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.

Examples in context

Example 1. Olympic Park steam-heating retrofit, Melbourne. Melbourne Olympic Park retrofitted a thermal-energy storage system using phase-change materials. The chosen salt-hydrate has a latent heat of fusion of $230$ kJ kg$^{-1}$ and a melting point of $32^\circ$C. A $5000$ kg tank stores $5000 \times 230 = 1.15 \times 10^9$ J during off-peak overnight charging, equivalent to $319$ kWh. Compared with sensible-heat storage in $5000$ kg of water across a $20^\circ$C range (storing only $mc\Delta T = 4.2 \times 10^8$ J), the latent storage holds $2.7\times$ more energy per kilogram, illustrating why phase-change materials are central to compact thermal storage.

Example 2. Eureka Tower spire wind-driven convective cooling. Eureka Tower's $300$ m spire experiences strong westerly winds that drive forced convection over the gold cladding. On a $35^\circ$C still day, the cladding sits at $50^\circ$C and radiates $\sigma T^4 \approx 617$ W m$^{-2}$. With a $15$ m s$^{-1}$ wind, the convective heat transfer coefficient rises to about $50$ W m$^{-2}$ K$^{-1}$, so additional convective loss is $h(T_s - T_\infty) = 50 \times 15 = 750$ W m$^{-2}$. Total heat loss per square metre jumps from radiation-only ($617$ W m$^{-2}$) to over $1300$ W m$^{-2}$, dramatically reducing facade temperature and easing chiller load on the building's HVAC.

Try this

Q1. State the three mechanisms of heat transfer and identify the dominant mechanism in air at low velocity. [3 marks]

• Cue. Conduction, convection, radiation. Natural convection dominates in still air alongside radiation; conduction is small in gases.

Q2. A $2$ kg copper block at $200^\circ$C is placed in $4$ kg of water at $20^\circ$C in an insulated container. Take $c_{\rm Cu} = 385$ and $c_{\rm water} = 4186$ J kg$^{-1}$ K$^{-1}$. Calculate the equilibrium temperature. [4 marks]

• Cue. $2 \times 385 \times (200 - T) = 4 \times 4186 \times (T - 20)$. $T \approx 28^\circ$C.

Q3. Refer to the Olympic Park thermal store. (a) Define latent heat of fusion. (b) Calculate the energy stored when $5000$ kg of salt-hydrate melts at $32^\circ$C with $L_f = 230$ kJ kg$^{-1}$. (c) Compare latent and sensible heat storage in terms of energy density. [2+2+2 marks]

• Cue. (a) Energy per kg to change phase at constant temperature. (b) $1.15 \times 10^9$ J. (c) Latent stores more energy per kg without temperature change; sensible requires a temperature swing.