PX154 - B2 - thermal expansion

thermometer

• heating causes expansion
  • liquid rises up the tube as the temperature increases
  • but the glass expands too
  • most materials expand as they heat up but different materials expand by different amounts
    • we define the expansion coefficient
      
• why do materials expand?
  • as the temperature increases, the mean atomic separation increases (atoms vibrating about the mean position)

linear expansion coefficient

• [YF17.8]
  • 
• new length: $L=L_0+\mathrm{\Delta }L$
  • $\mathrm{\Delta }L$ can be defined in terms of the change in temperature
  • $\mathrm{\Delta }L=\alpha L_0\mathrm{\Delta }T$
    • where $\alpha =$ linear expansion coefficient
  • works for moderate temperature changes
  • then we define
  $$\alpha =\frac{1}{L_0}\frac{\mathrm{\Delta }L}{\mathrm{\Delta }T}$$- its units are $K^{-1}$
  • eg: [YF table 17.1]
    

volume expansion coefficient

• in the same manner as in linear expansion coefficient, we can define the volume expansion coefficient:

- eg: [YF table 1.2]

- can see $\beta =3\alpha$
- [YF P576] for derivation:
- comments:
- we are considering isotropic materials which have the same properties in different directions
- we are assuming that the coefficients $\alpha$ and $\beta$ are constant
- some materials have odd behaviour
- eg: water near $0\mathrm{°}C$ or invar