A material that you are working with has a band gap of 4 eV but it is opaque (doesn’t transmit light) because it contains many pores. Explain the mechanism for low light transmission in this material.

d) Why do materials tend to expand with temperature?

e) You are working with an new material and have no idea of its heat capacity. What is a reasonable estimate? Why?

a) The light scatters on the boundary between the material and its pores. The scattering can be done by diffuse reflection of the light inside the material (not on its surface) at the boundaries between material and pores. Another possible mechanism of scattering of light is the Debye scattering which takes place when light is scattered by particles of material having large size (about the same of the wavelength).

b) When the temperature increases the internal energy increases. This in turn is equivalent to an increase of the vibrational (and rotational) energy of molecules (or atoms) (material constituents) and thus a larger average separation between molecules (or atoms) happen.

e) A reasonable estimate of the heat absorbed is (1-3)*NR. N is the number of moles of material, R is the gas constant. This is a good approximation for all materials from gasses to solids.

For solids about 3NR for the total heat absorbed is very good.

This comes from the total number of possible vibrations of crystal lattice (3 ways to vibrate for solids in 3D space). Each mode of vibration for solids is equivalent to a total heat absorbed of 1*NR.

The value is about $25 (=3*8.31) J/(mol*K)$ or equivalent $0.2-0.3 J/(g*K)$ for all solids.