MadSci Network: Physics

Re: Once and for all, is space hot or cold?

Area: Physics
Posted By: William A. Wheaton, Staff Scientist, IPAC, Infrared Processing Center
Date: Wed Nov 5 01:22:29 1997
Area of science: Physics
ID: 877786437.Ph

The Temperature of Space

Is Space Hot or Cold?


Once and for all, is space hot or cold?

Submitted 26 October 1997 by Todd Mitchell of Ranoke, Virginia, USA.

My coffee stays hot all day in my vacuum bottle, but the shuttle crew has to be protected from the 'cold of space.' What is the deal?


4 November 1997

If there is a "once and for all" answer to your question, it is probably that space, (insofar as it is nothing!), does not have a temperature at all -- only matter and radiation can be described by temperature. So we have to talk about the temperatures of the various things which are present in space, and the way those things may interact with whatever it is we are interested in, like an astronaut. The subject is intrinsically complicated, because we have to take inventory of all those components, consider their temperature and how they are coupled to the astronaut, and then add up their effects to get the result. It is basically a bookkeeping kind of thing. Depending on the circumstances, we may get very different answers in situations which at first seem similar, because the balance tips one way or the other.

I will return to the situation in space below, but first let's deal with your coffee, which gives a simple concrete example of what we are talking about.

The coffee stays hot, certainly not because the vacuum in the thermos bottle is hot, but because the bottle is carefully constructed to prevent the heat initially present in the coffee from leaking out into the colder room. There are in general three modes by which heat is transported, conduction (eg, when you touch a cold piece of metal), convection (eg, the violent boiling motion of a pot of water that carries heat from the bottom to the top), and radiation (eg, as the heat of the Sun reaches us through space). Of these three, two require matter as the transporting agent. Thus the vacuum bottle severely hinders both conduction and convection, because of the evacuated space surrounding the coffee. The remaining mode, radiation, does carry heat out slowly. (Note that by "radiation", here of course I mean not nuclear or ionizing radiation, but rather ordinary electromagnetic waves, including visible light and also radio and submillimeter waves, infrared, ultraviolet, x-rays, and gamma-rays. These are all exactly like light, except for the speed of vibration, which for visible light we call color.) The bottle is typically silvered because a perfectly shiny reflective surface can neither absorb nor emit radiation. (I grant that it is not entirely obvious that a perfect reflector, which cannot absorb radiation, also cannot emit any. This fact is a consequence of the Second Law of Thermodynamics, one simple form of which says that heat, of itself, cannot flow from a cold to a hot object. It is not difficult to understand, but it would take us too far afield to prove it here. However, please note one important related fact: a perfect absorber, or black body, is also the most efficient possible emitter. We will return to such emitters below.) Because the silvering is not perfectly reflective, some heat is radiated, and your coffee slowly cools off. Also, it is necessary to support the inner bottle and the coffee, by a thin layer of glass at the mouth. Some heat is conducted through this glass, and also through the cork at the top.

Returning to the astronaut, who may be disconnected from mechanical support or connection to external matter, the balance of radiation, emitted and absorbed, is often the dominant effect. Objects in space near the Earth when exposed to the direct Sun can, like hot pavement, quite easily become warm enough to burn the skin. especially if they happen to be relatively darkly colored in the visible wavelengths of sunlight, but cannot easily lose heat. Similarly, objects shaded from the Sun can, like the night side of the Moon, cool to near or below dry ice temperatures, cold enough to cause harm.

In the vicinity of the Earth, the dominant contribution to the radiation energy in space is the energy from the Sun, which is peaked around a wavelength of 5500 , or 5.5 X 10-5 cm, near the middle of the visible range, with a spectral shape which is fairly close to a universal mathematical form associated with the perfect black body emitter (or perfect absorber, as mentioned above), at a temperature of some 5760 K (degrees above absolute zero). The power at the Earth's distance from the Sum is about 1.38 kW per m. decreasing with distance R according to the same 1/R law that describes gravity. Another important source of radiation near here is the Earth itself, which has somewhat less power than the Sun (and drops rapidly, of course, as you depart from the immediate vicinity of the planet), and a complicated spectral shape, from the visible to the mid-infrared, a mixture of reflected light from the Sun, and thermal radiation from the surface and various layers of the atmosphere.

We are all generally familiar with the behavior of a piece of metal as it is heated. At lower temperatures we see nothing, but may feel the infrared radiation, which is already present, as heat on our hand. As the metal becomes hotter still, it glows deep red, then yellow, then brilliant white. Any actual piece of metal will melt long before it becomes as hot as the Sun, but many hot stars shine bluish-white, and we may have to protect our eyes from the copious ultraviolet light emitted at the high temperature of electric arcs.

Crucial to any understanding of radiation (or temperature) in space, is the fact that all macroscopic bodies emit electromagnetic radiation constantly, depending on their temperature, essentially due to the constant bumping and rattling of the electric charges (mostly the electrons, in practice) which they contain. In general, the hotter they are, the brighter, and the higher the frequency of the emission. The spectral shape is ideally of the universal black body form, but is modulated for real bodies by (often complicated) surface properties (emissivity / reflectivity, as noted earlier) of the body. The universal black body spectrum peaks at a frequency proportional to the temperature T; the total power emitted per unit area is proportional to T4. This thermal radiation, which is emitted by everything, means that the actual temperature of a body in space is determined by the balance between the rate at which it loses energy due to its own heat radiation, and the rate at which heat is received from surrounding bodies.

For the special case of a perfectly black, highly conductive sphere in the Solar System a distance R from the Sun, absorbing solar radiation from one side, but radiating in all directions equally, it turns out that the temperature drops with distance from the Sun as the square root of 1/R:

T = 277 K (1 AU/R)

where 1 AU is the average distance from the Earth to the Sun, and T is the "characteristic temperature" at a distance R from the Sun. This defines a kind of typical temperature around the Solar System, from earthlike-temperatures in our vicinity, to the cryogenic temperatures characteristic of the outer Solar System.

Looking out at the cosmos, we can actually see the red-shifted remnant of the Big Bang. When the Universe first became transparent, it emitted light like a black body with a temperature of about 3,000 K. Since this beginning, the expansion of the Universe has cooled that radiation (altering both its frequency and intensity) to correspond to the emission of a black body with a temperature of 2.73 K, roughly the temperature of liquid helium, which is pretty cold by normal earthly standards. The Cosmic Microwave Background radiation has a general spectral shape much like the spectrum of the Sun, but peaks at a wavelength of about 1 mm, and is some 20 trillion times dimmer.

This 2.73 K is the temperature which would finally be reached by a body far, far from any stars or planets, simply cooling by the radiation of its own initial warmth, until it reached a balance between the radiation received from space and the emission due to its own temperature. Because the 2.73 K Cosmic Microwave Background radiation is so far below room temperature, and because it pervades the cosmos, space may in this sense be fairly said to be "cold".

But the temperature of an object placed in space can in principle be anything between 2.73 K and the temperature of the hottest body illuminating it. With a large solar furnace in space near Earth we could theoretically arrange to heat an object to a temperature of nearly 5760 K, though it would have to be essentially completely surrounded with highly reflective mirrors, probably made of carefully-cooled SiC, or something similar. Similarly, by carefully shielding it from the Sun, Earth, Moon, and even Venus, one might in principle be able to cool a body to near 2.73 K (again, this is actually quite difficult in practice).

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