Latent heat

History

Background

Evaporative cooling

In 1748, an account was published in The Edinburgh Physical and Literary Essays of an experiment by the Scottish physician and chemist William Cullen. Cullen had used an air pump to lower the pressure in a container with diethyl ether. No heat was withdrawn from the ether, yet the ether boiled, but its temperature decreased. And in 1758, on a warm day in Cambridge, England, Benjamin Franklin and fellow scientist John Hadley experimented by continually wetting the ball of a mercury thermometer with ether and using bellows to evaporate the ether. With each subsequent evaporation, the thermometer read a lower temperature, eventually reaching 7 °F (−14 °C). Another thermometer showed that the room temperature was constant at 65 °F (18 °C). In his letter Cooling by Evaporation, Franklin noted that, "One may see the possibility of freezing a man to death on a warm summer's day."

Latent heat

The English word latent comes from Latin latēns, meaning lying hidden. The term latent heat was introduced into calorimetry around 1750 by Joseph Black, commissioned by producers of Scotch whisky in search of ideal quantities of fuel and water for their distilling process to study system changes, such as of volume and pressure, when the thermodynamic system was held at constant temperature in a thermal bath.

It was known that when the air temperature rises above freezing—air then becoming the obvious heat source—snow melts very slowly and the temperature of the melted snow is close to its freezing point. In 1757, Black started to investigate if heat, therefore, was required for the melting of a solid, independent of any rise in temperature. As far as Black knew, the general view at that time was that melting was inevitably accompanied by a small increase in temperature, and that no additional heat was needed beyond what this increase in temperature would require in itself. Soon, however, Black was able to show that much more heat was required during melting than could be explained by the increase in temperature alone. He was also able to show that heat is released by a liquid during its freezing; again, much more than could be explained by the decrease of its temperature alone.

Black would compare the change in temperature of two identical quantities of water, heated by identical means, one of which was, say, melted from ice, whereas the other was heated from merely cold liquid state. By comparing the resulting temperatures, he could conclude that, for instance, the temperature of the sample melted from ice was 140 °F lower than the other sample, thus melting the ice absorbed 140 "degrees of heat" that could not be measured by the thermometer, yet needed to be supplied, thus it was "latent" (hidden). Black also deduced that as much latent heat as was supplied into boiling the distillate (thus giving the quantity of fuel needed) also had to be absorbed to condense it again (thus giving the cooling water required).

Quantifying latent heat

In 1762, Black announced the following research and results to a society of professors at the University of Glasgow. Black had placed equal masses of ice at 32 °F (0 °C) and water at 33 °F (0.6 °C) respectively in two identical, well separated containers. The water and the ice were both evenly heated to 40 °F by the air in the room, which was at a constant 47 °F (8 °C). The water had therefore received 40 – 33 = 7 "degrees of heat". The ice had been heated for 21 times longer and had therefore received 7 × 21 = 147 "degrees of heat". The temperature of the ice had increased by 8 °F. The ice had thus absorbed 8 "degrees of heat", which Black called sensible heat, manifest as a temperature increase, which could be felt and measured. In addition to that, 147 – 8 = 139 "degrees of heat" were absorbed as latent heat, manifest as phase change rather than as temperature change.

Black next showed that a water temperature of 176 °F was needed to melt an equal mass of ice until it was all 32 °F. So now 176 – 32 = 144 "degrees of heat" seemed to be needed to melt the ice. The modern value for the heat of fusion of ice would be 143 "degrees of heat" on the same scale (79.5 "degrees of heat Celsius").

Finally, Black increased the temperature of a mass of water, then vaporized an equal mass of water by even heating. He showed that 830 "degrees of heat" was needed for the vaporization; again based on the time required. The modern value for the heat of vaporization of water would be 967 "degrees of heat" on the same scale.

James Prescott Joule

Later, James Prescott Joule characterised latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy that was indicated by the thermometer, relating the latter to thermal energy.

Specific latent heat

A specific latent heat (L) expresses the amount of energy in the form of heat (Q) required to completely effect a phase change of a unit of mass (m), usually 1kg, of a substance as an intensive property:

${\displaystyle L=\frac{Q}{m}.}$

Intensive properties are material characteristics and are not dependent on the size or extent of the sample. Commonly quoted and tabulated in the literature are the specific latent heat of fusion and the specific latent heat of vaporization for many substances.

From this definition, the latent heat for a given mass of a substance is calculated by

${\displaystyle Q=mL}$

where:

Q is the amount of energy released or absorbed during the change of phase of the substance (in kJ or in BTU),

m is the mass of the substance (in kg or in lb), and

L is the specific latent heat for a particular substance (in kJ kg⁻¹ or in BTU lb⁻¹), either L_f for fusion, or L_v for vaporization.

Table of specific latent heats

The following table shows the specific latent heats and change of phase temperatures (at standard pressure) of some common fluids and gases.

Specific latent heat for condensation of water in clouds

The specific latent heat of condensation of water in the temperature range from −25 °C to 40 °C is approximated by the following empirical cubic function:

${\displaystyle L_{\text{water}}(T)\approx \left(2500.8-2.36T+0.0016T^2-0.00006T^3\right)\text{J/g},}$

where the temperature ${\displaystyle T}$ is taken to be the numerical value in °C.

For sublimation and deposition from and into ice, the specific latent heat is almost constant in the temperature range from −40 °C to 0 °C and can be approximated by the following empirical quadratic function:

${\displaystyle L_{\text{ice}}(T)\approx \left(2834.1-0.29T-0.004T^2\right)\text{J/g}.}$

Variation with temperature (or pressure)

As the temperature (or pressure) rises to the critical point, the latent heat of vaporization falls to zero.