PhysicsLAB Resource Lesson
Thermal Expansion

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The formula used to calculate the linear expansion of a solid due to a change in temperature is
 
ΔL = αLΔT
 
  • α is the coefficient of linear expansion (m-1)
  • L is the original length (m)
  • ΔL is the change in length (m)
  • ΔT is the change in temperature
 
When ΔT is positive, ΔL is positive. The new length L' = L + ΔL. If you examine a graph of Length vs Temperature, the slope of this line will be the product of αL. Thus, the steeper the line, the greater the value of α.
 
 
Let's practice some examples.
 
 A piece of aluminum siding is 3.66 meters long on a cold winter's day, -28°C. How much longer is it on a very hot summer's day, 39°C?

 A piece of steel is 11.2 meters long at 22°C. Later, after being heated at the foundry, it was measured to be 11.7 meters long. What was the steel's final temperature?

 
Volume Expansion
 
The formula used to calculate the amount of volume expansion a solid experiences when there is a change in temperature is
 
ΔV = βVΔT
 
  • β is the coefficient of volume expansion (m-3)
 
For solids, β is approximately equal to 3α. This value seems reasonable since a solid expands equally in all three dimensions and α is the coefficient of linear expansion. For liquids and gases, there are only coefficients of volume expansion. In the case of gases, these coefficients principally depend on whether the gas is monatomic, diatomic, or polyatomic.
 
Some common coefficients of expansion are given in the following table.
 
material α x 106 β x 106
diamonds 1.2 3.5
iron/steel 12 36
brass 19 57
aluminum 25 75
mercury   182
gasoline   ~950
 
 
Ice
 
When most objects absorb heat, they usually expand; ice and water are exceptions. Due to the open-lattice structure of ice crystals, and the fact that the hydrogen bonds are strongest at particular angles, the volume of a certain amount of water in its solid (frozen) state is greater than its volume in its liquid (water) state. That is why ice floats on water. When frozen, ice's lower mass density results in the buoyant force of the surrounding water being greater than the weight of the ice cube. This accounts for floating icebergs and ice cubes.
 
As the ice beings to melt, the crystalline structure breaks down, initially creating a microscopic slush. This mixture of ice and water dramatically reduces the space between the water molecules, at about 10 ºC, all of the ice's crystalline structure has collapsed. At the same time as the ice crystals are collapsing, the rising temperature is increasing the molecular motion of the water molecules, resulting in expansion. These combined effects of contraction and expansion, result in water achieving its highest density at 4 ºC.
 
 
In its liquid state, the hydrogen bonds between the water molecules results in water achieving its maximum density at 4 ºC. This allows large bodies of water to never freeze solid since convection currents result in the bottom of the lakes or oceans remaining at 4 ºC. The top of the lake or ocean may be frozen, but in their depths, water is still present in its liquid state. Remember also that water's very high specific heat and the fact that it is a poor conductor of heat ensures Florida's and Hawaii's temperate climates,
 








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