complex calculations involving water vapor, simple correction factors can be used. In gas volume conversions, the three most common computations are as follows:

The values in the third column of Table 6-3, when multiplied by V₁, convert a gas volume from ATPS to BTPS. Table 6-5 provides the factors needed to convert a gas volume from ATPS to STPD. To use Table 6-5, simply multiply the ATPS volume by the factor corresponding to the specified temperature and uncorrected barometric pressure. Finally, Table 6-6 provides the factors needed to correct volumes from STPD to BTPS. To use Table 6-6, simply multiply the STPD volume by the factor corresponding to the ambient pressure.

TABLE 6-5

Factors to Convert Gas Volumes from STPD to BTPS at Given Barometric Pressures

Pressure	Factor	Pressure	Factor
740	1.245	760	1.211
742	1.241	762	1.208
744	1.238	764	1.203
746	1.235	766	1.200
748	1.232	768	1.196
750	1.227	770	1.193
752	1.224	772	1.190
754	1.221	774	1.188
756	1.217	776	1.183
758	1.214	778	1.181

TABLE 6-6

Factors to Convert Gas Volumes from ATPS to STPD

Observed Pa	15°	16°	17°	18°	19°	20°	21°	22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°
700	0.855	851	847	842	838	834	829	825	821	816	812	807	802	797	793	788	783	778
702	857	853	849	845	840	836	832	827	823	818	814	809	805	800	795	790	785	780
704	860	856	852	847	843	839	834	830	825	821	816	812	807	802	797	792	787	783
706	862	858	854	850	845	841	837	832	828	823	819	814	810	804	800	795	790	785
708	865	861	856	852	848	843	839	834	830	825	821	816	812	807	802	797	792	787
710	867	863	859	855	850	846	842	837	833	828	824	819	814	809	804	799	795	790
712	870	866	861	857	853	848	844	839	836	830	826	821	817	812	807	802	797	792
714	872	868	864	859	855	851	846	842	837	833	828	824	819	814	809	804	799	794
716	875	871	866	862	858	853	849	844	840	835	831	826	822	816	812	807	802	797
718	877	873	869	864	860	856	851	847	842	838	833	828	824	819	814	809	804	799
720	880	876	871	867	863	858	854	849	845	840	836	831	826	821	816	812	807	802
722	882	878	874	869	865	861	856	852	847	843	838	833	829	824	819	814	809	804
724	885	880	876	872	867	863	858	854	849	845	840	835	831	826	821	816	811	806
726	887	883	879	874	870	866	861	856	852	847	843	838	833	829	825	818	813	808
728	890	886	881	877	872	868	863	859	854	850	845	840	836	831	826	821	816	811
730	892	888	884	879	875	870	866	861	857	852	847	843	838	833	828	823	818	813
732	895	891	886	882	877	873	868	864	859	854	850	845	840	836	831	825	820	815
734	897	893	889	884	880	875	871	866	862	857	852	847	843	838	833	828	823	818
736	900	895	891	887	882	878	873	869	864	859	855	850	845	840	835	830	825	820
738	902	898	894	889	885	880	876	871	866	862	857	852	848	843	838	833	828	822
740	905	900	896	892	887	883	878	874	869	864	860	855	850	845	840	835	830	825
742	907	903	898	894	890	885	881	876	871	867	862	857	852	847	842	837	832	827
744	910	906	901	897	892	888	883	878	874	869	864	859	855	850	845	840	834	829
746	912	908	903	899	895	890	886	881	876	872	867	862	857	852	847	842	837	832
748	915	910	906	901	897	892	888	883	879	874	869	864	860	854	850	845	839	834
750	917	913	908	904	900	895	890	886	881	876	872	867	862	857	852	847	842	837
752	920	915	911	906	902	897	893	888	883	879	874	869	864	859	854	849	844	839
754	922	918	913	909	904	900	895	891	886	881	876	872	867	862	857	852	846	841
756	925	920	916	911	907	902	898	893	888	883	879	874	869	864	859	854	849	844
758	927	923	918	914	909	905	900	896	891	886	881	876	872	866	861	856	851	846
760	930	925	921	916	912	907	902	898	893	888	883	879	874	869	864	859	854	848
762	932	928	923	919	914	910	905	900	896	891	886	881	876	871	866	861	856	851
764	934	930	926	921	916	912	907	903	898	893	888	884	879	874	869	864	858	853
766	937	933	928	925	919	915	910	905	900	896	891	886	881	876	871	866	861	855
768	940	935	931	926	922	917	912	908	903	898	893	888	883	878	873	868	863	858
770	942	938	933	928	924	919	915	910	905	901	896	891	886	881	876	871	865	860
772	945	940	936	931	926	922	917	912	908	903	898	893	888	883	878	873	868	862
774	947	943	938	933	929	924	920	915	910	905	901	896	891	886	880	875	870	865
776	950	945	941	936	931	927	922	917	912	908	903	898	893	888	883	878	872	867
778	952	948	943	938	934	929	924	920	915	910	905	900	895	890	885	880	875	869
780	955	950	945	941	936	932	927	922	917	912	908	903	898	892	887	882	877	872

Laminar Flow

As discussed earlier, during laminar flow, a fluid moves in discrete cylindrical layers or streamlines. The difference in pressure required to produce a given flow, under conditions of laminar flow through a smooth tube of fixed size, is defined by Poiseuille’s law:

ΔP=8nlV˙πr4

where ΔP is the driving pressure gradient, n is the viscosity of the fluid, l is the tube length, is the fluid flow, r is the tube radius, and π and 8 are constants.

According to this formula, for fluids flowing in a laminar pattern, the driving pressure increases whenever the fluid viscosity, tube length, or flow increases. In addition, greater pressure is required to maintain a given flow if the tube radius decreases.

Turbulent Flow

Under certain conditions, the pattern of flow through a tube changes significantly, with a loss of regular streamlines. Instead, fluid molecules form irregular eddy currents in a chaotic pattern called turbulent flow (see Figure 6-21). This changeover from laminar to turbulent flow depends on several factors, including fluid density (d), viscosity (h), linear velocity (v), and tube radius (r). In combination, these factors determine Reynold’s number (N_R).

NR=v×d×2rh

In a smooth-bore tube, laminar flow becomes turbulent when N_R exceeds 2000 (the number is dimensionless). According to the previous formula, conditions favoring turbulent flow include increased fluid velocity, increased fluid density, increased tube radius, and decreased fluid viscosity. In the presence of irregular tube walls, turbulent flow can occur when N_R is less than 2000.

Mini Clini

Differential Pressure Pneumotachometer

 Problem

It is often necessary to measure and record changes in airflow as a patient breathes. How can we apply the formula for resistance to measure and record airflow?

Discussion

Airflow can be measured by using a device called a pneumotachometer. One of the simplest designs is the differential pressure pneumotachometer. A differential pressure pneumotachometer incorporates a flow tube with a known and constant resistance (R). If the formula for resistance is rearranged to solve for flow, it appears as follows:

V˙=(P1−P2)R

Flow through a tube with constant resistance is directly proportional to the pressure difference across the tube. By measuring this pressure difference (using a strain-gauge transducer, such as described in Figure 6-18), we can measure flow. To ensure linearity between pressure and flow, the flow pattern through the tube must remain laminar.

When flow becomes turbulent, Poiseuille’s law no longer applies. Instead, the pressure difference across a tube is defined as follows:

ΔP=flV˙24π2r5

where ΔP is the driving pressure, f is a friction factor based on the density and viscosity of the fluid and the tube wall roughness, l is the tube length, and is the fluid flow.

Figure 6-22 compares the relationship between pressure and flow under laminar and turbulent conditions. As can be seen, when flow is laminar (Poiseuille’s law), the relationship between driving pressure and flow is linear. However, when flow becomes turbulent, driving pressure varies with the square of the flow (). To double flow under laminar conditions, we need only double the driving pressure. To double flow under turbulent conditions, we would have to increase the driving pressure fourfold.

Transitional Flow

Transitional flow is a mixture of laminar and turbulent flow. Flow in the respiratory tract is mainly transitional in nature. When flow is transitional, the total driving pressure equals the sum of the pressures resulting from laminar and turbulent flow:

ΔP =(k1×V˙)+(k2×V˙2)

k₁ and k₂ are factors indicating the respective contribution of laminar and turbulent flow to overall driving pressure. When flow is mainly laminar, the pressure varies linearly with the flow. When flow is mainly turbulent, driving pressure varies exponentially with the flow. With all else equal, pressures generated during laminar flow are most affected by fluid viscosity, whereas fluid density is the key factor when flow is turbulent.