Supplemental Materials

Supplemental Materials

Thermal expansion is the tendency of matter to change shape, area, and volume in response to a change in temperature. When a substance is heated, the kinetic energy of the object increases and causes it to expand depending on its atomic structure. Likewise, when a substance is frozen, the kinetic energy of the object decreases and causes it to condense; this absence of heat is called negative thermal expansion, while the heating of an object is positive thermal expansion.

There are a few trends observed within the phenomenon of thermal expansion. The stronger the bonds are between the molecules, the less an object expands when heated, or condenses when cooled. Similarly, this same trend is seen with increasing bond energy. Solids tend to keep their shapes better when expanding or condensing; therefore it is sometimes hard to observe the change of a solid when it is being heated or cooled. Liquids and gases are easy to observe as they undergo thermal expansion as long as they are contained effectively.

In order to figure out the relationship between area and thermal expansion, a formula was made to calculate how much a solid would expand based on a fraction of the heat it is being subjected to and the original area of the solid. To calculate the area, the formula is below:

A = 1/A * dA/dT

Similarly, there is a relationship present between the volume of a liquid and thermal expansion; paired with its own formula to calculate the change in volume accounting for the original volume and a fraction of the subjected temperature. This formula can be found below:

V = 1/V * dV/dT

There are another set of similar equations that solve for both the area after thermal expansion of a solid, and the volume after thermal expansion of a liquid. Both of these equations include a new variable called the linear coefficient of thermal expansion. This variable is represented by a and it a material property that is indicative of the extent to which a material expands upon heating and has units of the reciprocal temperature. The linear coefficient of thermal expansion relies on the direction it is measured in; this is known as being anisotropic. 

On an atomic level, thermal expansion can be described as an increase in the average distance between the atoms present. This phenomenon can be easily shown through the use of a potential energy vs. interatomic spacing curve for solids. The equilibrium of this graph rests at 0 K; the graph usually dips down from 0 K in either an upward or downward curving parabola or an asymmetrical curve that evens out around a potential energy.

Figure 1: Potential Energy vs. Interatomic Distance Curves

Thermal expansion is due to the asymmetrical curving of the potential energy trough; there is an imbalance in potential energy, causing the object to increase or decrease in size to reflect that. If the curve was symmetrical, thermal expansion would not occur because there is no net change in interatomic separation. 

References:

Callister, William D., and David G. Rethwisch. "Chapter 19.3 Thermal Expansion." Materials Science and Engineering: An Introduction. 9th ed. Hoboken, NJ: Wiley, 2014. 790-93. Print.

G. Elert, “Thermal Expansion,” Thermal Expansion – The Physics Hypertextbook. [Online]. Available: http://physics.info/expansion/. [Accessed: 11-Apr-2017].