chemical principles exemplified ROBERT C. PLUMB Worcester Polytechnic lnltitute Worce,ter, Mass~chuseth01609
Space Vehicle Reentry and Thermal Effects of High Winds lllustroting principles o f the kinetic theory o f goser
If a person is exposed to a cold wind, he loses body heat more rapidly t,han he does under circumstances where heat loss is controlled by diffusion-it may even lead to a tragedy such as on Mt. Washington in New Hampshire when t v o persons "froze to deat,h" on July 20, 1958, even t.hough the temperature did not go below 3S°F, but the wind was as high as 65 mph. Why, then, does a space vehicle, in passing at high speed through the atmosphere, tend to get hotter than the gas? Why doesn't it get cooled to the temperature of the atmosphere? At \!-hat wind velocit,y would a person standing on a high mountain tend to heat up instead of cooling off, aud why in terms of molecular behavior would this occur? The at,mosphere 40 miles up, where thc maximum heating on reeutry occurs, does not differ significantly in compositiou from that, of the surface of the earth; the temperature is about 250°1i, and t,he pressure is about 0.2 tom, or 2.6 X lo-' atm. The mean free path for molecular trajectories is about 0.03 cm. Friction, such as that which occurs when two solids are rubbed together, is a simple answer which tells virtually nothing about the molecular origin of the heating cffect. h o r n a molecular point of view, the space ship is being bombarded with molecules which rebound elastically and there is no reason to suppose that inelastic collisions, with frictional effects, should take place. The power which fundamental scientific knowledge gives to the person who makes the effortt o acquire it is evidenced when the phenomena above are considered in terms of the kinetic theory of gases. Suppose that an object passes through a gas and the object is small compared to the mean free path of the molecules in the gas (e.g., a very small meteorite 40 miles above the earth). Thermal equilibrium of that object with the molecules which strike it requires that the temperature of the object he the same as the temperature of the molecules which are impinging on its The exempla are designed to show fundamental chemical pprinoiples in operation. They deal with phenomena in which students have intrinsio inlerest; they apply abstract ideas to easily visuslized situations. All of us have our pet aneodates and illustr~tians which we know will attract the students' interest. Your contributions and suggestions are invited. They may he sent to the author.
surface-otherwise impacts will, on the average, add or remove energy. However, the "temperature" of the molecules striking the object is deteimined by the average kinet,ic energy of the molecules relative to the object.
Siuce the collision specd is determined by t.he relat,ive speed of the object m d the molccules, the temperature of the molecules is an apparent temperature, its value also depending on the relative speed of the object and the molecules. If the object were at rest it would see molecules moving a t a root mean syuare speed of about 4 X l o 4 cm/sec. If t,he object moves a t a speed sohi then the kinetic energy of the molecules relative to the object is increased by an amount ms2,bj/2, and the tempcrature increases accordingly. The apparent temperature of the molecules is
As long as the object. is moving slowly in comparison t o the speed of the molecules, there is little effect, but suppose the object is moving at the speed of a. spacecraft on reentry, 18,000 mph, i.e., 8.2 X lo5 cm/sec. This is 20 times the average speed of the molecules and the "temperature" of the molecules is hence 400 X 250 = 10°K. The usual result, depending homever, on the particle's momentum and trajectory, will be t,hat the object will ignite and produce a streak of light in the sky to the awe of the observer. If the object is large compared to the mean free pat,h of t,he molecules through which it passes, as for example Volume 48, Number 2, February 1971
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a spacecraft at an altitude of 40 miles, another effect must be considered. The molecules rebounding from the surface of the object ill collide with other molecules in t,hc path of the object and a layer of molecules will be carried along in front of the object as a bumper, such that the molecules in the path mill not in general collide with the object but with the bumper-\vhat is commonly referred to as a shock wave. It is this bumper or shock front which now is the victim of the extraordinarily high apparent temperature of the molecules which strike it, and much of the energy is dissipated as ionized hot gaseous plasma in the coneshaped shock wave extending out from the object.
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The calculation of the surface temperature of the ohject itself is now more complicated and involves, in addition to the speed of the object, its shape and the distance between the surface of the object and the shock front as well. Suppose two very precise thermometers, which gave the same readings when calibrated, were used to measure the air temperature in a hurricane, one being a f i e d t o a tower in the wind and the other suspended from a weather balloon and carried along with the wind. If the wind speed were 35 m/sec (78 mph) how much difference would there be in the thermometer readings?
