Thermal energy, temperature and internal energy, methods of heat transfer (conduction, convection, radiation), specific heat capacity $Q = mc\Delta T$, latent heat of fusion and vaporisation, and applications including the greenhouse effect and climate

What this dot point is asking

VCAA wants you to define thermal energy and temperature, identify the three methods of heat transfer, apply the specific heat capacity formula in calorimetry problems, and apply the same principles to climate and the greenhouse effect.

Temperature, thermal energy, internal energy

Temperature measures the average kinetic energy of particles. Measured in Kelvin (K) or degrees Celsius (degrees C). The conversion is $T (\text{K}) = T (\text{degrees C}) + 273.15$.

Internal energy is the total energy of particles in a system: kinetic plus potential.

Thermal energy is the energy transferred between systems due to a temperature difference. Often used interchangeably with heat.

A hot object has high average kinetic energy per particle (high temperature). A large amount of cool water can have more total internal energy than a small amount of hot water, even though the water is cooler.

Heat transfer

Three mechanisms:

Conduction. Heat flow through a material by particle vibration and collision. Solids conduct best; gases conduct poorly. Metals are excellent conductors due to free electrons. Conduction rate: $\dot{Q} = -k A \Delta T / d$ where $k$ is thermal conductivity, $A$ area, $\Delta T$ temperature difference, $d$ thickness.

Convection. Heat transfer by bulk movement of a fluid (liquid or gas). Hot fluid is less dense, rises; cold fluid sinks. Drives weather, ocean currents, the slow circulation of the Earth's mantle.

Radiation. Heat transfer by electromagnetic waves (infrared mainly). Does not require a medium. Stefan-Boltzmann law: $P = \sigma A T^4$ where $\sigma = 5.67 \times 10^{-8}$ W m$^{-2}$ K$^{-4}$, $A$ surface area, $T$ absolute temperature.

Specific heat capacity

The specific heat capacity $c$ of a substance is the energy required to raise 1 kg by 1 K.

where $Q$ is energy (J), $m$ mass (kg), $\Delta T$ change in temperature (K or degrees C).

Common values:

• Water: 4186 J kg$^{-1}$ K$^{-1}$ (very high; why water is good for thermal storage).
• Iron: 449 J kg$^{-1}$ K$^{-1}$.
• Copper: 386 J kg$^{-1}$ K$^{-1}$.
• Aluminium: 900 J kg$^{-1}$ K$^{-1}$.
• Air: 1005 J kg$^{-1}$ K$^{-1}$.

The high specific heat capacity of water moderates Earth's climate (oceans buffer temperature changes).

Calorimetry

When two objects at different temperatures are placed in thermal contact in an insulated system, heat flows until they reach a common temperature.

Conservation of energy: $Q_{\text{lost by hot}} = Q_{\text{gained by cold}}$.

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

Solve for the final temperature $T_f$.

Latent heat

During a phase change (melting, vaporising), energy is absorbed but temperature does not change. The energy goes into rearranging molecules.

Latent heat of fusion $L_f$. Energy per kg to melt at the melting point. For water: $3.34 \times 10^5$ J/kg.

Latent heat of vaporisation $L_v$. Energy per kg to vaporise at the boiling point. For water: $2.26 \times 10^6$ J/kg.

Total energy for a phase change: $Q = m L_f$ or $Q = m L_v$.

For a heating problem involving phase changes, sum the contributions: heating solid, melting, heating liquid, vaporising, heating gas.

Greenhouse effect

The Earth's atmosphere contains "greenhouse gases" (water vapour, CO2, methane, ozone, N2O) that absorb infrared radiation from Earth's surface but transmit visible light from the sun. This keeps the planet warmer than it would be without an atmosphere.

Energy balance. Earth absorbs sunlight ($\sim 1370$ W/m$^2$ at the top of atmosphere, with about 30% reflected). The absorbed energy is re-emitted as infrared. Greenhouse gases absorb some of this infrared and re-radiate it (some down to the surface, some up). The result is a warmer surface than radiative equilibrium alone would predict.

Natural greenhouse effect. Without it, Earth's surface would average about -18 degrees C. With it, about +15 degrees C. Life as we know it depends on the natural greenhouse effect.

Enhanced greenhouse effect. Human activities (fossil fuel burning, deforestation, agriculture) have increased atmospheric CO2 from approximately 280 ppm (pre-industrial) to over 420 ppm (2024). The enhanced greenhouse effect drives observed climate change.

Climate sensitivity. A doubling of CO2 from pre-industrial values is estimated to produce 2.5 to 4 degrees C of warming at equilibrium.

Common errors

Confusing temperature and internal energy. A bath of cool water can have more total internal energy than a hot cup of tea.

Using degrees C in Kelvin formulas. For some thermodynamics formulas, absolute temperature (Kelvin) is required (Stefan-Boltzmann, gas laws). For $\Delta T$, either scale works because differences are the same.

Wrong specific heat capacity. Different materials have very different values. Use the value for the correct substance.

Forgetting latent heat at phase changes. During melting or boiling, temperature does not change but energy is absorbed. Include the latent heat term.

Greenhouse effect confused with ozone depletion. Different phenomena. The greenhouse effect is about heat trapping. Ozone depletion is about UV transmission through the upper atmosphere.

In one sentence

Thermal energy transfers by conduction (through solids), convection (through fluid motion) and radiation (through electromagnetic waves); calorimetry uses conservation of energy ($Q_{\text{lost}} = Q_{\text{gained}}$) with $Q = mc\Delta T$ for temperature change and $Q = mL$ for phase change; the natural greenhouse effect (atmospheric absorption of infrared) keeps Earth approximately 33 degrees warmer than it would be without it, and the enhanced greenhouse effect (from rising CO2 and other gases) drives observed climate change.