Chapter 1.1, Problem 8P

For a solid, we also define the linear thermal expansion coefficient, a, as the fractional increase in length per degree: $a\equiv \frac{\Delta L/L}{\Delta T}.$

1. For steel, a is $1.1\times {10}^{-5}{K}^{-1}$. Estimate that total variation in length of a 1-km steel bridge between a cold winter night and a hot summer day.
2. The dial thermometer in Figure 1.2 uses a coiled metal strip made of two different metals laminated together. Explain how this works.
3. Prove that the volume thermal expansion coefficient of a solid is equal to the sum of its linear expansion coefficients in the three directions: $\beta =a_x+a_y+a_z.$
4. (So for an isotropic solid, which expands the same in all directions, $\beta =3a.$
5. )