Thermal Physics

Question 1

What is the internal energy of a body?

Answer 1

The sum of random distribution of kinetic energies and potential energies of all its particles

Question 2

What two ways are there of increasing the internal energy of a system?

Answer 2

1) Do work on the system
2) Increase temperature of the system

Question 3

What is the first law of thermodynamics?

Answer 3

the change of internal energy of an object = the energy transfer due to work done and heating

Question 4

Describe the motion of particles in a solid.

Answer 4

• Vibrate randomly about a fixed point

Question 5

Describe how the motion of atoms changes as an object is heated without changing state.

Answer 5

The mean kinetic energy of the atoms increases so their mean speed also increases.

Question 6

What happens to an object when work is done on it as it changes state?

Answer 6

The mean potential energies of the particles increases and the mean kinetic energies remain the same

Question 7

Describe the properties of a liquid.

Answer 7

• Molecules move about at random in contact with each other
• Forces not strong enough to hold in fixed position

Question 8

Describe the properties of a gas.

Answer 8

• Molecules move about randomly but much further apart on average than a liquid

Question 9

What is the formula for specific heat capacity?

Answer 9

Q = mcΔθ
Q is energy required
m is the mass
c is specific heat capacity
θ is change in temperature

Question 10

What is the specific heat capacity of a substance?

Answer 10

The amount of energy required to increase the temperature of 1kg of a substance by 1 K without changing its state.

Question 11

What is the equation for specific latent heat?

Answer 11

Q=ml
Q is energy required
m is mass of substance
l is specific latent heat

Question 12

What is the specific latent heat of a substance?

Answer 12

The amount of energy to change the state of 1kg of a substance without changing its temperature.

Question 13

How to approach continuous flow questions?

Answer 13

1) Identify rate of flow
2) Identify energy transferred per second (power)
3) Use these values in specific heat capacity

Question 14

Example question with simultaneous temperature and state changes.

Answer 14

• The energy transferred is the same for both

Question 15

Describe energy changes in heating.

Answer 15

• Increase total kinetic energy of molecules
• No change to potential energies of molecules

Question 16

Describe energy changes in state changes.

Answer 16

• Increase in potential energies of molecules
• No change in kinetic energy of molecules

Question 17

What is absolute zero?

Answer 17

• The temperature at which the molecules in a substance have zero kinetic energy
• 0 K or -273.15°C

Question 18

What are the key assumptions for ideal gases?

Answer 18

• There are no potential energies between particles
• The gas always obeys pV = nRT
• The collisions are elastic
• The gas cannot be liquified
• The molecules have negligible volume

Question 19

What is Boyle’s Law?

Answer 19

pV = constant

or

Pressure and volume are inversely proportional for a fixed mass of ideal gas at a constant temperature (isothermal)

Question 20

What is Charles’ Law?

Answer 20

V/T = constant

or

Volume and temperature are proportional for a fixed mass of ideal gas at a constant pressure (isobaric)

Question 21

What is the pressure law?

Answer 21

P/T = constant

or

Pressure and temperature are proportional for a fixed mass of ideal gas at a constant volume (isometric)

Question 22

What is the ideal gas equation?

Answer 22

pV = nRT

p is pressure (Pa)
V is volume (m^3)
n is number of molecules
R is molar gas constant
T is temperature (K)

Question 23

What is the alternative ideal gas equation?

Answer 23

pV = NkT

p is pressure (Pa)
V is volume (m^3)
N is number of particles
k is Boltzmann’s constant
T is temperature (K)

Question 24

What is the equation for work done by a gas?

Answer 24

W = pΔV

W is work done (J)
p is pressure (Pa)
ΔV is change in volume (m^3)

same as area under pressure-volume graph

Question 25

What is the atomic mass unit?

Answer 25

The mass of a single nucleon (1.66 x 10^^-27)

Question 26

What is the equation for moles?

Answer 26

Question 27

What is the difference between molecular mass and molar mass?

Answer 27

Mass of all atoms in molecule vs a mole of a single atom

Question 28

What is the scientific distinction between gas laws and kinetic theory?

Answer 28

- Gas laws are **empirical** and are based on **observation** and **evidence** - Kinetic theory is based on **theory** so based on **assumptions**

Question 29

What is the internal energy of an ideal gas?

Answer 29

*U = NE_k* U is internal energy (J) N is number of particles E_k is the average kinetic energy of a single particle

Question 30

Why does kinetic theory produce the ideal gas internal energy equation?

Answer 30

- Ideal gases are assumed to have no intermolecular forces - No potential energy only kinetic energy - Internal energy is then simply the sum of all the kinetic energies - As temperature increases, average kinetic energy increases proportionally so this obeys this internal energy equation

Question 31

What are the key assumptions of the kinetic theory of gases equation?

Answer 31

- Molecules of a gas behave as identical (same mass) - Molecules are hard, **perfectly elastic** spheres - Volume of molecules are negligible compared to volume of container - Time of a collision is negligible compared to time between collisions - No intermolecular forces between molecules except during impact - Molecules move in **continuous, random linear motion** - Very large number of molecules

Question 32

What are the steps to the derivation of the kinetic theory of gases equation?

Answer 32

1) When molecules collide with wall of container, change in momentum causes a force (many molecules exert force which creates average overall pressure) 2) Molecule of mass *m* moves with speed *c₁* parallel to wall of side length L in a cube 3) Change of momentum of this molecule in a collision is *p = -2mc₁* 4) The time between collisions with that wall and particle is *t = 2L /c₁* 5) Force exerted by that molecule on wall is *F = mc₁² / L* - the change in momentum swaps sign as force on molecule from wall is opposite to the wall from molecule. 6) Area of one wall is *L²* so pressure created by single molecule is *p = F/A = mc₁² / L³* 7) To consider the effect of N molecules, we take the pressure as *p = F/A = m(c₁² + c₂² + … + c_N²)/ V* where the speed of each particle is *c² = c_x² + c_y² + c_z²* 8) We assume movement in each direction is same so ON ONE FACE (e.g. on one face) is 1/3 of the speed squared so pressure on one face is *p = F/A = m(c₁² + c₂² + … + c_N²)/ 3V* 9) We can simplify by using the *root-mean-square speed* which is *c_rms² = (c₁² + c₂² + … + c_N²) / N* allowing us to simply the pressure equation as *p = mNc_rms² / 3V* and a final Kinetic Theory of Gases Equation as *pV = Nmc_rms² / 3*

Question 33

What is the kinetic theory equation linking pressure and density?

Answer 33

Density is equal to mass on volume which is equal to *Nm / V* So rearranging gives us *p = ρc_rms² / 3*

Question 34

What is the kinetic theory equation for average molecular kinetic energy?

Answer 34

*pV = NkT = Nmc_rms² / 3* and by cancelling N *mc_rms² = 3kT* so we can use *KE = 1/2mv²* to get *E_k = mc_rms² / 2 = 3kT / 2*

Question 35

How can we rearrange the average kinetic energy formula to use molar gas constant (R) instead of Boltzmann’s constant (k)?

Answer 35

*k = R/N_A* where N_A is Avogrado’s constant

Question 36

What is the smoke particle experiment and what does it prove?

Answer 36

- We can observe smoke particles under a microscope to provide evidence for existence of atoms in a gas - Particles have random motion e.g. range of speeds and no preferred direction of movement - Observable particles in **Brownian motion** are bigger than molecules that cause the motion - E.g. smoke particles collide with smaller air particles causing them to change speed and direction randomly - The smaller particles can affect motion as they have a greater speed and a lot of momentum

Question 37

How do you keep temperature constant for Boyle’s Law experiment?

Answer 37

- Change pressure very slowly - Wait between readings to let oil level neutralise

Question 38

What happens when a gas expands?

Answer 38

The **gas** does work on the surroundings to expand. This means its internal energy **decreases**.

Question 39

What temperature is absolute zero?

Answer 39

-263.15 celsius

Question 40

State a property of an ideal gas that is equal to its internal energy.

Answer 40

The **total** kinetic energies of all of the gas particles.

Question 41

Why are light hydrogen atoms used in moderators instead of heavy atoms?

Answer 41

- Similar in **mass** to neutrons - Elastic collisions conserve **kinetic energy** - So collision of a high energy neutron with an atom of similar mass will transfer a significant amount of kinetic energy to the atom

Question 42

When is gamma radiation emitted?

Answer 42

When a **nucleus** is excited

Question 43

How to find the change in potential energy of particle moving in an electric field?

Answer 43

- Potential energy only changes moving parallel to field lines - For a positive charge : moving with field lines decreases potential energy so just do - force x distance where the force is from F = EV/d - For a negative charge: same thing but flip the sign