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

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