Chapter 4 + 5 - Thermal Expansion + Electric & Thermal Conduction

Question 1

What is the formula for a thermal expansion for a rod with length L?

Answer 1

DeltaL = alpha * DeltaT * L

alpha is the thermal expansion coefficient [1/K]

Question 2

What does a bigger thermal expansion coefficient mean for the material?

Answer 2

A higher value for alpha means that there is more expansion.

Question 3

Why does thermal expansion happen?

Answer 3

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.

Question 4

What is the relation between the E-modulus and the thermal expansion coefficient?

Answer 4

Alpha = (1.6*10^-3) / E

Question 5

How does melting and vaporising work?

Answer 5

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.

Question 6

What is the relation between the thermal expansion coefficient and the melting point?

Answer 6

Alpha = 0.02 / T_melt

Question 7

Which factors decide the electric resistance of a material?

Answer 7

The geometry (form) and the resistivity of the material (Rho_e)

Question 8

What is the relation between resistivity and geometry?

Answer 8

R (resistance) = (L (length) / A (area of cross section)) * Rho_e (resistivity)

Question 9

What is conductivity?

Answer 9

The opposite of resisitivity: sigma_e = 1 / Rho_e

Question 10

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)

Answer 10

Always write down your units, if it doesn’t result in the same on both sides of the equation, something is wrong.

Question 11

What is Pauli’s exclusion principle?

Answer 11

No two electrons of an atom can have the same set of (4) quantum numbers.

Question 12

When atoms bond, it means that there will be electrons with the same set of quantum numbers. What happens when this happens?

Answer 12

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

Question 13

Why does copper have such good conductivity?

Answer 13

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.

Question 14

Why is magnesium such a good conductor even though there are no empty spaces?

Answer 14

This is because the valence band and conduction band overlap.

Question 15

What is the Fermi-energy?

Answer 15

The difference between the valence band and the conduction band.

Question 16

What influences the conductivity of materials?

Answer 16

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.

Question 17

What is an insulator according to band theory

Answer 17

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.

Question 18

What is the valence band?

Answer 18

The highest band that has an electron on it.

Question 19

Explain band theory

Answer 19

https://www.youtube.com/watch?v=zdmEaXnB-5Q

Question 20

What are semiconductors according to the band theory?

Answer 20

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

Question 21

Why is carbon not a semiconductor even though it has the same amount of valence electrons as Si or Ge?

Answer 21

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

Question 22

Why does graphite conduct but diamond doesn’t?

Answer 22

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.

Question 23

If we know the Fermi-energy, how can we calculate whether we have a conductor, semiconductor or insulator at a given temperature T?

Answer 23

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

Question 24

What are superconductors?

Answer 24

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.

Question 25

What are the 3 types of heat transfer?

Answer 25

1. Thermal conduction
2. Radiation
3. Convection

Question 26

What is thermal conduction?

Answer 26

Transfer of heat through a material or 2 materials that are in direct contact.

Question 27

What is radiation? (related to heat transfer)

Answer 27

Heat transfer due to electromagnetic radiation. This can go through a material.

Question 28

What is convection?

Answer 28

Transfer of heat by movement of fluids.

Question 29

What is Fourier’s law and what does it mean?

Answer 29

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.

Question 30

How does heat conduction through a material happen?

Answer 30

1. Phonons: a vibration wave that goes through the material

2. movement of free electrons

Question 31

What are phonons?

Answer 31

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.

Question 32

What influences thermal conductivity?

Answer 32

Heat capacity, density, free path length, speed of sound (which in its turn is influenced by E-modulus, density and poison coefficient)

Question 33

Can electrons carry heat?

Answer 33

Yes, they get extra kinetic energy and that way they are able to transfer this to other entities.

Question 34

Why do foams have such low thermal conductivity?

Answer 34

Foams have a lot of pores that are filled with gas (likely air) which also have a very low thermal conductivity.

Question 35

Give an application (a good one and a bad one) of thermal conductivity and of thermal expansion.

Answer 35

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)