Chapter 4 + 5 - Thermal Expansion + Electric & Thermal Conduction Flashcards
What is the formula for a thermal expansion for a rod with length L?
DeltaL = alpha * DeltaT * L
alpha is the thermal expansion coefficient [1/K]
What does a bigger thermal expansion coefficient mean for the material?
A higher value for alpha means that there is more expansion.
Why does thermal expansion happen?
There is an equilibrium distance between atoms, however, this equilibrium distance is defined at 0 K. So no thermal vibration has to be taken into consideration. At normal temperatures, other than the attraction forces and repulsion forces of charges, there is also some thermal energy causing the atoms to oscillate and the average distance between the 2 will be higher, thus the material will expand. The more heat you add, the further apart they will be.
What is the relation between the E-modulus and the thermal expansion coefficient?
Alpha = (1.6*10^-3) / E
How does melting and vaporising work?
When the temperature is increased, the average bond length increases as well due to oscillations (vibration) of the atoms at a certain point the distance becomes big enough that the attraction forces can’t hold together anymore and it will liquefy. A further increase will make them vibrate even more until the vibrations cause the vapour pressure to be equal to the external pressure and it will vaporise.
What is the relation between the thermal expansion coefficient and the melting point?
Alpha = 0.02 / T_melt
Which factors decide the electric resistance of a material?
The geometry (form) and the resistivity of the material (Rho_e)
What is the relation between resistivity and geometry?
R (resistance) = (L (length) / A (area of cross section)) * Rho_e (resistivity)
What is conductivity?
The opposite of resisitivity: sigma_e = 1 / Rho_e
How can we prevent confusion with the same name for 2 different things or the same symbol for 2 different things (Rho means both density and resistivity)
Always write down your units, if it doesn’t result in the same on both sides of the equation, something is wrong.
What is Pauli’s exclusion principle?
No two electrons of an atom can have the same set of (4) quantum numbers.
When atoms bond, it means that there will be electrons with the same set of quantum numbers. What happens when this happens?
The 2 energy levels that used to be the same in the atoms apart will slightly deviate, creating 2 or more different energy levels. We call these energy bands
Why does copper have such good conductivity?
When we fill in the bands, what happens is that instead of 1 empty space in the 3d orbital; there is 1 empty space at the 4s orbital. The conduction band is equal to the valence band.
Why is magnesium such a good conductor even though there are no empty spaces?
This is because the valence band and conduction band overlap.
What is the Fermi-energy?
The difference between the valence band and the conduction band.
What influences the conductivity of materials?
Temperature due to vibration of the atoms; The way that it is fabricated or formed: cold forming the metal creates disorder and displacement of atoms making it harder for an electron to find its way through.
What is an insulator according to band theory
When the valence band and the conduction band have such a high difference (so such a high bandgap) between them that no amount of potential difference can cause electrons to go through the gap.
What is the valence band?
The highest band that has an electron on it.
Explain band theory
https://www.youtube.com/watch?v=zdmEaXnB-5Q
What are semiconductors according to the band theory?
The bandgap is there, but it is rather small which means that when sufficient (thermal) energy is added. Examples of this are Si and Ge
Why is carbon not a semiconductor even though it has the same amount of valence electrons as Si or Ge?
Carbon has its outer shell closer to the nucleus, so the electrons on that shell experience more attraction force from the nucleus. This results in a higher bandgap and this makes diamond and insulator
Why does graphite conduct but diamond doesn’t?
Graphite conducts electricity because not all electrons on the outer shell are used for covalent bonds, this results in graphite have a free electron to be able to move when a potential difference is applied.
If we know the Fermi-energy, how can we calculate whether we have a conductor, semiconductor or insulator at a given temperature T?
Boltzmann constant (k_B) * T:
if E_f <= k_B * T –> conductor
if E_f < 10 * k_B * T –> semiconductor
if E_f >= 10 * k_B * T –> insulator
What are superconductors?
At really low temperatures, there is little to no vibration of atoms. This means that electrons are able to move through the material with a resistance of/close to 0. Also, some complex metallic structures have this property even at relatively high temperatures.
What are the 3 types of heat transfer?
- Thermal conduction
- Radiation
- Convection
What is thermal conduction?
Transfer of heat through a material or 2 materials that are in direct contact.
What is radiation? (related to heat transfer)
Heat transfer due to electromagnetic radiation. This can go through a material.
What is convection?
Transfer of heat by movement of fluids.
What is Fourier’s law and what does it mean?
J_x / S = Lambda * dT/dx
J_x is heat flow
S = cross section
dT/dx = temperature change in x-direction
Lambda = coefficient of heat conduction
It means that heat conduction depends both on geometry, the temperature difference and the material.
How does heat conduction through a material happen?
- Phonons: a vibration wave that goes through the material
2. movement of free electrons
What are phonons?
small packets of energy, similar to photons. When the temperature is above 0 K, building blocks (atoms, molecules, ions) will vibrate, this will cause them to bounce against each other, handing over vibrational energy to the next atom/ion/molecule etc. The speed at which this happens is limited by irregularities in the material.
What influences thermal conductivity?
Heat capacity, density, free path length, speed of sound (which in its turn is influenced by E-modulus, density and poison coefficient)
Can electrons carry heat?
Yes, they get extra kinetic energy and that way they are able to transfer this to other entities.
Why do foams have such low thermal conductivity?
Foams have a lot of pores that are filled with gas (likely air) which also have a very low thermal conductivity.
Give an application (a good one and a bad one) of thermal conductivity and of thermal expansion.
Thermal expansion: railroads can deform due to heat (bad); Can be used to break an electric circuit once the temperature gets too high (good).
Thermal conductivity: When stirring with a metal spoon you might burn your hand (bad); heat sinks in electronics (good)
