Latent heat and energy transfer

Latent heat

When a substance melts or boils, energy goes in but the temperature stays the same until the change of state is complete. The energy is not raising the average kinetic energy of the particles; it is being used to separate them, overcoming the attractions between them and increasing their potential energy. This energy is called latent heat ("latent" means hidden).

$Q = mL$

• The specific latent heat of fusion $L_f$ is the energy needed to melt 1 kg of a solid at its melting point. For water, $L_f = 3.34 \times 10^5$ J kg$^{-1}$.
• The specific latent heat of vaporisation $L_v$ is the energy needed to turn 1 kg of liquid into gas at its boiling point. For water, $L_v = 2.26 \times 10^6$ J kg$^{-1}$.

The same energy is released when the change goes the other way (freezing, condensing). $L_v$ is much bigger than $L_f$ because boiling separates the particles completely, while melting only loosens them.

Evaporation also needs latent heat. The fastest molecules escape from the surface, so the average kinetic energy of those left behind falls and the liquid cools. Sweat, the "Coolgardie safe" used in the Australian goldfields to keep food cool with wet hessian, and evaporative air coolers all use this.

Heating curves

On a heating curve with a steady energy supply (constant power $P$, so $Q = Pt$):

• On sloping sections one state is warming. The gradient is $\dfrac{\Delta T}{Q} = \dfrac{1}{mc}$, so a gentler slope means a larger specific heat capacity (water's slope is gentler than ice's).
• On flat sections the state is changing at constant temperature, and the length of the flat section is $mL$. The boiling plateau is about 6.8 times as long as the melting plateau for water.

Conduction

Conduction is the transfer of energy through a material without the material itself moving. Faster-vibrating particles at the hot end collide with their neighbours and pass energy along. In metals, free (delocalised) electrons also carry energy quickly through the lattice, which is why metals are good conductors.

The rate of conduction through a slab is

$\dfrac{Q}{t} = \dfrac{kA\Delta T}{d}$

where $Q/t$ is the rate of energy transfer (W), $k$ the thermal conductivity of the material (W m$^{-1}$ K$^{-1}$), $A$ the cross-sectional area (m²), $\Delta T$ the temperature difference across the slab (K), and $d$ its thickness (m).

Convection and radiation

Convection is energy transfer by the bulk movement of a fluid (liquid or gas). Fluid near a heat source warms, expands and becomes less dense, so it rises, and cooler, denser fluid sinks to take its place, forming a convection current. Convection drives sea breezes (land heats faster than sea, warm air rises over the land and cool sea air flows in), heats a room from a single heater, and circulates water in hot-water systems. Convection cannot happen in a solid, and it does not happen in a vacuum. Insulation such as fibreglass and double glazing works by trapping air in small spaces where it cannot circulate, leaving only slow conduction through still air.

Radiation is energy transfer by electromagnetic waves, mostly infrared at everyday temperatures. It needs no medium, which is how the Sun's energy reaches Earth. Every object emits radiation, and the hotter it is the more it emits (the rate rises very steeply, with the fourth power of the absolute temperature). Dark, matt surfaces are good absorbers and good emitters; shiny, light surfaces are poor at both. That is why many Australian roofs are now light-coloured ("cool roofs"), why emergency blankets are shiny, and why car radiators are painted black.

A vacuum flask attacks all three: the vacuum between two glass walls stops conduction and convection, and silvered walls reduce radiation.