B.1 thermal energy transfers

macroscopic properties

bulk properties of a material e.g. volume, shape, density and temperature

microscopic properties

the arrangement and movement of particles in a substance

what is temperature?

a measure of the mean kinetic energy particles have

the motion of particles

higher energy= higher Ek

what is the internal energy of a substance defined as?

total random kinetic energy + total intermolecular potential energy of the particles within the substance

what 2 things can happen as thermal energy is transferred to a substance?

• an increase in the average kinetic energy of the molecules in the substance

• an increase in the potential energy of the molecules in the substance

what is potential energy?

energy stored due to the positions of particles and the intermolecular forces between them

equation for density

$$p=m/V$$

• $p$ = density (kg m⁻³)

• $m$ = mass (kg)

• $V$ = volume (m³)

explain the physical differences between solids, liquids and gases

• solids have a fixed shape, fixed volume and high density

• liquids have changing shape, fixed volume and high density

• gases have changing shape, non-fixed volume and low density

Describe the state changes: melting, freezing, evaporating, boiling and condensing

melting - solid to liquid

freezing - liquid to solid

evaporating - liquid to gas at the surface

boiling - liquid to gas throughout the liquid

condensing - gas to liquid

how does potential energy and kinetic energy change from solid→liquid→gas?

potential energy increases as molecules move further part on average and overcome some intermolecular forces

as temperature increases, so does kinetic energy (but not during state changes at fixed temperatures)

what does temperature difference depend on?

temperature difference depends on thermal energy transfer between bodies from hot to cold

why does temperature not change during a phase change?

during a phase change, the energy transferred is used to change the potential energy of the molecules (intermolecular bonds strengthen/loosen), rather than their average kinetic energy

order of a natural convection current near a heater

1) fluid near the heater warms up

2) warm fluid expands and becomes less dense

3) the warm, less dense fluid rises

4) cooler, denser fluid sinks to replace it

5) the cycle repeats, forming a convection current

equation for the relationship between temperature and average kinetic energy

$$Eₖ = ³⁄₂ kᵦT$$

conduction

Thermal energy is transferred through a substance by collisions and vibrations between neighbouring particles.

Particles in the hotter region have greater average kinetic energy and transfer energy to neighbouring particles.

In metals, free electrons also transfer thermal energy rapidly through the material.

There is no overall movement of the substance.

what is convection, what is a convection current and what medium does convection occur in?

when thermal energy is transferred by the bulk movement of a fluid (a liquid or gas).

When a fluid is heated, it usually expands and becomes less dense, so it rises.

Cooler, denser fluid sinks to replace it, creating a convection current that transfers thermal energy.

Convection occurs in fluids, not solids.

radiation

Thermal energy is transferred by electromagnetic waves, mainly infrared radiation at everyday temperatures.

The waves are emitted by the charged particles in matter due to their thermal motion.

Radiation does not require a medium, so it can transfer energy through a vacuum, such as from the Sun to Earth.

thermal energy transferred

Q - energy transferred by heating (units: J)

specific heat capacity definition and equation

amount of energy needed to raise the temperature of 1kg of a substance by 1K.

equation used: $Q=mc\Delta T$

• 
  m = mass of the substance (kg)

• ∆T = change in temperature (K or °C)

• c = specific heat capacity of the substance (J kg^–1 K^–1)

• 
  

specific latent heat$L$

energy needed to change phase of 1kg of a substance at constant temperature

units: $L$ in $Jkg^{-1}$ $Q$ in J, $m$ in kg,

equation: $Q=mL$

2.0kg of water warms from 20°C to 80°C. Using c=4200 $Jkg^-1K^-1$ , calculate the energy transferred?

504000J

what is the specific latent heat defined as

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

Conduction and insulation

Good conductors=bad insulators

bad conductors=good insulators

factors affecting rate of thermal conduction

• Temperature difference of insides outside (K)

• Material's conductivity (K)

• Material's thickness x,(m)

• Surface area A ($m^2$)

calculation for thermal energy during a phase change

Q = mL

• Where:

  • Q = heat energy transferred (J)

  • m = mass of the substance in kilograms (kg)

  • L = specific latent heat of the substance (J kg^–1)

SO the higher $L$ , the greater the energy needed to change its state

define the specific latent heat of fusion

• Energy required to change 1 kg of a substance from solid to liquid at a constant temperature.

• The same amount of energy is released when 1 kg freezes.

what is the difference between the latent heat of vaporisation and fusion?

• for a given substance, L_v > L_f

• so more energy is required to evaporate/condense a substance than is needed to melt/solidify it

• during fusion, the intermolecular forces of attraction only need to be partially overcome to turn from solid→liquid

• during vaporisation, the intermolecular forces of attraction need to be completely overcome to turn from liquid→gas (requires a lot more energy)

heating and cooling curves

shows how the temperature of a substance changes with time

flat sections show

• no change in temp over time

• the substance is undergoing a phase change

• thermal energy supplied/removed from the substance only affects the potential energy of the particles

non-flat sections show

• changes in temperature over time

• the substance is heating up or cooling down

• that the thermal energy supplied to/removed from the substance changes the average kinetic energy of the particles, resulting in an overall change in the temperature of the substance

in what 2 ways can conduction occur?

when a substance is heated, the atoms/ions start to vibrate more

• atoms at the hotter end of the solid will vibrate more than the atoms at the cooler end

• as they do, they bump into each other, transferring energy from atom to atom

• these collisions transfer internal energy until thermal equilibrium is achieved throughout the substance

• this occurs in all solids

metals are especially good at conducting heat due to their high number of delocalised electrons

• these can collide with the atoms, increasing the rate of transfer of vibrations through the material

• this allows metals to achieve thermal equilibrium faster than non-metals

thermal conductivity

• the conductivity of a material can be quantified by its thermal conductivity

• it is defined as the ability of a substance to transfer heat via conduction

• denoted by symbol k and has units W m⁻¹ K⁻¹

good vs poor thermal conductors

good thermal conductors:

• have high values of thermal conductivity

• transfer thermal energy at a fast rate

• usually contain a large number of delocalised electrons

poor thermal conductors (insulators):

• have low values of thermal conductivity

• transfer thermal energy at a slow rate

• contain few delocalised electrons

equation for the rate of the heat transfer via conduction

• Where

  • ∆Q∆t = flow of thermal energy per second (W)

  • k = thermal conductivity of the material (W m⁻¹ K⁻¹)

  • A = cross-sectional area (m²)

  • ΔT = temperature difference (K or °C) 

  • Δx = thickness of the material (m)

what can we consider the flow of thermal energy per second to be?

The flow of thermal energy per second can be considered to be uniform across a temperature gradient, provided A is constant, regardless of material

A composite rod is made of three rods; steel, aluminium and copper. Each rod has the same length and cross-section, as shown in the diagram.

The steel end is held at 100°C and the copper end is held at 0°C.

Determine the temperatures at the steel-aluminium junction and the aluminium-copper junction.

Assume that the rods are perfectly insulated from the surroundings.

• Thermal conductivity of steel = 60 W m⁻¹ K⁻¹

• Thermal conductivity of aluminium = 240 W m⁻¹ K⁻¹

• Thermal conductivity of copper = 400 W m⁻¹ K⁻¹

T1 = 29°C

T2 = 11°C

Stefan-Boltzmann Law - definition, what is it used to calculate and what do the formula values represent?

total power radiated per unit surface area of a black body across all wavelengths in terms of the thermodynamic temperature. For a spherical body (like a star), we use it to calculate Luminosity (L):

where:

L = Luminosity (Total power radiated by the object), measured in Watts (\text{W}).

$\sigma$ $=$ Stefan-Boltzmann constant (5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4} — always found in your IB Data Booklet).

A = Surface area of the object, measured in square meters (\text{m}^2). For a sphere (star), A = 4 \pi r^2 (where r is the radius).

T = Absolute temperature of the surface, measured in Kelvin (\text{K}).

Black bodies are…

perfect absorbers and emitters of electromagnetic radiation

what do all black bodies radiate?

em waves of a range of wavelengths, which depends on temperature

what do perfect black bodies depend on?

only on temperature

what does the intensity of each wavelength of em wave only depend on?

temperature

what is luminosity?

total power radiated (W or Js^-1)

what is intensity?

power per unit area

what is the definition of wien’s displacement law?

The wavelength at which a black body emits the maximum intensity of radiation is inversely proportional to its absolute temperature.

(peak intensity shifts towards the blue end of the spectrum - shorter wavelengths)

hotter objects have greater ____

luminosity

inverse square law

as the distance from a light source increases, the area it spreads over also increases by 1/r²

define thermal equillibrium

when 2 objects in contact have the same temperature and there is no net transfer of thermal energy between them

as temperature increases, what happens to peak wavelength?

it decreases - they are inversely proportional

good absorbers are ___ emitters

good

poor absorbers are ____ emitters

poor

how does a black-body spectrum change as temperature increases?

• peak intensity increases

• total area under graph increases

• peak wavelength decreases (moves left)

define the specific latent heat of vaporisation

• Energy required to change 1 kg of a substance from liquid to gas at a constant temperature.

• The same amount of energy is released when 1 kg condenses.

why is L_v>L_f

completely overcoming intermolecular forces to form a gas requires more energy than partially overcoming them to form a liquid.

What is Wien's displacement law equation?

λ_max​T=2.90×10^-3 m K

• λ_max​ = peak wavelength (m)

• T = absolute temperature (K)

As temperature increases, peak wavelength decreases.

State the Stefan-Boltzmann law.

P=σAT⁴

P = power radiated (W)

σ = Stefan-Boltzmann constant

A = surface area (m²)

T = temperature (K)

Total power radiated per unit surface area of a black body depends on T⁴

What is the Stefan-Boltzmann equation for luminosity of a star?

L=4πr²σT⁴

• L = luminosity (W)

• r = radius of star (m)

• T = surface temperature (K)

What is the relationship between mean kinetic energy and temperature?

E_k​=2/3 ​k_B​T

• E_k​ = mean kinetic energy

• k_B = Boltzmann constant

• T = absolute temperature (K)

Mean kinetic energy is directly proportional to absolute temperature.