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Theme B — The Particulate Nature of Matter

B.1.4 Temperature and Kinetic Energy — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 6 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision
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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.
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Lesson summary

B.1.4 Temperature and Kinetic Energy — IB PHYSICS SL notes: Relate absolute temperature to the mean random kinetic energy of particles and use E = (3/2)kBT.Range of speeds — molecules in a gas move randomly with a range of speeds.Equation — for an ideal gas, Ek = (3/2)kBT.Ek is t…

  • Proportionality
  • Speed from temperature
  • Higher temperature
  • Evaporation
  • High-energy tail
  • Definition

Part 1 of 7Temperature as average kinetic energy

Range of speeds
  • Range of speeds molecules in a gas move randomly with a range of speeds.
Equation
  • Equation for an ideal gas, Ek = (3/2)kBT.
  • Ek is the mean random translational kinetic energy per molecule in J.
  • kB = 1.38 × 10−23 J K−1 is the Boltzmann constant.
  • T is the absolute temperature in K.
Proportionality
  • Proportionality the absolute temperature is directly proportional to the mean kinetic energy, so doubling T doubles Ek.
Speed from temperature
  • Speed from temperature equate (3/2)kBT with ½mv2 to find a typical speed.

Part 2 of 7Distribution of speeds

Shape
  • Shape the curve rises from zero, peaks and has a long tail at high speed; it is not symmetrical.
Higher temperature
  • Higher temperature the peak moves to a higher speed, the curve broadens and the area stays constant.
    • (number of particles)
Evaporation
  • Evaporation a small fraction of liquid molecules always have enough energy to escape, even below the boiling point.
High-energy tail
  • High-energy tail it also matters for chemical reaction rates.

Part 3 of 7Root-mean-square speed

Root-mean-square speed
Definition
  • ½mcrms2 = (3/2)kBT.
Result
  • Result crms = √(3kBT/m).
Lighter particles
  • Lighter particles they have the same mean kinetic energy at the same temperature but a higher typical speed.
Doubling T
  • Doubling T it increases crms by a factor √2.

Part 4 of 7Molar form

1Per mole
  • Per mole multiply by Avogadro's constant NA = 6.02 × 1023 mol−1.
2Molar mean kinetic energy
  • (3/2)RT, where R = kBNA = 8.31 J K−1 mol−1.
3n moles
  • n moles the total translational kinetic energy is (3/2)nRT.
4Link
  • R = NAkB connects the single-particle and bulk quantities.

Part 5 of 7Solids, liquids and equilibrium

Solids
  • Solids particles vibrate and have both kinetic and potential energy.
Every state
  • Every state the temperature measures the average random kinetic energy of the particles.
Equilibrium
  • Equilibrium two objects at the same temperature have the same average kinetic energy per particle, so there is no net transfer.
Mixing gases
  • Mixing gases collisions share energy until the mean kinetic energy per particle is equal everywhere.

Part 6 of 7Limits and cautions

Limits and cautions
Statistical
  • Statistical temperature only makes sense for a large number of particles.
Single particle
  • Single particle it has a kinetic energy but not a temperature.
Bulk motion
  • Bulk motion only the random motion relative to the centre of mass counts, so a fast bottle of water is not hotter.
Diatomic and complex gases
  • Diatomic and complex gases extra energy is stored in rotation and vibration, so the internal energy exceeds the translational part.

Part 7 of 7More from the specification

1
Mean molecular speeds across Earth atmospheres
  • Mean molecular speeds across Earth atmospheres ambient thermal kinetic energy determines gas escape velocities from gravitational planetary atmospheres on Earth.
2
Temperature and Internal Kinetic Energy
  • Absolute temperature in kelvin is directly proportional to the average translational kinetic energy of the molecules in a substance;
  • when two bodies are in thermal contact, heat flows until thermal equilibrium is reached.
3
Specific Heat Capacity and Calorimetry
  • Specific heat capacity c is the thermal energy required per unit mass to change the temperature of a substance by 1 K without a phase change (Q = m·c·ΔT);
    • in calorimetry, a heated copper block transfers thermal energy to water until temperatures equalize.
4
Specific Latent Heat and Phase Changes
  • During a phase change, thermal energy supplied goes into altering intermolecular bonds rather than changing temperature; specific latent heat L is the energy transferred per unit mass during this change (Q = m·L).
    • (such as melting or boiling)
5
Density
  • Mass per unit volume.
6
Wavelength
  • Distance between a point on one wave and the same point on the next wave
7
Fusion
  • Joining of light nuclei into a heavier one.
8
Intensity
  • Power per unit area perpendicular to the wave direction.
9
Apparent brightness
  • The power received per unit area at the observer
10
Phase change
  • Change of matter from one state to another
11
Thermal conductivity
  • Material constant relating the rate of conduction to the temperature gradient and area
12
Surface temperature
  • Effective temperature of the star's radiating surface.
13
Thermal
  • A convection current in the air.
14
Radiation
  • Transfer by electromagnetic waves, requiring no medium
15
Copper
  • Metal widely used for electrical wires.
16
Convection
  • Transfer of thermal energy by the movement of a heated fluid
17
Conduction
  • Transfer of thermal energy by lattice vibrations and free electrons
18
Luminosity
  • The total power of radiation emitted by a star.
19
Capacity
  • Charge a cell can supply, in A h or C.

Key terms

TermMeaning
Boltzmann constantkB = 1.38 × 10−23 J K−1, linking temperature and energy per particle
Mean kinetic energyAverage random translational kinetic energy of a particle, (3/2)kBT
R.m.s. speed√(3kBT/m), the root of the mean squared speed
Molar gas constantR = 8.31 J K−1 mol−1
Avogadro constantNA = 6.02 × 1023 mol−1
Speed distributionCurve showing how many particles have each speed

Avoid these mistakes

1
Giving a single particle a temperature — temperature is a statistical property.
2
Using °C in Ek = (3/2)kBT — use kelvin.
3
Thinking all particles have the mean energy — the energies are widely spread.
4
Thinking heavier gas particles have more energy at the same temperature — the mean kinetic energy is the same.
5
Counting the motion of the whole object as thermal — only random motion counts.

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