Latent heat and changes of state

Supplying heat to a body, one sooner or later reaches the melting point (solid → liquid) or the boiling point (liquid → vapour). At that point something surprising happens: even though heat continues to be supplied, the temperature stays constant for the whole duration of the transition.

The explanation is microscopic. The energy supplied no longer serves to make the molecules oscillate faster (i.e. to raise the temperature), but to break the bonds holding them together in the starting phase. Melting means breaking the solid lattice; vaporising means pulling the liquid’s molecules completely apart. Until the transition is complete, every extra joule goes into changing state, not into heating.

Principle — Latent heat

To change the state of a mass $m$ of a substance requires an energy $\ev{Q = m\,L}$ where $L$ is the latent heat, a property of the substance and of the transition. A distinction is made between $L_f$ (fusion) and $L_v$ (vaporisation), with units J/kg.

Substance	$L_f$ (kJ/kg)	$L_v$ (kJ/kg)
Water	334	2260
Ethanol	108	846
Mercury	11	295
Nitrogen	25.7	200
Lead	24.5	870

Why sweating cools you down

Water has an enormous $L_v$: every gram that evaporates from the skin carries away $2260$ J. This is why perspiration is such an effective cooling mechanism — far more so than simple contact with the air.

Note the hierarchy of numbers: for water, $L_v$ is almost seven times $L_f$, and the latent heat of vaporisation far exceeds the energy needed to bring water from $0$ to $100\,°$C. Boiling is, energetically, much “costlier” than heating.

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Topics: Thermology Concepts: Latent heat and changes of state

Related exercises: Worked exercise — Coffee and steam exchange · Problem — The pot on the stove · Problem — Ice in hot tea