The art of anesthesiology is essentially practical. For this reason anesthesiologists must have an understanding of the physical aspects of the apparatus they use, not only to use it efficiently but also to understand its limitations and to use it safely. Many avoidable accidents and near misses have occurred as the result of the misuse of equipment or misinterpretation of measurements because the anesthesiologist did not understand the basic principles concerned.
One of the problems facing the medical profession today is the clinician’s inability to discuss his or her requirements with the engineer in terms that they both understand. This problem occurs not only with the development of new equipment but also with the discussion of faults and difficulties with existing equipment.
This chapter is therefore devoted to the basic physics of gases, liquids, vapors, and solids and to the principles of modern control systems, which are increasingly a part of the latest anesthetic machines. Where reference is made to units of measurement, the International System of Units, known as the SI System (Système International d’Unités), is generally used (see Appendix ).
States of Matter
An understanding of the physical principles applicable to the practice of anesthesiology can begin with a consideration of the differences between three states of matter: solid, liquid, and gas. The difference between these states is best explained by considering the effects of the interactions between the atoms and molecules of which they are made. Atoms or molecules are subject to forces of attraction known as Van der Waals forces, which act to hold individual atoms or molecules near to each other.
In a solid, these intermolecular forces cause the molecules to maintain a fairly fixed position relative to each other. Although the kinetic energy of the molecules causes them to move about a mean position, these mean positions are fixed and may form a regular geometric structure or lattice. When a solid is heated, the kinetic energy of the molecules increases, so the range of movement about this mean position increases and the volume of the solid increases as expansion occurs.
As more heat is added to the solid, the range of movement of the molecules eventually becomes sufficiently great to disrupt the fixed structure and the molecules are able to move past each other. The solid has changed state to become a liquid. Nevertheless, the kinetic energy is insufficient to overcome the intermolecular forces completely and the molecules remain close to each other. Because the molecules remain near each other in a solid or a liquid, matter in either of these states is not easily compressed.
As more heat is added to the liquid, the kinetic energy of the molecules increases until the intermolecular forces are no longer sufficient to hold the molecules near each other. The state changes to the gaseous state, in which the molecules move freely throughout the volume in which they are contained. Because of the large distances between molecules in the gaseous state, matter in this state is comparatively easily compressed.
Heat and Temperature
Relationship Between Heat and Temperature
The internal energy of an object is composed of the kinetic and potential energies of the molecules of which it consists. Transfer of heat energy to or from an object alters this internal energy. The temperature of an object determines the direction in which a transfer of heat energy occurs, the energy being transferred from the object with the higher temperature to the object with the lower temperature. Objects at the same temperature are in thermal equilibrium and no transfer of energy occurs.
Temperature Scales
Temperature scales are based on fixed temperatures that can be reproduced by appropriate physical conditions. Two of these fixed temperatures are needed to define a temperature scale.
The SI unit of temperature is the Kelvin (K). The lower fixed point used to define the Kelvin scale is the temperature at which no further heat energy can be extracted from any object. This point is often referred to as the absolute zero of temperature and the Kelvin temperature as absolute temperature . The upper fixed point is the triple point of water, which is the temperature at which ice, water, and water vapor exist in equilibrium ( Figure 27–1 ). The temperature range between these fixed points is divided into 273.16 equal parts; thus the Kelvin is defined as 1/273.16 of the temperature of the triple point of water.
This rather strange definition of the Kelvin arises from its relationship to another temperature scale, the degree Celsius (°C) scale, the latter based on the freezing and boiling points of water, which are given the values 0° C and 100° C, respectively. The Celsius temperature is now defined by the relationship:
temperature(K)=temperature(°C)+273.15
temperature(K)=temperature(°C)+273.15
temperature ( K ) = temperature (° C ) + 273.15
Thus the temperature of the triple point of water is 0.01° C and a difference of 1 K is identical to a difference of 1° C.
Heat
The SI unit of energy is the joule (J), although an alternative unit, the calorie (cal) is sometimes used specifically for heat energy. As the calorie is a rather small quantity of heat energy, the energy available from food is often quoted in terms of kilocalories and the symbol Cal is used to represent kilocalories.
The relationship between these various units is:
1calorie(cal)=4.187joule(J)
1calorie(cal)=4.187joule(J)
1 calorie ( cal ) = 4.187 joule ( J )
1calorie(Cal)=1kilocalorie(kcal)=1000calories
1calorie(Cal)=1kilocalorie(kcal)=1000calories
1 calorie ( Cal ) = 1 kilocalorie ( kcal ) = 1000 calories
Heat Capacity and Specific Heat Capacity
Objects differ in the temperature change produced by the gain or loss of a given quantity of heat energy. For example, a large object made of the same material as a small object exhibits a lesser change in temperature than the small object. Objects of the same mass but made of different materials generally also differ in the temperature change produced by the same change in heat energy. The change in heat energy and temperature are related by the heat capacity of the object:
change in heat energy=change in temperature×heat capacity
change in heat energy=change in temperature×heat capacity
change in heat energy = change in temperature × heat capacity
To be able to compare different objects and different materials, the term specific heat capacity is used. The specific heat capacity, also referred to as the specific heat , is the quantity of heat energy required to change the temperature of 1 kg of a substance by 1 K. The units are therefore J kg -1 K -1 .
For example, it takes 4200 J of energy to raise the temperature of 1 kg of water by 1° C. Therefore the specific heat capacity of water is 4200 J kg -1 K -1 . In comparison, it takes 910 J to raise the temperature of 1 kg of aluminum by 1° C. Therefore, the specific heat capacity of aluminum is 910 J kg -1 K -1 .
Latent Heat
A comparatively large alteration in the kinetic energy of molecules occurs when a substance changes state; moreover, this change of state occurs at a fixed temperature that depends on the pressure. In the case of the transition from solid to liquid, this is the melting point and in the case of liquid to gas, the boiling point . The addition of heat energy is needed for the change of state to occur, even though this change takes place at a fixed temperature. The energy is needed to increase the kinetic energy of the molecules sufficiently to overcome the forces of attraction between them and is known as the latent heat . These processes occur in reverse when heat energy is removed from a substance. The transition from gas to liquid is termed the dew point, and the transition from liquid to solid, the freezing point .
The heat required to melt a solid is known as the latent heat of fusion . For ice this is 333 kJ kg -1 at 0° C and normal atmospheric pressure. The heat required to vaporize a liquid is called the latent heat of vaporization . For water, this is 2257 kJ kg -1 at 100° C and normal atmospheric pressure. It is noteworthy that considerably more heat is required to vaporize a liquid than to raise its temperature from room temperature to its boiling point.
Transfer of Heat
Heat may be transferred from one object to another or from one part of an object to another by the processes of conduction, convection , and radiation .
Conduction
In conduction, heat energy diffuses along an object from molecule to molecule. For example, metals such as copper are good conductors of heat, whereas glass and expanded polystyrene are poor conductors. Very poor conductors of heat are termed thermal insulators .
Convection
If part of a fluid is heated, it expands and becomes less dense than the fluid surrounding it. Being free to move, it rises, and as it travels upward, its place is taken by the cooler, denser fluid from around it, which in turn is heated and rises. There is, therefore, a constant rising stream of fluid above the source of heat. These currents are known as convection currents ( Figure 27–2 ), and the heat energy is carried by them.
Radiation
The transfer of radiated heat energy does not require the source of heat to be in contact with any other object. The rate at which heat energy is radiated is described by Stefan’s law:
P=seAT4
P=seAT4
P = seAT 4
where s is Stefan’s constant, e is the emissivity, A is the area of the radiating surface, and T is the absolute temperature. The emissivity, which ranges from 0 to 1, quantifies the difference in emission from surfaces at the same temperature. A matte black surface, for example, has a greater emissivity than a reflective white surface, so the rate at which it radiates energy is greater under the same conditions.
Stefan’s law shows that the net transfer of heat between two objects at different temperatures is proportional to the difference between the fourth power of their temperatures (i.e., P a T 1 4 − T 2 4 ). Even though the ambient temperature is comparatively high, heat can still be lost to a cooler object through the radiation of heat energy.
Because of its dependence on temperature, radiated heat energy can be used as the basis of temperature measurement techniques.
Properties of Ideal Gases
As is the case with all substances, the smallest particle of a gas that can exist separately is a molecule, or in the case of some gases such as xenon, an atom. Gas molecules are in constant motion, moving in all directions and rebounding from each other and from the walls of the space in which they are confined. It is the change in momentum resulting from the collisions of gas molecules with the walls that appears as the pressure of the gas.
The physical properties of gases under certain conditions of temperature and pressure approximate those of a collection of noninteracting particles of negligible size that undergo collisions with each other and the walls of the container in which they are situated. These properties are known as the properties of an ideal gas. The state of such a gas in a closed container can be described by four variables: the volume of the container, the number of molecules of gas present, the temperature, and the pressure. These variables are related by several gas laws, which describe the behavior of an ideal gas.
The Gas Laws
Boyle’s Law
Boyle’s law states that, at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure:
Vα1PorPV=kBwherekBis a constant
Vα1PorPV=kBwherekBis a constant
V α 1 P or PV = k B where k B is a constant
Charles’ Law
Charles’ law states that, at constant pressure, the volume of a fixed mass of gas is proportional to its absolute temperature:
VαTorVT=kCwherekCis a constant
VαTorVT=kCwherekCis a constant
V α T or V T = k C where k C is a constant
Gay-Lussac’s Law
Gay-Lussac’s law states that, at a constant volume, the pressure of a fixed mass of gas is proportional to its absolute temperature:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='VαTorPT=kGwherekGis a constant’>VαTorPT=kGwherekGis a constantVαTorPT=kGwherekGis a constant
VαTorPT=kGwherekGis a constant
VαTorPT=kGwherekGis a constant
V α T or P T = k G where k G is a constant
Combined Gas Law
These three gas laws can be combined to give the following relationship for a fixed mass of gas:
P1V1T1=P2V2T2
P1V1T1=P2V2T2
P 1 V 1 T 1 = P 2 V 2 T 2
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