Thermal energy, temperature and kinetic theory of matter, methods of heat transfer (conduction, convection, radiation), specific heat capacity $Q = mc\Delta T$, and latent heat

What this dot point is asking

QCAA wants Year 11 students to apply kinetic theory and heat transfer concepts to thermal problems, and to use the specific heat capacity formula in calorimetry.

Kinetic theory of matter

All matter is made of particles in constant motion.

• Temperature is a measure of the average kinetic energy of particles.
• Internal energy is the total energy of particles (kinetic + potential).
• In a solid, particles vibrate in fixed positions. In a liquid, they slide past each other. In a gas, they move freely with mostly straight-line motion between collisions.

Heat transfer

Conduction. Energy flow through a material by vibration and collision. Solids best (especially metals with free electrons).

Convection. Heat carried by bulk movement of fluid. Hot fluid is less dense, rises; cold sinks. Drives weather, ocean currents.

Radiation. Heat by electromagnetic waves (mostly infrared). Does not require a medium. $P = \sigma A T^4$ (Stefan-Boltzmann).

Specific heat capacity

$Q = m c \Delta T$

where $Q$ is energy, $m$ mass, $c$ specific heat capacity, $\Delta T$ temperature change.

Water: $c = 4186$ J kg$^{-1}$ K$^{-1}$. High value moderates Earth's climate.

Latent heat

During phase change, energy is absorbed/released without temperature change.

Latent heat of fusion ($L_f$): energy per kg for melting/freezing.

Latent heat of vaporisation ($L_v$): energy per kg for boiling/condensing.

$Q = m L$.

For water: $L_f = 3.34 \times 10^5$ J/kg, $L_v = 2.26 \times 10^6$ J/kg.

Calorimetry

Heat lost = heat gained in insulated systems.

$m_1 c_1 (T_{1,i} - T_f) = m_2 c_2 (T_f - T_{2,i})$

Solve for final temperature.

Common errors

Confusing temperature with internal energy. A large mass of cold water can have more total internal energy than a small hot cup.

Forgetting latent heat at phase changes. No temperature change during melting/boiling but energy is absorbed.

Using degrees C in Kelvin formulas. For Stefan-Boltzmann ($T^4$) you need absolute temperature (K).

In one sentence

Thermal physics applies kinetic theory (temperature = average kinetic energy of particles) and heat transfer (conduction, convection, radiation) to thermal problems; specific heat capacity formula $Q = mc\Delta T$ underpins calorimetry and latent heat ($Q = mL$) accounts for energy absorbed at phase changes.