# Latent heat

Although phase change phenomena such as the solidification of lava, the melting of ice, the evaporation of water, and the precipitation of rain have been observed by mankind for centuries, the scientific methods used to study phase change were not developed until the seventeenth century because a flawed understanding of temperature, energy, and heat prevailed. It was incorrectly believed that the addition or removal of heat could always be measured by a change in temperature. Based on the misconception that temperature change always accompanies heat addition, a solid heated to its melting point was thought to require only a very small amount of additional heat to completely melt. Likewise, it was thought that only a small amount of extra cooling was required to freeze a liquid at its melting point. In both of these examples, the heat transferred during phase change was believed to be very small, because the temperature of the substance undergoing the phase change did not change by a significant amount.

Temperature profile for phase change from subcooled ice to superheated steam.

Between 1758 and 1762, an English professor of medicine, Dr. Joseph Black, conducted a series of experiments measuring the heat transferred during phase change processes. He found that the quantity of heat transferred during phase change was in fact very large, a phenomenon that could not be explained in terms of sensible heat. He demonstrated that the conventional understanding of heat transferred during phase change was wrong, and he used the term “latent heat” to define heat transferred during phase change. Latent heat is a hidden heat, and it is not evident until a substance undergoes a phase change. Perhaps the most significant application of Dr. Black’s latent heat theory was James Watt’s 500% improvement of steam engine thermal efficiency. James Watt was an engineer and Dr. Black’s assistant for a time. The concept of latent heat can be demonstrated by tracing the phase change of water from subcooled ice below 0 °C, to superheated vapor above 100 °C. Let us consider a 1-kg mass of ice with an initial temperature of –20 °C. When heat is added to the ice, its temperature gradually increases to 0 °C, at which point the temperature stops increasing even when heat is continuously added. During the ensuing interval of constant temperature, the change of phase from ice to liquid water can be observed. After the entire mass of ice is molten, further heating produces an increase in temperature of the now-liquid, up to 100 °C. Continued heating of the liquid water at 100 °C does not yield any increase in temperature; instead, the liquid water is vaporized. After the last drop of the water is vaporized, continued heating of the vapor will result in the increase of its temperature. The phase change process from subcooled ice to superheated vapor is shown in the figure on the right. It is seen that a substantial amount of heat is required during a change of phase, an observation consistent with Dr. Black’s latent heat theory.

The heat required to melt a solid substance of unit mass is defined as the latent heat of fusion, and it is represented by ${h_{s\ell }}$. The latent heat of fusion for water is about 335 kJ/kg. The heat required to vaporize a liquid substance of unit mass is defined as the latent heat of vaporization, and it is represented by ${h_{\ell v}}$. The latent heat of vaporization for water is about 2251 kJ/kg. The latent heats of other materials, shown in the table below, demonstrate that the latent heat of vaporization for all materials is much larger than their latent heat of fusion, because the molecular spacing for vapor is much larger than that for solid or liquid. The latent heat for deposition/sublimation, hsv, for water is about 2847 kJ/kg.

Latent heat of fusion and vaporization for selected materials at 1 atm

 Substance Melting point (°C) ${h_{s\ell }}({\rm{kJ/kg}})$ Boiling point (°C) ${h_{\ell v}}({\rm{kJ/kg}})$ Oxygen –218.18 14 –183 220 Ethyl Alcohol –114 105 78 870 Water 0 335 100 2251 Lead 327 25 1750 900 Silver 961 88 2193 2300 Tungsten 3410 184 5900 4800

## References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.