ROBERT C. PLUMB
chemical exemplified
Are We Teaching the Most Useful Ideas about Transport? Illurtroting Einstein's Laws o f Diffusion
Suggestion by Paul Goldberg, Polaroid Corporation Graham's law of diffusion, according to which the rate of diffusion in a gas is inversely proportional to the square root of the mass, is commonly included in courses in elementary chemistry. For most purposes, who cares! Of much more frequent practical importance, but not usually discussed, are Einstein's laws of diffusion; they tell how the rate of diffusion varies with the temperature. According to one of Einstein's diiusion laws, the mean square distance that random molecular motion will carry a molecule from its initial position in a time t, is proportional to the diffusioncoefficient
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(AX)l = 2Dt
Einstein also showed that the diffusioncoefficient varies with the absolute temperature as
where f is the frictional coefficient, a measure of the retarding force to the motion. The frictional coefficient in liquids is proportional to the viscosity which in turn depends upon temperature
standing on the ski slope will not only give you frostbite but will upset the photographic color balance of your girl's outfit. So on many Polaroid cameras two aluminum plates are provided for processing picture-in-aminute film in a cold environment. Put the film, sandwiched between the plates, under your arm and let the diffusion proceed a t the temperature and rate for which the film is designed. Knowing SomeThermodynamicsCan Save a Life Illustroting Thermodynamic Principles o f Energy Transport, Phase Transformations, and Spontaneity o f Phase Transformations
Suggestions and information provided by David E. Bass, U . S . A ~ m Research y Institute of Environmental Medicine and Professor Charles E. Carraher, Jr., University of South Dakota Acclimation to work in a hot environment, discomfort in hot, humid weather, and heat stroke collapse under adverse conditions, can all be understood in terms of elementary thermodynamic considerations. A knowledge of the principles can be useful, even to the point of saving a life. Consider the human body as a thermodynamic system. reauired hv nhvsiolo~vand biochemistrv to he isothekal but generating thermal energy through metabolism. The rate of metabolic heat generation varies from 70 kcal/hr when reclining quietly in the morning before breakfast, up to 1400 kcal/hr during vigorous physical activity. This thermal energy must be dissipated to maintain the optimal inner (deep body) temperature. If heat dissipation suddenly stopped, man's temperature would rise a t a rate of 1-30°F/hr, with heat stroke a t 1 0 6 T and death at 110-112°F. Nature makes extraordinarily good use of physical chemical principles to keep the hody functioning isothermally. "
where E is the activation energy for viscosity Combining these we have a fundamental relationship which is of importance in a host of phenomena. Lower the temperature T and diflusion through distance takes a - a Riven longer time t. Although one is hard pressed to find examples of Graham's law in action in real-life situations, it is not hard to find an example where a large number of people have manipulated matter in a way that demonstrates Einstein's laws of diffusion. We're sure Einstein did not think about photographic applications when he developed his laws, but the people a t Polaroid did! When Polaroid film is developed, several dyes in the Polacolor negative must diffuse through distances of the order of 250 p to the positive. If the film is cold, the dyes will not reach the positive in the normal development time. Increasing the developing time when 1 12
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Journal o f Chemical Education
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When Conductive Heat Transfer Fails
How does man survive when the temperature of his surroundings is above normal hody temperature, e.g., when he is laboring in a foundry or on Army maneuvers on a desert, or just doing nothing on a scorching hot summer day? The second l a x of thermodynamics tells us that thermal energy will not flow from a cooler object,
man, to hotter surroundings, yet if the metabolic heat is not removed the consequences are fatal. Of course the answer is sweating and the attendant evaporative cooling. Thermal energy can be used to break the hydrogen bonds in liquid water, raising the intermolecular potential energy, and the energy together with the water molecules is transferred from the body to the surrounding atmosphere. The hody "turns up" this mechanism of energy dissipation when the surrounding temperature is so high and the metabolic heat production so rapid that convective heat transfer will not suffice. In a resting man, sweating begins when the air temperature reaches 89°F. Acclimation to Heat-Nature Transfer More Efficient
Makes Heat
Sometimes man's external or internal motivations (his military commander or his employer, or his pride in his well-trimmed lawn) cause him to tax the cleverness of nature in disposing of the metabolic heat. The strain results from the fact that thermal energy generated by metabolism is produced within the body, not on the surface where it can be disposed of by evaporative cooling. This energy must be transported by the cardiovascular system, i.e., blood flow, to the surface and if undue demands of hard labor in high temperature are imposed, heat exhaustion, cardiac strain, and even heat stroke result. However, it is common experience that although the sudden advent of hot weather results in impaired ability to perform work, if a heat wave persists for several days there is a gradual return of ability to work with little or no discomfort. One has become "acclimated" to heat. What trick does Nature have to do this? Although the matter is the subject of ongoing research and there are many subtleties which are not understood, the principal effect is a simple application by Nature of a principle of heat transport. The rate of heat transport, either by diiusion or with convective flow, depends upon the temperature diierential between the heat source and the receiver. The larger the temperature diierential, the more rapid the transport. In this case the source of heat is deep hody tissue, liver, kidneys, brain, heart, and skeletal muscles and the receiver is the skin, cooled by evaporation. From comparative measurements of skin and deep body temperature, Eichnal found that during acclimation the
mean skin temperature decreases to a level which permits the transport of the deep body heat to the surface without overtaxing the circulation. The temperature diierential between the deep hody and skin increases by as much as 1°F, permitting, after acclimation, 0.6 1 of blood to carry as much heat as 1 1 of blood before acclimation. It's Nof the Heat but the Humidity
What is the basis in chemistry of the adage, "It's not the heat but the humidity"? Why, in Oregon, can it he 95°C but comfortable while in South Dakota, where the humidity is generally only a little lower than the temperature, is it hot a t 80°C? It is simply that the rate of evaporation, and the attendant evaporative cooling, decrease as the pressure of water in the air approaches the saturation or equilibrium pressure. In the language of thermodynamics, the Gihbs free energy driving force for the reaction HtO(I) = HzO(g)
is and is favorable if PH~O is low, and zero if PHlois the equilibrium vapor pressure. When Energy Transfer Becomes Thermodynamically impossible
Through carelessness or callousness, a human being may he subjected to a combination of high metabolic heat production, high temperature, and high humidity in which even the healthiest of individuals cannot long survive. We see from the previous considerations that if man exerts himself when the temperature of the surroundings is above body temperature and the humidity is near saturation, the body can be confronted with a thrrmudy~~an~icnlly impwiihle heat trm.if?r pn~blem. Tlrc tmaic r x t ~ ~ n ~of) lt iel e wmmw Olvmuics in Home in 1960, tce slave ;hip deaths of the i8th century, and intolerable "sweat shop" industrial conditions in factories and mines a few decades past, exemplify the danger to man.
w.,
EICHNA, L. PARK,C . R.,NELSON, N. HORVATH, S. M., PALMES, E. D., Arne?. J. Physiol., 163.585 (1950).
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Volume 49, Number 2, February 1972
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