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previous index next Thermal Expansion and the Gas Law Michael Fowler 4/8/06 Coefficients of Expansion Almost all materials expand on heating—the most famous exception being water, which contracts as it is warmed from 0 degrees Celsius to 4 degrees. This is actually a good thing, because as freezing weather sets in, the coldest water, which is about to freeze, is less dense than slightly warmer water, so rises to the top of a lake and the ice begins to form there. For almost all other liquids, solidification on cooling begins at the bottom of the container. So, since water behaves in this weird way, ice skating is possible! Also, as a matter of fact, life in lakes is possible—the ice layer that forms insulates the rest of the lake water from very cold air, so fish can make it through the winter. Linear Expansion The coefficient of linear expansion α of a given material, for example a bar of copper, at a given temperature is defined as the fractional increase in length that takes place on heating through one degree: ( ) 0 1 w h e n 1 LLL L TT →+ Δ=+ C Of course, might vary with temperature (it does for water, as we just mentioned) but in fact for most materials it stays close to constant over wide temperature ranges. For copper, 6 17 10 . Volume Expansion For liquids and gases , the natural measure of expansion is the coefficient of volume expansion, β . ( ) 0 w h e n 1 VV V V C Of course, on heating a bar of copper, clearly the volume as well as the length increases—the bar expands by an equal fraction in all directions (this could be experimentally verified, or you could just imagine a cube of copper, in which case all directions look the same). The volume of a cube of copper of side L is V = L 3 . Suppose we heat it through one degree. Putting together the definitions of , αβ above, () 33 1, 1 o r 1 LL L L V βα . V
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2 So () ( 3 11 ) β α += + . But remember is very, very small—so even though 3 2 3 3 3 ααα + ++ , the last two terms are completely negligible (check it out!) so to a fantastically good approximation: 3. = The coefficient of volume expansion is just three times the coefficient of linear expansion. Gas Pressure Increase with Temperature In 1702, Amontons discovered a linear increase of P with T for air, and found P to increase about 33% from the freezing point of water to the boiling point of water.
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ThermProps - previous index next Thermal Expansion and the...

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