Theme B — The Particulate Nature of Matter
Theme B — The Particulate Nature of Matter — IB Physics HL Revision Notes & Topical Questions
10 min read 12 parts Lesson 1 of 53 Unit quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
Theme B — The Particulate Nature of Matter — IB PHYSICS HL notes: Describe thermal transfer, black-body radiation, the greenhouse effect, gases, entropy, heat engines and electric current.MethodMediumMechanismConductionMainly solidsParticle collisions and free electronsConvection…
- Emission and absorption
- Dark, matt surfaces
- Light, shiny surfaces
- Black body
- Approximation
- Luminosity L
Section 1 of 12Methods of thermal energy transfer
| Method | Medium | Mechanism |
|---|---|---|
| Conduction | Mainly solids | Particle collisions and free electrons |
| Convection | Liquids and gases | Bulk movement from density differences |
| Radiation | None needed | Electromagnetic waves |
Emission and absorption
- Emission and absorption both depend on temperature, surface area and the nature of the surface
Dark, matt surfaces
- Dark, matt surfaces good absorbers and emitters
Light, shiny surfaces
- Light, shiny surfaces poor absorbers and emitters but good reflectors
Examples
- Examples a black roof heats in the sun, emergency blankets are shiny and a thermos flask has silvered walls
Section 2 of 12Black bodies and luminosity
Black body
Black body an idealised object that absorbs all radiation and emits the maximum power at every wavelength for its temperature
Approximation
- Approximation a small hole in a hollow blackened cavity approximates one, and stars behave approximately as black bodies
Spectrum
- Spectrum it is continuous with a peak wavelength that depends on temperature
- Hotter bodies emit more power and peak at shorter wavelengths.
- 300 K is infrared, 1000 K dull red and 6000 K visible.
Luminosity L
Luminosity L the total power emitted by a star, in W
Intensity I
Intensity I the power per unit area perpendicular to the direction of travel, in W m⁻², and for a point source I ∝ 1/d²
Stefan–Boltzmann law
- L = 4π r² σ T⁴
Wien's law
- λmax T = 2.9 × 10⁻³ m K
Section 3 of 12Greenhouse effect and energy balance
1Solar constant S
Solar constant S the mean solar power per unit area at the top of Earth's atmosphere, about 1.36 × 10³ W m⁻²
- It is defined at a given distance, so it differs for each planet.
2Average intensity
- Average intensity a planet intercepts sunlight over π R² but radiates from 4π R², so the average intensity is S ÷ 4
3No atmosphere
- (1 − a) S ÷ 4 = σ T⁴
- With albedo a = 0.30 this gives about 255 K, against the observed 288 K.
4Greenhouse gases
- CO₂, CH₄ and water vapour transmit visible light but absorb outgoing infrared and re-emit it in all directions
5Effect
- Effect the equilibrium surface temperature rises, and more gas enhances the effect
6Emissivity e and albedo a
- Emissivity e and albedo a the power emitted is P = e σ A T⁴
Section 4 of 12Gases and kinetic theory
1Preparation
- Preparation convert temperatures to kelvin and volumes to m³, and decide what is constant
2Fixed mass
- Fixed mass p₁V₁ ÷ T₁ = p₂V₂ ÷ T₂
3Equation of state
- Equation of state pV = nRT for one state, and N = n NA for the number of molecules
4Kinetic theory
- Kinetic theory p = ⅓ ρ ⟨v²⟩
5Mean kinetic energy per molecule
- (3/2) kB T
6Internal energy
- U = (3/2) n R T for a monatomic ideal gas
Section 5 of 12Thermodynamics and the first law
1Work done by a gas at constant pressure
- W = p ΔV, and in general the area under a p–V graph
2First law
- Q = ΔU + W, with Q positive for heat in and W positive for work done by the gas
| Process | Constant | Result |
|---|---|---|
| Isobaric | Pressure | W = pΔV |
| Isovolumetric | Volume | W = 0, Q = ΔU |
| Isothermal | Temperature | ΔU = 0, Q = W |
| Adiabatic | No heat transfer | Q = 0, W = −ΔU, pV5/3) = constant for a monatomic gas |
Section 6 of 12Entropy
Macrostate
Macrostate a state described by large-scale variables such as p, V, T and U
Microstate
Microstate a complete specification of the position and energy of every particle
Multiplicity Ω
Multiplicity Ω the number of microstates that correspond to one macrostate
- With four coins, 2 heads and 2 tails occurs in 6 ways, but 4 heads occurs in only 1 of 16.
- For a mole of molecules the evenly spread arrangements are overwhelmingly more probable.
Boltzmann entropy
- S = kB ln Ω
Change in entropy
- ΔS = Q ÷ T at constant temperature
Section 7 of 12Second law of thermodynamics
1Statement
- Statement the entropy of an isolated system always increases
2Clausius form
- Clausius form heat cannot spontaneously pass from a cold body to a hot body
3Kelvin form
- Kelvin form heat from a single reservoir cannot be wholly converted to work
4Reversible process
- Reversible process an idealised process that is always in equilibrium with no friction, so ΔSuniverse = 0
5Irreversible process
- Irreversible process a real process with ΔSuniverse > 0, caused by friction, turbulence, rapid expansion, mixing or heat flow across a temperature difference
6Consequence
- Consequence irreversibility wastes useful work, which is why perpetual motion machines of the second kind cannot exist
Section 8 of 12Heat engines and heat pumps
1Heat engine
- Heat engine it takes QH from a hot reservoir, does work W = QH − QC and rejects QC to a cold reservoir
2Efficiency
- η = W ÷ QH = 1 − QC ÷ QH, and the area of the p–V loop is the net work per cycle
3Carnot cycle
- Carnot cycle isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression
4Maximum efficiency
- η_C = 1 − TC ÷ TH
5Reverse cycle
- Reverse cycle it takes QC from a cold region and delivers QH = QC + W to a hot region, as in a refrigerator or heat pump
6Clausius statement
- Clausius statement it is not broken because work is supplied, and these devices are rated by their coefficient of performance
Section 9 of 12Electric current and circuits
1Ohm's law
- R = V ÷ I, and a conductor is ohmic if V ÷ I is constant at constant temperature
- (a straight I–V line through the origin)
2Filament lamp
- Filament lamp non-ohmic because its resistance rises as it heats
3Definitions
- Definitions current I = Δq ÷ Δt, potential difference V = W ÷ q and resistance R = ρL ÷ A
4Charge carriers
- Charge carriers free electrons in metals, ions in electrolytes, and electrons and holes in semiconductors
- (charge −e, e = 1.60 × 10⁻¹⁹ C)
- Charge is quantised, Δq = n e.
5Drift speed
- Drift speed free electrons move randomly at about 10⁶ m s⁻¹, and a potential difference sets up a small net drift speed v, with I = n A v q
- Drift speeds in copper are fractions of a millimetre per second, yet a lamp lights almost instantly because the field propagates at nearly c.
- A thinner wire needs a larger drift speed for the same current.
6Number density
- Number density about 10²⁸ to 10²⁹ m⁻³ for a metal and 10¹⁶ m⁻³ for silicon, so a semiconductor has a much higher resistivity
7Temperature effect
- Temperature effect heating a metal raises its resistance, while heating a semiconductor lowers it (more carriers), as in a thermistor or LDR
- (more lattice vibrations)
8Insulator breakdown
- Insulator breakdown insulators break down in a strong field, for example a spark in air at about 3 × 10⁶ V m⁻¹
Section 10 of 12More from the specification
1
First Law of Thermodynamics
- The first law of thermodynamics states that the change in internal energy of a closed system is given by ΔU = Q - W,
- where Q is heat added to the system and W is work done by the gas on its surroundings.
2
Work Done During Volume Changes
- When a gas expands against a movable piston from an initial to a final volume, work done on the surroundings is W = pΔV;
- when compressed such that volume decreases, work is done on the gas by the surroundings.
3
Internal Energy and Thermodynamic Temperature
- For an ideal gas, internal energy is directly proportional to its thermodynamic temperature T (in kelvin); in an isothermal process, internal energy change ΔU is equal to zero.
- (constant temperature)
4
Adiabatic and Isochoric Processes
- In an adiabatic process (Q = 0), a gas expanding against a piston does work solely from its internal energy so temperature decreases; in an isochoric process, work done is zero and ΔU = Q.
- (constant volume)
5
First Law of Thermodynamics
- The first law of thermodynamics states that the change in internal energy of a closed system is given by ΔU = Q - W,
- where Q is heat added to the system and W is work done by the gas on its surroundings.
6
Work Done During Volume Changes
- When a gas expands against a movable piston from an initial to a final volume, work done on the surroundings is W = pΔV;
- when compressed such that volume decreases, work is done on the gas by the surroundings.
7
Internal Energy and Thermodynamic Temperature
- For an ideal gas, internal energy is directly proportional to its thermodynamic temperature T (in kelvin); in an isothermal process, internal energy change ΔU is equal to zero.
- (constant temperature)
8
Adiabatic and Isochoric Processes
- In an adiabatic process (Q = 0), a gas expanding against a piston does work solely from its internal energy so temperature decreases; in an isochoric process, work done is zero and ΔU = Q.
- (constant volume)
9
Piston
- A moving part in a cylinder that applies or receives pressure.
10
Surroundings
- Everything outside the system.
Section 11 of 12Key terms
| Term | Meaning |
|---|---|
| Black body | Ideal object that absorbs all radiation and emits maximum power at each wavelength. |
| Luminosity | Total power emitted by a star. |
| Solar constant | Mean solar power per unit area at the top of Earth's atmosphere. |
| Microstate | Complete specification of positions and energies of all particles. |
| Multiplicity | Number of microstates for a given macrostate. |
| Irreversible process | Real process that increases total entropy. |
| Drift speed | Small net average velocity of charge carriers along a conductor. |
| Number density | Number of charge carriers per unit volume. |
Section 12 of 12Exam technique
1
Forgetting the factor 1/4 when finding the average intensity over a planet.
2
Saying intensity falls as 1/d instead of 1/d².
3
Quoting the solar constant in W rather than W m⁻², or thinking it is the same for every planet.
4
Saying a battery stores charge — it stores chemical energy.
5
Adding the e.m.f.s of cells in parallel — in parallel the e.m.f. stays the same.
Last updated:
\n