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How Cold

  1. Sep 9, 2003 #1
    is it in the shade in outer space?
     
  2. jcsd
  3. Sep 9, 2003 #2
    I'm sure someone more qualified to answer this will chime in soon, but I'd expect it to be around 3 degrees Kelvin, in other words the same temp as the cosmic background radiation.
     
  4. Sep 9, 2003 #3
    That is much colder than I
    thought. How do they prevent the
    shuttle, say, from breaking apart
    because of the temperature dif-
    ferences between the sunny and
    shady sides?
     
  5. Sep 9, 2003 #4

    selfAdjoint

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    I believe it does creak a bit, as astronauts have reported. The ISS still more. This is a good point and thermal stress is one of the things the space engineers have to deal with.

    Notice that satellites and space craft are mostly made out of thermally conductive metal. So they tend - only tend - to assume a thermal equilibrium, and that is actuallly pretty hot for objects close to earth's orbit. I believe the black body temperature due to the sun's radiation at earth distance is about 80o F.
     
  6. Sep 9, 2003 #5

    marcus

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    I understand that skylab was always rather noisy because of expanding
    and contracting of various parts---creaking, popping, drum-booming----the sounds that metal structures make under uneven thermal stress. Maybe they just allow for it in the design.

    this is a fun question
    and I am not offering an actual answer---only a discussion of it
    I agree with radagast about 3 kelvin
    but it makes one think about temperature and how its defined
    (strictly speaking for systems in equilibrium, and yet
    practically nothing is ever completely in equilibrium
    so there is always a rakish ad hoc element in applications.)

    and to extend the question of Zooby to the moon:
    "how do they keep the moon from breaking apart
    because of the temperature differences between
    the sunny and shady side" which might be
    one of those classic evocative questions
    like "why is the sky blue"

    There is always conduction laterally from the hot frontside around to the cold backside, or thru the body if it isnt hollow
    but forgetting about conduction think about how a side of the moon which has been in the sun and now finds itself in the shade could cool off
    what could cool it, since it is in vacuum?

    only its own radiation-----so it gradually radiates off infrared.
    The neat thing about this is that it follows an amazing fourth-power law discovered by two Viennese gentlemen of the Victorian era and half raised to the fourth is a sixteenth

    so that after the temp has fallen down to one half of what it was, the thing is radiating away heat only a sixteenth as fast

    and so it goes----slower and slower
    when it is down to 1/3 of its original temp then
    the rate energy is leaving it is down to 1/81 of
    the original rate----very slow.

    so once a thing has been exposed to sunlight and soaked up a little heat, if you put it in shade it will take a REALLY long time
    to cool down to 3 kelvin----sitting in the vacuum with nothing
    but its own radiation as a way of getting rid of heat.

    this is just one thought evoked by that question
    I could imagine people writing in with quite a few other
    observations about it, and related questions like why
    does the equilbrium temp of planets go as the square root
    of the distance from the sun so that if a planet is 9 times
    farther away its temperature is not 1/9 but instead is 1/3
    as high, and stuff like that
     
  7. Sep 9, 2003 #6

    marcus

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    Self Adjoint, I didnt see your reply when I wrote mine, could have simply not replied! Yes, you say something like 80F

    What I find in a battered handbook is 394 kelvin for the flat surface facing sunlight at this distance from the sun
    (the hot sidewalk on which one fries the egg, on the moon
    to make sure there are no clouds)

    and beautifully enough a generic black ball or let us say a cannonball of any size at this distance from the sun has an equilibrium which is
    394 kelvin divided by the square root of 2

    which is 279 kelvin

    so I guess it would not be quite 80 F but more like 50 F (and my handbook can be a bit off) but both our estimates would be in the ballpark
    -------------------------
    edit:
    numbers often frustrating, using 1370 watt per square meter as
    solar constant and 5.67E-8 for StefanBoltzmann I actually
    calculate 394 kelvin, in agreement with handbook.
    But there is a bit of play in the solar constant and some people
    use 1380, so they'd calculate something a bit higher for
    the equilibrium temp
     
    Last edited: Sep 9, 2003
  8. Sep 9, 2003 #7
    SelfAdjoint,

    What's your guess on how close a
    satellite gets to blackbody?

    I think I'd jump right out of my
    skin if I were on the shuttle and
    heard it start creaking.


    Marcus,

    Fascinating stuff! It's comforting
    to learn the moon won't be crack-
    ing apart from temperature dif-
    ferentials in the near future.

    I completely blanked out on the
    subject of air and was imagining
    that as soon as a thing went into
    the shade in outer space it would
    be assaulted by unbelievable cold.
    But of course, as you point out,
    it isn't. All that happens is that
    it begins to radiate its heat. It
    is nice to find out that even this
    becomes increasingly slower as it
    progresses. I feel better about
    the shuttle. I don't like the
    sound of those Skylab noises, tho.

    -Zooby
     
  9. Sep 9, 2003 #8

    marcus

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    Zooby, to me the most aesthetic aspect
    is a certain squareroot of two
    that gets into the picture


    in vacuum at any distance from sun
    a generic flat surface facing sunlight reaches some equilibrium temp
    (which depends on the distance)
    and that temperature is the squareroot of two
    times the temp that a generic cannonball object reaches


    because the ball has four times the surface area
    of a flat plate that is intercepting the same amount of sunlight
    and because the fourth-root of four is the squareroot of 2

    Pythagoras would have liked that, too bad no one told him

    equilibrium temp depends on balancing incoming and outgoing
    so it is determined by the fourthpower radiation law
     
    Last edited: Sep 9, 2003
  10. Sep 9, 2003 #9

    LURCH

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    Regarding sattelites and such, have you evernoticed that most sattelites spin along their own axis while orbiting? That's one way of deminishing the problems that come with unneven heating. Keep in mind, an object in orbit doesn't just have to deal with the thermal differences involved in going from the Sunward side of a body to its dark side; the object also has its own shade. The Shuttle and stations have "circulatory systems" to help cope. Thay continually circulate fluid around just under the skin, taking heat from one side to the other, while the craft is exposed to sunlight.
     
  11. Sep 9, 2003 #10
    Yes, this huge difference between
    the sun side and shade side of
    an object in space is exactly what
    got me wondering if it posed a
    threat to the shuttle. Not that
    the sun side would get very hot
    but that the shade side was SO
    dam cold that the temperature
    difference would cause an
    untenable contraction of the mat-
    erial on that side.

    Do you have any idea what fluid
    they circulate, Lurch? What
    earthly anti-freeze could with-
    stand 3 Kelvin?

    Yes, I had this notion that satel-
    lights rotated on their own axis
    but I could figure how they keep
    their antennae oriented if they
    rotate. Or cameras or reflectors?

    -zoob
     
  12. Sep 9, 2003 #11

    selfAdjoint

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    My 80oF figure came out of an old Willy Ley book or article. He was pointing out that the problem in space stations (which did not exist when he wrote) was not keeping warm, but getting rid of heat.
     
  13. Sep 9, 2003 #12
    And did that actually turn out to
    be a problem? Given what marcus
    brought up about the slow rate
    of radiation it doesn't seem
    unlikely.
     
  14. Sep 9, 2003 #13

    marcus

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    Zooby indeed because of the slow rate of radiating heat
    it is hard and even costly to dump waste heat
    every energy conversion process, life, electric power generation,
    even running a computer, produces low-grade waste heat which
    if it builds up is unconfomfortable (and eventually worse than uncomfortable)
    but at room temperature waste heat radiates slowly and so
    you need a very large radiator surface
    The good Willy calculated this using the fourth power law
    of radiation.

    both willy and selfadjoint are right. if I have said anything inconsistent with them I must have made an error.
     
  15. Sep 9, 2003 #14

    LURCH

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    I'm not sure what they use, I always assumed it was regular anti-freeze. Keeping in mind, of course, that the fluid never actually drops to 3o K; the problem is getting cool enough. As the fluid gets 'round to the cold side, it begins to radiate heat, but it never gets rid of all the heat it picked up on the warm side. So the whole sattelite maintains a (nearly) uniform temperature, and the fluid doesn't experience any real extremes.

    As an example, I do know what fluid ciculates in an EVA suit to perform the same function. It's water. Or at least, it used to be, I'm not sure if that's what they still use.
     
  16. Sep 10, 2003 #15
    For someone like myself who lived
    in the frozen wastes of Minnesota
    for eight years this all comes as
    a counterintuitive realization.
    It takes a bit of work to grasp
    that without convection and con-
    duction a Minnesotan could end
    up being cozier on a space station
    where the temperature outside is
    three degrees above absolute zero
    than he would just about anywhere
    inside in Minnesota during the
    winter.[/B][/QUOTE]
     
  17. Sep 10, 2003 #16

    LURCH

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    This week in Space Weekly:

    New McDonald's technology allows NASA engineers to "keep hot side hot; cool side cool"!
     
  18. Sep 11, 2003 #17
    I have been thinking about this a little and nothing obvious strikes
    me about Vienna during the reign
    of Victoria that would induce two
    gentlmen to start wondering about
    radiation in the cold vaccuum of
    space. What is their story?
     
  19. Sep 11, 2003 #18

    selfAdjoint

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    Yes, in spite of frigid phenomena due to earth's tilt guaranteeing that its subpolar regions are shaded for months at a time, the earth is sensitive to waste heat radiation. Futurists predict that if all the third world were brought up to US standrds of energy usage the resulting waste heat would warm the earth by several degrees. This is in addition to the usual greenhouse sources of global warming.
     
  20. Sep 11, 2003 #19

    marcus

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    Dont have time to research it adequately. Probably answer is in
    some biography or history of science book. Here is some
    background detail (but cannot answer main question):

    Stefan was secretary of the Vienna Academy of Sciences from 1875 and discovered this thing about radiation in 1879. which then Boltzmann explained on theoretical grounds in 1884.
    So Stefan was already a recognized Austrian science dude when he discovered the fourth-power law experimentally.
    It was waltz time in Vienna and the Impressionists were
    painting in Paris. Europe hadnt had a major war since Napoleon (going on 70 years)

    Ludwig Boltzmann (1844-1906) was known for being something of a dandy and a playboy. He explained the second law of thermodynamics by the statistical behavior of atoms and molecules at a time when a lot of physicists refused to believe in atoms. As he got older he suffered from depression and eventually shot himself at some scenic vacation spot in Italy. It was not always easy to have as much fun as Boltzmann thought he should be having. He managed to lead a rather flamboyant life and be world-class creative theoretical physicist to boot.

    Josef Stefan was an experimentalist. As far as I know he was just this Middle European guy who happened to measure the glow from hot objects and who happened to find out that if you made an object twice as hot it would radiate 16 times as much power.
    It's very generic stuff, the hot object does not have to be in space. It can be an electric hotplate. It can be the sun. If the sun were twice the temp it is then it would make 16 times as much light.

    Boltzmann, the bon vivant with the big beard, developed theory around this experimental fact. It became known as the
    "Stefan-Boltzmann Law" or more formally as the
    "Stefan-Boltzmann Fourth Power Radiation Law".

    But Boltzmann did a lot else besides. He invented the fundamental physical constant known as "Boltzmann's k"
    A lot of formulas in a bunch of different fields have a "kT" in them.
    If you look at formulas for how a transistor works you see kT, or about heat capacities and melting points, kT, or how pressure and volume are related to temperature in gasses, kT, or the speed of sound, chemical reaction rates, whatall. If you looked up the formulas for how a star works inside, and how it is structured, they would have a lot of kT terms.

    the unit in which Boltzmann's k is expressed is the unit of entropy,
    or if you like to think of it another way, the unit of heat capacity:
    amount of energy per degree of temperature.
    Boltzmann's k gets into about as many formulas as Planck's hbar.

    the Stefan-Boltzmann Fourth Power Radiation Law says the power (watts) that something radiates is proportional to the fourth power of its temp

    power = sigma T4

    where the constant sigma is a hairy combination of k, hbar and c:

    sigma = k4/hbar3c2 multiplied by, of all things, pi2/60

    Now this, I am afraid, is only background. Your question is how did they happen to investigate the relation between how hot she is and how brightly she glows, where she is a generic object, and how did they happen to find out this deep hidden proportion in nature. And why in Vienna.
     
    Last edited: Sep 11, 2003
  21. Sep 11, 2003 #20

    russ_watters

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    You have to remember that since there is no air in space heat can only be carried away by radiation. So its not like the skin temperature of the shuttle is 3K.
     
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