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Linear Expansivity
Most solids (and liquids*) expand when the temperature increases.  
According to the Kinetic Theory of Matter, the expansion is due to the increased amplitude of vibration of the particles.  
*see below for an important exception  
   
Consider a metal rod of original length, Lo  
Let the temperature change by ΔT, causing an increases in length, ΔL, as shown below.  
 
   
Experiments show that, for a wide range of temperatures, ΔL is directly proportional to ΔT.  
   
Now consider a rod of original length 2Lo (made of the same metal).  
Along the length of this rod there will be twice as many "layers" of atoms all increasing their amplitudes of vibration as the temperature increases.   
We would therefore expect this rod to expand by 2ΔL, for the same increase in temperature.  
Experiments confirm this hypothesis.  
   
Summarizing the above:  
 
 
therefore  
 
which means that  
 
The constant is called the linear expansivity of the metal, given the symbol a (which is why I kept writing out "is proportional to"!).  
Definition:  
The linear expansivity of a substance is the fractional change in length of a sample of the substance per degree C change in temperature.  
units C-1 (or K-1)  
   
Rearranging the above equation gives an expression for finding the length, L, of a sample of material, after a given temperature change, ΔT.  
 
   
The "Anomalous" Expansion of Water  
The important exception, mentioned above, is the case of water.  
Although most substances expand when the temperature increases and contract when the temperature decreases, water does the opposite but just between 0C and 4C in other words, just in the region where it is changing into ice.  
The shape of a water molecule is something like this:  
 
The next diagram shows a group of water molecules in a sample that we will imagine is at, say, 20C (so, well away from its freezing point).  
 
The continual oscillation of the molecules prevents them from forming bonds and the substance is in the liquid state.  
However, if we decrease the temperature, the amplitude of the oscillations decreases and the molecules start to bond together in a more regular arrangement which takes up a bit more space, as shown here.  
 
The forces resulting from this expansion can be quite large.  
If water freezes inside sealed pipes in winter, the pipes can be damaged.  
Water freezing in cracks in roads sometimes damages the road surface as this expansion occurs.  
   
However, there is some good news here.  
Fish in ponds can survive in winter because the frozen water, being less dense, floats up to the surface and then prevents the whole pond from freezing (unless, of course, the temperature goes unusually low).  
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