Brit. J. Anaesth. (1966), 38, 219
PHYSICS APPLIED TO ANAESTHESIA IV: HEAT BY
D. W. HILL
Research Department of Anaesthetics, Royal College of Surgeons of England, London
Temperature scales. A scale of temperature consists of a series of uniform intervals, with an upper fixed point and a lower fixed point defining the ends of the scale. On the Centigrade scale, the upper fixed point is taken as the temperature of the boiling point of water (100°C) at a pressure of 760 mm Hg. The lower fixed point is the freezing point of water (0°C). The difference beween the two fixed points amounts to 100 degrees. On the Fahrenheit scale the upper and lower fixed points are the same but are given the values of 32°F and 212°F, the interval amounting to 180 c F. The rather odd values of 32°F and 212°F arise from the fact that Fahrenheit originally took for his fixed points, the temperature of a freezing mixture of ammonium chloride and ice, and the normal temperature of the human body (100°F). The conversion between the two scales is given by t ° F = £ (t - 32)°C, and t ° C = ( l t + 32)°F. In dealing with gas law calculations, it is necessary to use another temperature scale, the absolute or Kelvin temperature scale. As would be expected from the name, the zero on this scale is the absolute zero, which is the lowest temperature it is possible to obtain. It is also the temperature at which the volume and temperature of ideal gases become zero, and has a value of — 273 CC. Modern low temperature physics
techniques enable temperatures of within a fraction of a degree of the absolute temperature to be realized. Many hospitals now use cryogenic systems to supply pipeline oxygen systems (Wilke, 1964), or to pressurize hyperbaric operating and treatment rooms (Heringman et al., 1964). Here liquid oxygen boiling at - 183°C is evaporated to provide a steady supply of gaseous oxygen. Since 0°K corresponds to - 273 °C, the lower fixed point 0°C corresponds to +273°K, and the upper fixed point 100°C corresponds to +373°K. Thus °C can be simply converted to °K by adding 273. Units of heat. The upper and lower fixed points were denned in terms of ice and water, since this makes the points easily realizable. Similarly, it is convenient to define the unit of heat in terms of the amount of heat required to raise the temperature of 1 g of water by 1"C. This is the unit which is used in scientific work, and for strict accuracy, the 1°C temperature interval is denned as between 14.5 and 15.4°C. Another engineering unit which may be encountered is the British Thermal Unit (BTU). This is the heat required to raise the temperature of 1 pound of water by 1°F. The cooling capacity of large refrigerators for hypothermia, or the output of air conditioning plants for operating rooms, may be expressed in BTU per hour. Specific heat. The quantity of heat required to raise 1 g each of various substances through 1°C will not be the same as that for 1 g of water. The specific heat of a substance is denned as the quantity of heat required to raise 1 g of that substance through 1°C. Thus the specific heat of copper is 0.1 calories per g, of ether 0.5 calories per g, and that of whole blood 0.87 calories per g. Any substance of specific heat s and mass m g can be expressed in terms of its water equivalent W g in respect of the heat required to raise its temperature by I°C
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Heat is simply another form of energy, and is interchangeable with other forms, such as electrical and mechanical energy. The addition of heat to a system will generally increase the temperature and the total energy of the system. Thus, if a closed volume of gas is heated, the energy of motion of its atoms or molecules is increased and this is indicated by a rise in pressure as they make more energetic impacts with the walls of the container. The heating or cooling of a body is expressed in terms of its temperature. The temperature is an expression of the average kinetic energy of its molecules.
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Specific heats of gases. The specific heat of gases, and hence their thermal capacity, is much smaller than is the case for solids or liquids, as is simply illustrated by the fact that one can comfortably smoke a short cigarette the end of which is glowing. Unless careful precautions are observed, gases quickly reach ambient temperature when passed along a tube. The specific heat of a gas reflects the amount of work that has to be done on it in order to raise its temperature by 1°C. A gas really has an infinite number of specific heats, depending on whether its volume is held constant during the heating or, if not, as to how it is allowed to expand. In practice there are two main specific heats for a gas, the specific heat at constant pressure, and the specific heat at constant volume. The ratio c p /c v is known as y, and usually has a value close to 1.4. For the cases of air at 20°C, cp = 0.241 cal/g, c, = 0.171 cal/g, and y=1.41. Gamma occurs in calculations dealing with rapid "adiabatic" compressions or expansions of gases. Such changes can occur at normal respiratory rates with an artificial thorax (Hill and Moore, 1964). Latent heat. Matter can normally exist in one or more of three states: solid, Liquid and gas or vapour. Work must be done on the system to bring about a change of state. Normally, the addition or subtraction of heat is manifested by a change in temperature. Whilst a change of state is being brought about, however, the temperature remains constant for a pure substance. Hence the heat required to change the state is known as latent heat. This is because, due to the temperature remaining constant, the action of the latent heat is hidden.
Consider a substance such as pure naphthalene placed in a test-tube and gently heated in a water bath. The form of the graph of naphthalene temperature against time is illustrated in figure 1. At first, the temperature of the solid naphthalene rises steadily, assuming a uniform rate of heating. TEMPERATURE
ALL
MELTING POINT 80«2*C
TIME 1 Temperature changes during the melting of pure naphthalene. FIG.
When the naphthalene starts to melt, the temperature of ths mixture of solid and liquid naphthalene remains constant whilst the change of state is taking place. This gives rise to the characteristic temperature "plateau" at the melting point. As soon as all the naphthalene is melted, the temperature rises uniformly again. If the substance was impure, a series of steps would be obtained, rather than a single well-defined plateau. The melting point of ice (0°C) occurs at the change of state from ice to water, and the boiling point of water (100°C) at the change of state from water to water vapour. The latent heat of ice is 80 cal/g and that of steam 540 cal/g. The formation of a layer of snow around the lowest part of a cylinder containing liquid carbon dioxide or nitrous oxide when a steady stream of gas is drawn off, is due to the marked cooling arising from evaporation of the liquid. Application to anaesthetic vaporizers. The main problems in the design of a precision anaesthetic vaporizer lie in securing constancy of the output concentration with change in the perfusing gas flow rate, and constancy with time. The latter is really securing constancy with respect to temperature. In order to evaporate each gram of liquid anaesthetic, the relevant latent heat of vaporization must be provided. In the case of ether this is 87 cal/g at 20°C. Unless an efficient means of transferring heat from the exterior is provided, the result of evaporation will be to cause
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Equating the amounts of heat required for the substance and water, mxsx t — W x 1 x t, so that W=mx s. For example, the thermal capacity of a body is defined as the quantity of heat required to raise the temperature of the body by 1°C. In the case of a composite body such as a soda lime canister, the various parts (brass body and soda lime), can be expressed in terms of their equivalent masses of water and added to give the thermal capacity. This technique was used by AinleyWalker (1959) to find the temperature rise occurring in a soda lime canister when absorbing carbon dioxide.
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the temperature of the liquid to fall. This will reduce the rate of evaporation, and the vapour concentration will diminish. One approach to the problem is to construct the vaporizer from a massive block of copper which has a high thermal capacity, and to fix it to a copper table in order to provide a large surface for the transfer of heat from the warm air of the operating room. This is the basis of the well-known Copper Kettle vaporizer (Morris, 1952). Another approach is to make use of a thermostatically controlled valve to allow the passage of additional saturated vapour from the vaporizing chamber as the liquid temperature falls. This is the method of the well-known EMO and Fluotec vaporizers. An ingenious approach was that adopted for the Oxford Vaporizer. The ether vaporizing chamber is surrounded with a layer of calcium chloride hexahydrate crystals. As the temperature of the liquid ether falls, the previously warmed calcium chloride gives out its latent heat of crystallization to hold the temperature of the ether constant at 30°C.
dense than cold air, and therefore rises, is an example of natural convection. The cooling of a patient by means of an air blast from a fan is an example of forced convection. Since a moving medium such as a gas or liquid is involved, again the process cannot take place in a vacuum. During anaesthesia, the process of breathing gives rise to a heat loss, since the inspired gases will be almost at ambient temperature, and the temperature of the expired gas will be some 34-36 °C. Let the minute volume of ventilation be 5 l./min, the temperature of the inspired gas (oxygen) be 20°C, and that of the expired gas 36 °C. The specific heat of oxygen is 0.0003 cal/ml The heat loss caused by warming of the gas during respiration is 5000x16x0.0003 = 24 cal/min. There will also be an additional heat loss introduced by the fact that water is being evaporated from the patient in order to saturate the expired gases with water vapour. The oxygen from a cylinder can be assumed to be dry, whilst the water concentration in the expired gas is some 6 per cent. The loss of water vapour per minute amounts to 6 per cent of the minute volume of 5 l./min, i.e., 300 ml/min. At body temperature, 1 ml of liquid water vaporizes to 1400 ml of water vapour, so that a mass of approximately 0.2 g/min of water is vaporized. The latent heat of vaporization of water is 540 cal/g, so that the heat loss due to this cause is some 110 cal/min, giving a total heat loss of 134 cal/min.
Application to hypothermia and local refrigeration. In neurosurgery it is sometimes convenient to produce hypothermia by application of ice bags and by directing a stream of air on to the patient. The evaporation of the water aids cooling, as in sweating. The evaporation of a jet of ethyl chloride vapour directed at the skin gives rise to local cooling and analgesia. The transfer of heat. The transfer of heat from one body to another can take place by one or more of three main mechanisms: conduction, convection and radiation. Conduction. This involves a direct transfer of heat energy from molecule to molecule. Hence it cannot occur in a vacuum. Heat transfer by conduction occurs when a patient is in contact with a hot or cold object. It is the process by which the ear of an unconscious patient, in contact with the lamp of an earpiece oximeter, may be burned, or a patient cooled during hypothermia by placing him in contact with a rubber mattress through which circulates cold water. Convection. This is the process by which a moving stream of gas or water can bring heat to or from a patient. The fact that warm air is less
Radiation. Radiation consists in the emanation, in the form of electromagnetic radiation, of heat energy from a body. Radiant electric fires immediately give rise to the idea of heat in the form of radiant energy. Radiation can traverse a vacuum, and does not need a physical medium to support its passage. Hence the sun's heat can reach us from outer space. The greater the temperature difference between a body and its surroundings, the greater will be the radiant heat loss from the body. Thus radiant heat lamps are used in physical medicine for the heat treatment of some musculo-skeletal disorders. At body temperature, heat loss due to radiation will be small, but cannot be neglected. Losses due to convection and radiation are minimized by keeping the patient covered as much as possible. Good radiators of heat are also good receivers of radiant heat and vice versa. A shiny surface will be a poor
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PHYSICS APPLIED TO ANAESTHESIA—IV
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emitter and absorber of radiant heat. Hence a Dewar or Thermos flask consists of a doublewalled glass container, with the space between the wall evacuated and silvered on the inside. The vacuum stops heat losses from the inside to the outside by convection and conduction, and the silvering reduces radiation losses.
RESEARCH FELLOW DEPARTMENT OF ANAESTHESIA, THE UNIVERSITY OF LEEDS Applications are invited for a Research Fellowship sponsored by the Association of Anaesthetists of Great Britain and Ireland for studies during the postoperative period. The Fellowship will be for two years. The successful candidate will be known as the "Association of Anaesthetists Research Fellow" and will also be encouraged to undertake a small amount of clinical anaesthesia and teaching. His work will be supported by good laboratory and workshop facilities and advanced methods of data processing. Remuneration (maximum £2,000 p.a.) will be in accordance with previous clinical salary scale. Applications to Professor J. F. Nunn, Department of Anaesthesia, The University of Leeds, 24 Hyde Terrace, Leeds 2, by April 22,1966.
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REFERENCES
Ainley-Walker, J. C. (1959). The heat mechanics of the Waters canister. Brit. J. Anaesth., 31, 2.
Heringman, E. C , Massel, T. B., Greensone, S. M., and Garon, R. J. (1964). A new approach to the design, construction and operation of a hyperbaric chamber. In Clinical Applications of Hyperbaric Oxygen (eds. I. Boerema, W. H. Brummerkamp and N. G. Meijnc), p. 235. Amsterdam: Elsevier. Hill, D. W., and Moore, Virginia (1964). The action of adiabatic effects of the compliance of an artificial thorax. Brit. J. Anaesth., 37, 19. Morris, L. E. (1952). A new vaporizer for liquid anesthetic agents. Anesthesiology, 13, 587. Wilke, H. J. (1964). Central gas supply systems. World Med. Electron., 2, 217.