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Boiling is vaporization through the formation and growth of vapor bubbles within a liquid. It differs from surface evaporation, which can occur without bubbles in the bulk. At equilibrium, the boiling point of a pure liquid is set by equality of its saturation vapor pressure and the external pressure.

A real bubble must also overcome local hydrostatic pressure and the capillary pressure of its curved surface. Creating the interface costs energy, giving a nucleation barrier; a smooth clean vessel can therefore permit superheating. Surface cavities and boiling chips supply sites where bubbles form more readily. The observed onset depends on these sites and heating conditions, while the equilibrium boiling point remains a property specified at the chosen pressure.

Evaporation cools the remaining material when the escaping vapour takes energy from it faster than the surroundings supply heat. For an observable demonstration, compare two similar thermometer bulbs at the same initial temperature, one dry and the other wetted with a volatile liquid. Expose both to the same controlled airflow. The wetted bulb falls in temperature; the effect depends on vapour removal and environmental conditions. Another demonstration is continued heating during boiling at constant pressure: vapour is produced while the boiling liquid's temperature remains nearly constant. The supplied energy has not vanished; it contributes to the latent heat and expansion associated with the phase transition.

One calorimetry method estimates the specific latent heat of vaporization by condensing a known mass $m_s$ of dry saturated steam at $T_s$ into a known mass $m_w$ of cooler water. Let $C_{\mathrm{cal}}$ be the vessel's heat capacity, and $T_i,T_f$ the initial and final water temperatures. Assuming complete condensation without escaped steam or thermal losses,soThe last term removes the sensible cooling of the condensed steam. Weighing the receiving vessel before and after gives $m_s$ only if splashing, evaporation and liquid carried in with the steam are controlled. A steam trap and an insulated transfer path address two distinct errors: droplets falsely counted as condensing steam, and cooling before the calorimeter.

The historical local application was Richardson's ether spray. A bellows atomizer dispersed diethyl ether into fine droplets, promoting rapid vaporization and withdrawal of heat from the surface; the cooling could produce local loss of sensation. Benjamin Ward Richardson's 1866 account describes this evaporative method and its apparatus. Its historical physiological language is not adopted as a modern description of nerve signalling, and the account does not establish that the method is appropriate for every operation.^[ref]

Three phase coexistence curves meet at the triple point, where ice, liquid water and water vapour have equal chemical potential. In the ordinary-pressure region, the low-temperature phase is ice, the high-pressure moderate-temperature phase is liquid, and the low-pressure high-temperature phase is vapour. The triple point is approximatelyBelow $p_t$, warming stable ordinary ice crosses the sublimation boundary directly into vapour; there is no intervening stable liquid. Above $p_t$, melting and then boiling can occur. The liquid–vapour curve terminates at the liquid-gas critical point, approximately $647.1\mathrm{K}$ and $22.06\mathrm{MPa}$, beyond which there is no liquid–vapour phase boundary.

The distinctive feature is the negative slope of the ordinary ice–water melting line. The Clapeyron equation givesMelting increases entropy but reduces volume because ordinary ice is less dense than liquid water, so $\Delta s>0$ and $\Delta v<0$. Increasing pressure consequently lowers the melting temperature locally. Sublimation and vaporization both increase volume and entropy, giving positive slopes. The following original schematic shows these signs; it is not a quantitative fit and omits the additional high-pressure ice polymorphs.

A historical local anaesthesia method described by Benjamin Ward Richardson in 1866: an atomizer distributes diethyl ether, whose rapid vaporization cools the surface. The physical cooling mechanism and the author's historical account of nerve signalling should be distinguished.^[ref]

Vaporization changes a liquid into a gas. It includes evaporation at a surface and boiling within the liquid. Below the liquid-gas critical point, equilibrium conversion along the liquid-vapour phase coexistence curve involves latent heat; the liquid and vapour have equal chemical potential there.

W. J. M. Rankine was a Scottish engineer and physicist who contributed to thermodynamics, classical mechanics and the teaching of engineering. As professor of civil engineering and mechanics at Glasgow from 1855 to 1872, he emphasized connecting theory with practice and worked with shipbuilders on vessels and engines.^[ref]

The Rankine cycle connects his name with the analysis of heat engines using a working fluid that undergoes vaporization and condensation. Its idealized sequence of pumping, heating, expansion and cooling connects a practical steam engine to a calculation of mechanical work and thermal efficiency. The broader importance of his work lies in making quantitative physical theory part of systematic engineering design.

Institutional historical profile: Imperial College historical plaque booklet: William John Macquorn Rankine.