General Principles of Gas Physics
I Basic Units and Relationships
A Mass: The ability of matter to occupy space, and if in motion to remain in motion, and if at rest to remain at rest.
B Weight: The quantification of the mass of an object; the effect of gravitational attraction on an object.
C Velocity: The speed that an object moves between two points; expressed in miles per hour or centimeters per second.
D Acceleration: The rate at which the velocity of an object increases. The units of acceleration are cm/sec2 or miles/hour2.
E Work: The force needed to move an object multiplied by the specific distance the object is moved.
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1. Force is defined as mass × acceleration. The units of force are:
2. Work is not performed unless the applied force causes movement; if no movement, no work.
F Energy is defined as the ability to do work.
1. Potential and kinetic energy are the two types of mechanical energy.
2. Potential energy (PE) is the energy of position.
where M = mass, g = gravitational attraction of the earth, and h = height.
4. Mass times gravitational attraction is frequently represented as weight (W):
5. Kinetic energy (KE) is the energy of motion.
G Pressure is the force applied per unit area. The units of pressure are:
A All matter exists in one of three basic states (Figure 2-1):
1. Solid: High degree of order, little random molecular motion, and strong intermolecular attraction
2. Liquid: Limited degree of order, some freedom of movement, and moderate intermolecular attraction
3. Gas: No order, complete freedom of motion, and weak intermolecular attraction
B The state of a substance is determined by the relationship of two forces.
C The KE of a substance is directly related to temperature.
1. The greater the KE of a substance, the greater its tendency to exist as a liquid or gas.
2. Molecules of every substance are in constant motion as a result of KE.
3. At absolute zero, the KE of a substance is theoretically zero.
D Intermolecular attractive forces oppose the KE of molecules and tend to force them to exist in less free (solid or liquid) states. Basically there are three types of intermolecular attractive forces: dipole, hydrogen bonding, and dispersion.
1. Dipole forces: Forces that exist between molecules that have electrostatic polarity; the negative aspect of one molecule is lined up and attracted to the positive aspect of another molecule, as seen with NaCl. These substances frequently form crystals.
2. Hydrogen bonding: A force that exists between molecules formed by hydrogen reacting with fluorine, oxygen, or nitrogen.
a. As a result of the electronegative difference between hydrogen and fluorine, oxygen, or nitrogen, the hydrogen atom in the molecule exists essentially as a pure proton.
b. The hydrogen end of one molecule is thus attracted to the negative aspect of another molecule of the same substance.
c. Hydrogen bonding occurs only with compounds of fluorine, oxygen, and nitrogen because of these atoms’:
3. Dispersion forces (London or van der Waals forces): Forces between molecules of relatively nonpolar substances.
a. In nonpolar substances the electron cloud normally is distributed equally among all of the atoms in the molecule.
b. However, at some point in time the electron cloud may be instantaneously concentrated at one end of the molecule. When this occurs, a polarity is set up on the molecule.
c. This instantaneous polarity allows weak attraction between adjacent molecules.
d. Dispersion forces are the weakest of all intermolecular forces.
1. The first law of thermodynamics states that energy (heat) is neither created nor lost but simply transformed from one form to another.
2. That is, any energy a substance gains must be lost by its surrounding environment.
3. Heat (energy) always moves from the hotter object to the cooler object until there is thermal equilibrium between the two objects.
4. Heat transfer occurs in four ways:
a. Conduction: Transfer of heat by direct contact between objects. Thermal conductivity is a measure of a substance’s ability to absorb heat.
(1) Metals have high thermal conductivity; they tend to feel cool because they readily absorb heat from the body.
b. Convection: Heating by the mixing of two fluids (liquids or gases). Heat is allowed to freely transfer in the mixture. Fluid currents carrying heat energy are called convection currents.
c. Radiation: Heating without direct contact, heat energy in the visible and infrared light ranges transferred to the objects they encounter—heating by the sun.
d. Vaporization/condensation: Heating by the transfer of energy as water changes from one state to another.
5. Heat and moisture exchangers function by the process of vaporization and condensation. Water is condensed, and heat is transferred to the device during exhalation. During inspiration the inhaled gas picks up water vapor by vaporization, and heat as a result is transferred to the inhaled gas (see Chapter 35).
6. Calorie: Unit of heat in the metric system. Essentially it is the amount of heat necessary to cause a 1° C increase in the temperature of 1 g of water.
7. British thermal unit (BTU): Unit of heat in the British system. Essentially it is the amount of heat necessary to cause a 1° F increase in the temperature of 1 lb of water.
8. One BTU is equal to 252 calories of heat.
9. Heat capacity: Number of calories needed to raise the temperature of 1 g of a substance 1° C.
10. Specific heat: Ratio of the heat capacity of a substance compared with the heat capacity of water.
1. A specific defined amount of heat is needed to cause the molecules of a substance to change their state of matter without a change in temperature.
2. Latent heat of fusion is the amount of heat necessary to change 1 g of a substance at its melting point from a solid to a liquid without causing a change in temperature.
a. The melting point is the temperature (at 1 atm of pressure) at which a substance changes from a solid to a liquid.
b. The total volume of a substance must change from a solid to a liquid before its temperature can change.
c. Generally, a large amount of heat gain is required to change from a solid to a liquid.
d. Changing from a liquid to a solid requires the same amount of heat loss.
e. Latent heats of fusion and melting points for various substances:
| Substance | Heat of fusion (calories/g) | Melting point (° C) |
| Water | 80 | 0 |
| Hydrogen | 13.8 | − 259.25 |
| Carbon dioxide | 43.2 | − 57.6 |
| Nitrogen | 6.15 | − 210 |
| Oxygen | 3.3 | − 218.8 |
3. The latent heat of vaporization is the amount of heat necessary to change 1 g of a substance at its boiling point from a liquid to a gas without causing a change in temperature.
a. Boiling point is the temperature at 1 atm of pressure at which a substance changes from a liquid to a gas.
b. The total volume of a substance must change from a liquid to a gas before its temperature changes.
(1) For a substance to boil, its vapor pressure must equal the pressure of the atmosphere above it.
(2) Evaporation is a surface phenomenon whereby individual molecules of a substance gain enough heat to change their state. Boiling, on the other hand, occurs throughout the entire volume of the substance.
c. Latent heats of vaporization are generally much greater than latent heats of fusion.
d. Latent heats of vaporization and boiling points for various substances:
| Substance | Heat of vaporization (calories/g) | Boiling point (° C) |
| Water | 540 | 100 |
| Hydrogen | 40 | − 252.5 |
| Carbon dioxide | 83 | − 78.5 |
| Nitrogen | … | − 196 |
| Oxygen | 50 | − 183 |
G Effects of pressure on melting and boiling points
1. In general, the greater the pressure over a substance, the higher the temperature necessary to cause the substance to change its state. However, pressure has a greater effect on the boiling point of a substance than on its melting point.
2. Critical temperature: The highest temperature at which a substance can exist as a liquid, regardless of the amount of pressure applied to it (O2 = −118.8° C).
3. Critical pressure: The lowest pressure necessary at the critical temperature of a substance to maintain it in its liquid state (O2 = 49.7 atm pressure).
4. Critical point: The combination of the critical temperature and the critical pressure of a substance.
H Triple point: Specific combination of temperature and pressure in which a substance can exist in all three states of matter in dynamic equilibrium.
I Sublimation: Transition of a substance from a solid directly to a gas without existence in a liquid state. The heat of sublimation equals the heat of fusion plus the heat of vaporization.
A Liquids flow and assume the shape of their containers.
B Liquids exert pressure that varies with the depth of the liquid and its density.
C According to Pascal’s principle the shape or volume of a container does not affect the pressure of a liquid; pressure is only affected by the liquid’s height and density.
D Variations in liquid pressure in a column produce an upward force referred to as buoyancy.
E As a result of buoyancy, objects in water appear to weigh less in water than in air.
F Liquids exert a buoyancy force because the pressure below a submerged object always exceeds the pressure above the object.
G According to Archimedes principle, the buoyancy force must equal the weight of the fluid displaced by the object.
H If the weight of the object exceeds the weight of the displaced water, it sinks, but if it weighs less than the displaced water, it floats.
I Archimedes principle is used to determine the specific gravity of liquids such as urine.
A The kinetic theory of gases normally is applied to relatively dilute gas volumes.
B Principles of the kinetic theory of gases are:
1. Gases are composed of molecules that are in rapid continuous random motion.
2. The molecules undergo near collisions with each other and collide with the walls of their container.
3. All molecular collisions are elastic, and as long as the container is properly insulated, the temperature of the gas remains constant.
4. The KE of molecules of a gas is directly proportional to the absolute temperature.
a. An increase in temperature causes an increase in KE of the gas.
b. The increased KE causes an increase in the velocity of the gas molecules.
c. The increased velocity causes an increase in the frequency of collisions.
d. The increased frequency of collisions causes an increase in the pressure in the system.
e. With an increase in temperature, the degree of increase in the velocity of gas molecules is indirectly related to their molecular weight (MW).
A One gram molecular weight (GMW), 1 g atomic weight, 1 g ionic weight, and so on, of a substance contains 6.02 = 1023 particles of that substance.
B The above mass of any substance is referred to as a mole.
C One mole of a gas at ° C and 760 mm Hg (standard temperature and pressure; STP) occupies a volume of approximately 22.4 L. (There is a small percent variation in this number for individual gases; e.g., CO2 = 22.3 L.)
D An equal number or fractions of moles of different gases at a specific temperature and pressure occupy the same volume and contain the same number of particles.
A Density (D) is the mass of an object per unit volume (V) and usually is expressed as g/L:
B On the surface of the earth, mass in equation 7 may be replaced by weight.
C Calculation of densities of solids and liquids is straightforward because their volumes are relatively stable at various temperatures and pressures.
D The volumes of gases, on the other hand, are severely affected by temperature and pressure.
E For this reason, the standard density of all gases is determined at STP (0° C and 760 mm Hg pressure) conditions where the volume used is 22.4 L and the weight used is the GMW of the particular gas:
F Standard densities of various substances:
G The density of a mixture of gases is determined by the following equation:
(9)Example: The density of a gas containing 40% oxygen, 55% nitrogen, and 5% carbon dioxide would be computed as follows:
H Specific gravity: Ratio of the density of a substance to the density of a standard. The specific gravity of solids and liquids is determined using water as the (density, 1 kg/L) standard; for gases, oxygen is used as the standard. When it is stated that the specific gravity of urine is 1.10, it means the urine is 1.10 times heavier than H2O because of the dissolved substances in the urine.
A Pressure (P) in any sense is equal to force per unit area:
B The pressure of a gas is directly related to the KE of the gas (see Section II, States of Matter) and to the gravitational attraction of the earth.
C With an increase in altitude, the gravitational attraction of the earth on the molecules of gas in the atmosphere decreases.
1. This causes a decrease in density of the atmospheric gases.
2. Decreased density results in fewer molecular collisions.
3. Thus, with increasing altitude there is a nonlinear decrease in the pressure of the total atmosphere and of individual gases.
4. Even though there is a steady decrease in the pressure of the atmosphere with altitude, the concentration of gases in the atmosphere remains stable to an elevation of approximately 50 miles.
D The barometric pressure (Pb) of the atmosphere is equal to the height of a column of fluid times the fluid’s density (Figure 2-2):
If the fluid used is mercury, normal atmospheric pressure is equal to psi:
E Mercury’s density in the metric system is 13.6 g/ml; in the British system it is 0.491 lb/in.3.
F Gas pressure is frequently expressed as the height of a substance (i.e., mm Hg, cm H2O). These are not true pressure expressions, but they may be easily converted to the proper pressure notation by use of equation 11 if necessary.
G Atmospheric pressure can be determined by a number of pressure-measuring devices (Figure 2-3).
A Water vapor content of the air under atmospheric conditions is variable. Temperature is the factor that most significantly affects water vapor content in the atmosphere.
1. The process of a liquid changing into a gas at a temperature lower than its boiling point is referred to as evaporation.
2. The process of a gas changing into liquid at a temperature lower than its boiling point is called condensation.
B At a particular temperature, there is a maximum amount of water that a gas can hold, capacity for water vapor.
C Because the boiling point of water (100°C) is considerably higher than the normal temperature of the atmosphere, the maximum water vapor content of the atmosphere varies with temperature.
1. As the temperature increases, the rate of evaporation of water accelerates, and the capacity of the atmosphere to hold water increases.
2. All other standard gases in the atmosphere have boiling points much lower than atmospheric temperature. This causes stability in their concentrations.
3. Water is the only standard atmospheric gas that responds to temperature changes in this manner.
D Expressions of water vapor content
1. Absolute humidity is defined as the actual weight of water vapor contained in a given volume of gas.
a. Absolute humidity may be expressed as grams per cubic meter or milligrams per liter.
b. The maximum absolute humidity at 37° C is 43.8 g/m3, or 43.8 mg/L.
2. Partial pressure (Pp) of water vapor (PH2O), maximum PH2O at 37° C, is equal to 47 mm Hg.
3. Maximum weight of water and water vapor pressure at different temperatures:
| Temperature (° C) | Weight (mg/L) | PH2O (mm Hg) | Temperature (° C) | Weight (mg/L) | PH2O (mm Hg) |
| 20 | 17.30 | 17.5 |
