|MadSci Network: Physics|
Believe it or not, the answer depends on a lot of little details in how you run the "experiment". I would have to say that in the most general interpretation of the experiment you are describing, the two objects will end up at the same temperature. Here is the idealized experiment to confirm this: Two objects of exactly the same material, one coated white and one coated black, are placed into a room that is completely shielded from ALL radiation. Hypothesis: Both plates will eventually reach the ambiant temperature of the room and stay that way. WHY? The mechanism by which dark objects get warmer is a function of the amount of radiation that is absorbed by them. In fact, objects are dark in color, BECAUSE they absorb radiation in the visible band (i.e., the bands that we can see with our eyes). It also happens that many dark materials that absorb visible band radiation also absorb radiation in other bands (for example infrared, uv, xrays, microwaves). The absorbed radiation is turned into thermal energy by "exciting" the atoms in the absorbing material, thus heating the object. Lighter objects reflect visible radiation making them appear bright. Many light objects also happen to reflect many other bands of radiation. Because the radiation is reflected away, the material stays cool. Almost all materials are a combination of "light" and "dark", which means that they both absorb some radiation in some bands and reflect some radiation in other bands. If you remove all sources of radiation, then eventually both objects will reach the ambient temperature of the room through conduction between the objects and the air. Conduction is another form of heating that occurs when one molecule touches another molecule at a different energy level and they exchange some of the energy, like a pan on a heating element. In this case, like an oven or a refrigerator, the air molecules at one temperature bump into the "plate" molecules at a different temperature causing them to eventually get to the same temperature if you wait long enough. THE OTHER SIDE OF THE STORY: By coating the objects, you have changed the material makeup of the objects, so they are NOT THE SAME, and it is particularly true of the critical outer surface, which is where most absorption of radiation will occur. Furthermore, it is difficult, or perhaps impossible to create a room completely devoid of radiation, since all objects that exist above absolute zero give off some radiation (black body radiation), including the air in the room and the plates. WILL THE DARK PLATE BE WARMEST? Not necessarily. First, the radiation bands that are absorbed depend upon the type of coating. Thus a plate with a dark coating that absorbs mostly in the visible bands (making it dark to our eyes), but does not absorb well in other bands, may well absorb less energy and be cooler than a coating that reflects visible light, but absorbs microwave and infrared radiation. Complicating this, there is the issue of "emission". So called "black bodies" that absorb radiation well also give up their energy in the form of radiation better than "white bodies". Thus, the "black" plate may cool (give up its thermal energy) faster than the "white" plate, since it is more like an ideal "black body". Since cooling is an "infinitely" long process, the black plate MAY ALWAYS BE COOLER than the white one in the dark room. SO, WHATS THE ANSWER? For most purposes in the real world, the "black" and "white" plates in the "dark" room will converge to the ambient temperature of the room. From a strictly physics-based point of view, however, it is more complicated. It would be difficult (or perhaps impossible) to create the idealized conditions needed to prove this and the results depend heavily upon the makeup of the objects and the surrounding room. Let me know if this answers your question. I am curious to hear what you decide is "your" answer after reading this. Yours in science, Todd Jamison email@example.com
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