Lightning heats the air, causing it to fly away from the channel of the bolt. That creates a vacuum.
Allright, I’ve at least figured out the equation I wanted was related to the Stephan-Boltzman law.
Total energy flux = (lower case sigma)*T[sup]4[/sup]
But thats for absolute radiance of a black body. I was thinking more along the lines of relative radiance from one temperature to another (delta)T.
Just subtract the “out” flux from the “in” flux:
net power out = [symbol]s/symbol
where T[sub]1[/sub] is the temperature of the stuff you’re surrounded by (e.g., the air.) If your 2 m[sup]2[/sup] worth of skin is at 305 K and the air is at 295 K, you’re losing
P = [symbol]e[/symbol](5.67*10[sup]-8[/sup] W m[sup]-2[/sup] K[sup]-4[/sup])(2 m[sup]2[/sup])[(305 K)[sup]4[/sup]-(295 K)[sup]4[/sup]]
P = [symbol]e[/symbol](123 W)
where [symbol]e[/symbol]~1 is the emissivity of skin. At infrared wavelengths, skin is not a bad blackbody, and [symbol]e[/symbol]=1 is pretty close. If you’re sitting idle, you’re generating (from the food you ate) about 90 W internally, so this radiation is sufficient to maintain your temperature (assuming you wear some clothes to reduce 123 W down to 90 W so you don’t get cold.) Of course, this is oversimplified since the air can conduct heat away (especially well if it’s moving), and if it’s calm, you’ll have a shell of warmer air around you (certainly within your clothes). Presumably you aren’t sweating, but if you are, evaporation (which depends on the relative humidity, among other things) will cool you down more.
In outer space, if you’re shaded from the sun, T[sub]1[/sub] is nearly zero, so P is big. If you are in sight of the sun, you’ll get the full flux at 1 AU. The ~1 m[sup]2[/sup] of you that faces the sun will intercept about 1000 W of energy, although much of that is in the visible wavelengths and will be largely reflected away by your white spacesuit.
{symbol}d{/symbol} for delta (but with square brackets instead of curly ones.) Use “s” for sigma.
Also note: Boltzmann
Thanks Pasta on all accounts.
Why do you assume space is cold? If the sun were shining on you strongly enough, it would probably get pretty hot.
I believe that spacesuits need to be equipped with mechanisms for both cooling and warming, depending on whether the astronaut is in the sun or in the shade.
I think in fact, our bodies rely entirely on internal sources to keep warm/keep a steady temperature, and external forces are more helpful for cooling:
Based on wikipedia :
I am lead to believe the following:
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That we can ignore the loss of heat due to evaporation, convection, and conduction since they basically don’t occur in a (space) vacuum.
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That since evaporation, convection, and conduction aren’t available, overheating could actually be a bigger concern if one is closer to a star than say, Jupiter.
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That metabolism (eating + muscle activation) is sufficient to replace all heat lost to the human body by radiation alone.
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Finally: If one could someone survive the other more relevant dangers such as inadequate air pressure, lack of oxygen, cosmic radiation, impact of high speed space rocks, etc., given enough to eat one could stave off freezing to death indefinitely.
Of course this would not be true for space reptiles and other steller ecotherms, who would have to find a nice space rock on which to bask in sunlight to keep warm.
Good link, thanks buddy.
It’s more accurate to say that the temperature of space is not well-defined than that it’s cold. A true vacuum simply has no temperature, as there is nothing there to measure. Space in the real universe is not quite a true vacuum, as there are a few hydrogen atoms per cubic meter and some background radiation. However, this is not really enough that you can say space is cold in the same way that a mass of liquid helium is cold.
Despite all that, an object in space can still be quite hot. A fast, hot particle can spontaneously emit a photon, thus losing energy and speed and becoming cooler. This photon can strike another particle, which then gains the energy and warms up. This is how the Sun warms the Earth, for instance. Note that the intervening space doesn’t change temperature, barring the occasional hydrogen atom that gets hit with a photon.
A partial vacuum. I don’t believe the area around a lightning bolt is especially close to zero pressure, at least not for more than a small fraction of a second.
Here’s a more general way of looking at it:
Absent any external heat sources, something placed into an environment will lose heat until it is at equilibrium with its surroundings. If the surroundings are hotter, the body will absorb heat until it’s at equilibrium with its surroundings.
The rate at which this happens depends on how the body is capable of shedding heat. Surrounded by atmosphere, or in contact with a colder surface, heat can be lost through conduction or convection, which is a rapid process. Absent any physical materials to conduct with, the body will lose heat through radiation, a slower process.
In the case of humans, we generate our own heat. Put a human in a vacuum, and he’ll rapidly overheat as his body generates heat vaster than he can radiate it away. Put the person in the arctic without a jacket and he’ll freeze because the environment around him can absorb heat faster than his body can make it.
The environment of space is mostly an insulator. However, the sun is a powerful radiation source, and will heat up objects that are exposed to it. An airless planet with one side facing the sun will have one very hot side and one very cold side, unless the planet is so efficient at transferring heat through itself that it can warm the dark side faster than the dark side can radiate the heat away. Same with a spaceship - the side facing the sun will heat up, and the side facing away will cool down. It won’t drop to 2.7K because energy is transferred from one side to the other, but there will be a big temperature differential. So you rotate the spaceship.
If you land on an airless body like the moon, heat will be transferred between the soles of your feet and the surface. There will be additional heat transfer due to a slight micro-atmosphere. So if you’re in an area that the sun doesn’t hit, you could lose heat rapidly through your feet if they’re not well insulated.
A planet like Mars, which has an atmosphere and temperates that can plummet well below -100 degrees C is very cold in temperature. But the atmosphere is much thinner, and therefore won’t be as effective at transferring heat away from a warm body. So it won’t take as much energy to stay warm as it would in an equivalently cold environment on earth. You’d want really good insulators on your feet and gloves, because everything you touch will be really, really cold. But you might get by with a light spacesuit with a small heat source, or even just a well insulated space suit.
The intergalactic medium in the Bootes void is also a partial vacuum, and it contains maybe 1 proton per 2 cubic meters.
What’s your point?
You have an odd definition of the word “vacuum.” While you’re correct that the air in the channel will expand (and very rapidly, too, since the bolt heats the air it passes through to around 30,000 C in just a teeny fraction of a millisecond) thus reducing the particle density, however, the pressure will spike enormously, since the surrounding air can only move out of the way at the local speed of sound; it therefor acts like an elastic container pushing back on the expanding air inside. This outward pressure pulse is what we hear as thunder, of course. I certainly wouldn’t call that a vacuum, partial or otherwise.
My point is that I suspect the volume of air around a lightning bolt is many orders of magnitude denser than 1/2 proton per cubic meter, although I haven’t been able to find any data about it one way or another. I realize that space is technically a partial vacuum rather than a true vacuum, but usually when you see the words “partial vacuum” it’s meant to indicate something that’s less dense than normal but still denser than space.
Not at all. A vacuum is a volume of space which is devoid of matter. We usually measure pressure to determine how good a vacuum is, but that measurement alone doesn’t tell us how many particles there are per cubic meter of space. At a high enough temperature, even the vacuum of the Bootes void could exert 1 atm of pressure. Would that suddenly make it not a good vacuum? No.
The earth is kept warm by the sun. The earth continually receives and absorbs energy from sunlight. This results in the earth getting hotter and hotter. However as the earth gets hotter it radiates more energy into space. Eventually a balance is reached and the input radiation from the sun equals the output radiation from the earth.
I’m not at all sure that you would freeze to death in space near the earth. After all, the earth isn’t freezing cold and it’s in space. True, the earth’s atmosphere provides a greenhouse effect but I don’t think the termperature would be below 0 C even without that.
The black body temperature for objects at earth’s distance from the sun is -2°F.
You wouldn’t be toasty even if you wrapped yourself in a black quilt.
The Aristotlian process of deducing the result of a real-world process via the application of an ontological framework is an old and timeworn tradition of almost invariably getting the wrong answer, or on rare occasions, the correct answer via a completely and utterly incorrect understanding of the underlying mechanics, which then had to be rectified, often at great personal cost and sometimes injury, by succeeding experimentalists and emperical theoreticians who were ill-regarded for challenging the “perfect” symmetry of Plato’s worldview. In the case of your original post, you seem to be confirming the o.p.'s presupposition that a vacuum is cold before reasoning that “heat”–a quality you later deigned unworthy of actual definition–is “stopped” from being transmitted through a vacuum.
Later, you use an analogy of basketballs which are somehow embedded in space to represent heat, and subsquently reasoned that could therefore be no basketballs (heat) in space. Analogy and metaphor can be useful for the purposes of illustration–indeed, we’d have a great deal of problem explaining quantum mechanics nonmathematically without resorting to analogies–but reasoning from an analogy will typically give you a totally wrong conclusion, because an analogy is a comparison between unlike things and outside the immediate scope of the analogy the relationship being illustrated likely diverges. An astute and quite amusing example of this is the “Burn The Witch!” skit in Monty Python’s The Holy Grail. It is useless to talk about heat transfer without first figuring out what in the heck heat is, just as one cannot define a witch by whether she floats like a duck because she burns like wood, which you also burn just like a witch.
Heat–that is, particles in energetic motion–have no difficulty whatsoever travelling through a vacuum; indeed, the lack of pressure guarantees that they’ll travel far. Similarly, heat energy that is radiated away from a body in the form of electromagnetic energy (infrared or otherwise) will transit unimpeded through a vacuum. However, the normal methods of heat transfer that we’re accustomed to on terra firma–convection, conduction, and evaporation–don’t occur in a pure vacuum owing to–by definition–the lack of other particles for your particles to bump up against and give away some of their energy. That’s why a vacuum is a good insulator for conductive and convective heat transfer. Vacuum itself has no temperature, again by definition; the background radiation of the cosmos has a very low temperature, thanks to the expansion of the universe, but in the close proximity to a flaming ball of gas, you’re going to absorb a lot of incoming solar radiations, which you’ll absorb and will make you hot, and then reradiate part of that energy on your shaded side, which will make that cold.
In fact, on the airless surface of the Moon, objects in direct sunlight can get up to 390 Kelvin (about 240°F), which requires that pressure suits for Lunar excursions have both a protective layer to reflect thermal energy absorbed by the outer protective shell, and a conditioning unit that keeps the air in the suit a pleasent temperature for the occupant.
However, if ejected out of a spacecraft sans suit, you probably wouldn’t have much time to appreciate the temperature before the effects of vacuum and asphixiation wrested your attention. If you’re really, really lucky a passing spacecraft might flit by and pick you up spontaneously, but the odds are about 2 to the power of an Islington flat phone number at which there was once a fancy dress party at which you met a girl that you totally failed to get on with. I don’t think I’d play the odds; I’d wear my pressure suit and be sure to bring along the helmet, even if I was just going on an excursion in the maintenance pod.
Stranger
Not too comfortable.
Why does the black body temperature matter? All that tells you is that after you die, your body will cool down over time until it gets to that temp. As long as you’re alive, you’re a heat generator. To determine whether or not you’ll be toasty warm or freezing cold you have to know how much energy is hitting you vs how much you are generating. If the combination of your internal heat plus the energy from the sun is greater than the rate at which you can radiate heat away, you will get warmer, which will increase the rate at which you radiate away the heat. Eventually, you’ll reach a new, higher equilibrium temperature or you’ll die.
If you radiate heat faster than the combination of internal heat plus solar radiation hitting you, you’ll cool down until you hit a new equilibrium temperature or freeze to death.