B.1 Thermal energy transfers

UNIT SYLLABUS

SL/HL 6 hours

Heat is energy on the move, and this unit explains both why it moves and how fast. The molecular picture comes first: temperature in kelvin measures the average kinetic energy of particles ($\bar{E}_k = \frac{3}{2}k_BT$), while internal energy adds up all the random kinetic energy plus the potential energy stored in intermolecular bonds. That picture explains phase changes (energy rearranges bonds at constant temperature) and the workhorse equations $Q = mc\Delta T$ and $Q = mL$. Then come the three transfer mechanisms — conduction, convection and radiation — with the Stefan–Boltzmann and Wien laws powerful enough to take the temperature of a star from its light alone.

Guiding Questions

? How do macroscopic observations of temperature relate to the microscopic behaviour of particles?
? How is thermal energy transferred within and between systems?

✓ What the IB expects you to master

Describe solids, liquids and gases with molecular theory, and use density $\rho = m/V$ .
Convert between Kelvin and Celsius scales, noting that temperature differences are identical in both.
Interpret absolute temperature as a measure of average particle kinetic energy: $\bar{E}_k = \frac{3}{2}k_B T$ .
Define internal energy as total intermolecular potential energy plus total random kinetic energy of the molecules.
Explain that thermal energy flows from higher to lower temperature, and that phase changes occur at constant temperature.
Calculate thermal energy transfers with $Q = mc\Delta T$ (specific heat capacity) and $Q = mL$ (specific latent heat of fusion or vaporization).
Compare conduction (particle collisions), convection (fluid density differences) and radiation (electromagnetic waves).
Use the conduction rate equation $\frac{\Delta Q}{\Delta t} = kA\frac{\Delta T}{\Delta x}$ .
Apply the Stefan–Boltzmann law $L = \sigma A T^4$ , apparent brightness $b = \frac{L}{4\pi d^2}$ , and Wien's law $\lambda_{max}T = 2.9\times10^{-3}\ \text{m K}$ to blackbody radiators including stars.

1 Key Formulas

Density

\rho = \frac{m}{V}

Average particle KE

\bar{E}_{k} = \tfrac{3}{2}k_{B}T

Specific heat capacity

Q = mc\Delta T

Latent heat

Q = mL

Conduction rate

\frac{\Delta Q}{\Delta t} = kA\frac{\Delta T}{\Delta x}

Stefan–Boltzmann law

L = \sigma A T^{4}

Apparent brightness

b = \frac{L}{4\pi d^{2}}

Wien's displacement law

\lambda_{\text{max}} T = 2.9 \times 10^{-3}\ \text{m K}

2 Exam Preparation & Topic Explanations

Mixture problems without tears

Calorimetry questions reduce to one statement: energy lost by hot = energy gained by cold. Write each term as $mc\Delta T$ or $mL$ , keep every $\Delta T$ positive by thinking physically about direction, and solve.

When phase changes are involved, check whether there is enough energy to complete the change before assuming a final temperature — as in ice-and-water problems, the answer may sit exactly at the phase-change temperature.

Pro Exam Strategy

Latent heat questions: no $\Delta T$ term during the phase change itself.
Kelvin is compulsory in $\bar{E}_k = \frac{3}{2}k_BT$ and all radiation laws.
Stefan–Boltzmann uses surface area: $4\pi R^2$ for a sphere — forgetting the 4 is the classic slip.
Apparent brightness vs luminosity: luminosity is intrinsic power; brightness is what reaches you, diluted by $4\pi d^2$ .

3 MCQ Practice

Q1. Ice at 0 °C melts to water at 0 °C. During melting, the thermal energy supplied goes to:

Increasing the average kinetic energy of the molecules
Increasing the potential energy of the molecules
Increasing both kinetic and potential energy equally
Increasing the temperature of the water

Q2. Star X has twice the surface temperature and half the radius of star Y. The ratio of luminosities $L_X/L_Y$ is:

Q3. A metal spoon and a wooden spoon are both at room temperature. The metal one feels colder because:

Metal is at a lower temperature
Metal has a higher specific heat capacity
Metal conducts thermal energy away from the hand faster
Wood radiates more energy than metal

4 Short Answer Questions

PDF

Download the practice worksheet

All questions from this unit + answer key — free, printable.

↓

Formula Booklet →

Every data-booklet equation, searchable.

Simulations →

See this physics in motion.

Daily Question →

Practise one concept a day.

← Previous unit

A.5 Galilean and special relativity

Next unit →

B.2 Greenhouse effect

Stuck on Thermal energy transfers?

Get it explained properly — 1-on-1, by a specialist who has taught this unit for 13+ years. Newtonine students average 6.8 in IB Physics.

Book a Free Consultation