# Physics of humidity and evaporation

This chapter is most relevant to Section F10(iv) from the 2017 CICM Primary Syllabus, which expects the exam candidates to "define humidification, outline the mechanisms of humidification and its importance".  It seems reasonable to expect this, as the main substrate of the respiratory system are gases and vapours, and it makes sense to start the discussion of respiratory physiology with this as a foundation. Humidification is discussed in greater detail in the chapters dealing with the normal physiological mechanisms of humidification and with the technological solutions used to replicate it for mechanical ventilation. For the purpose of this chapter, it will suffice to discuss the colligative properties of liquids which are relevant to the evaporation of water and anaesthetic gases.

In summary:

• Vapour pressure is the pressure exerted by a vapour above the surface of a liquid
• Saturation vapour pressure is the pressure exerted by a vapour in equilibrium with liquid of the same substance. It is influenced by the colligative properties of the liquid (eg. solute concentration) and the temperature.
• The boiling point temperature is the temperature at which vapour pressure equals atmospheric pressure. A lower atmospheric pressure will result in a lower boiling point temperature
• Critical temperature is the temperature above which it is not possible to liquefy a given gas by increasing its pressure
• A substance is a gas when it is above its criticial temperature, and a vapour when it remains in gaseous phase below its critical temperrature
• Critical pressure is the minimum pressure which would suffice to liquefy a substance at its critical temperature
• Critical point is the point of minimum pressure and maximum temperature at which both a gaseous and a liquid phase of a given compound can coexist.
• Specific crritical volume is the volume of space occupied by 1kg of a gas at its critical point
• Latent heat of vapourisation is the heat required to convert a substance from liquid to vapour at a given temperature. Latent heat of vapourisation decreases as ambient temperrature increases, and is reduced to zero at the critical temperature of that substance.
• Absolute humidity is the mass of water vapour present in a given volume of air.
• Relative humidity is the percentage ratio of the mass of water vapour in a given volume of air to the mass required to saturate that given volume of air at the same temperature.

This topic appears to have some exam relevance. Occasionally, ICU trainees are asked these questions in the CICM Part One written paper. Question 13 from the second paper of 2010 and the identical Question 7(p.2) from the second paper of 2009 both asked for details about humidity and evaporation. Like virtually all the questions in those early papers, these were answered poorly ( 27% and 11% respectively), the college comments reflecting the faculty's disappointment. Specific complaints from the examiners were related to the trainees consistently being unable to produce succinct definitions for terms like "absolute humidity" and "latent heat of vaporisation". For purposes of rapid revision, the most important exam-ready terms have been gathered up into a bundle in the grey box above.

The best references for this topic remain the (paywalled) article by Thomas & Stamatakis (2009). One may also recommend Ben Gupta's article for Update in anaesthesia (2012), even though the paper consistently misspells the Amedeo Avogadro's surname as "Avagadro". The official college resource for this topic is probably Davis & Kenny's Basic Physics and measurement in Anaesthesia, of which the latest edition is the 5th (2003). The author owns a more ancient 1995 version, which is surely identical in almost every way, and references it heavily for this chapter.

## Colligative properties of liquids

All fluid properties related to freezing or boiling are colligative properties, which is to say those of those properties which depend upon the number of molecules in solution, rather than on what sort of molecules they are. It’s all determined by the ratio of the number of solute particles to the number of solvent particles. There could be any particles whatsoever.

The colligative properties are:

• Vapour pressure
• Boiling point
• Freezing point
• Osmotic pressure

Osmotic pressure, being more relevant to fluid-shifting rather than respiratory function, enjoys a more thorough discussion elsewhere. For the others, it will suffice to say that introducing solutes into your solvent changes the colligative properties. Doesn’t matter what solute- these properties don’t discriminate. The number of particles is the most important issue. In summary:

• Boiling point increases in proportion to the molar concentration of the solutes
• Freezing point decreases in proportion to the molar concentration of the solutes
• Vapour pressure is dependent on the vapour pressure of each chemical component and the mole fraction of that component in the solution (Raoult’s law)

## Saturation vapour pressure

The definition of vapour pressure is relatively straightforward. It is the pressure exerted by a vapour. The terms  "saturated vapour pressure" and "equilibrium vapour pressure" are essentially synonymous. The IUPAC Gold Book (specifically, their 2008 Glossary of Terms Related to Solubility) only lists "saturation vapour pressure" in its list of definitions, even though some authors (Gupta, 2012) complain that the term  incorrectly implies that the vapour is "dissolved" in the atmosphere, whereas of course it is not (gases freely interpenetrate gases without any need for "solvent").  The IUPAC definition is as follows:

"The pressure exerted by a pure substance (at a given temperature) in a system containing only the vapour and condensed phase (liquid or solid) of the substance."

In short, it is the pressure exerted by a vapour (i.e. a gas) when it is in equilibrium with its liquid phase. To illustrate this concept, the author found an opportunity to play with shiny flask transparencies.

Behold, a flask of gas. It is attached to a manometer. At first, we catch this flask at a paused instant in time,  where the bottom of it is filled with sloshing liquid gas, and the rest of the volume is pure vacuum.

The moment you unpause this simulation, the gas will boil. Vapour will fill the evacuated chamber. This boiling will, of course, not continue forever; i.e. the entire gas is not expected to turn into vapour.  The rate of vapourisation will slow down as the gas concentration in the upper chamber increases. Some of the vapour will also condense in the flask and precipitate back down to the bottom. In short, there will be a rate of evaporation, and a rate of condensation. At some point in time, these processes will be in equilibrium.

At this stage, we can say that the number of molecules entering the vapour phase is equal to the number of molecules entering the liquid phase.

So: once this equilibrium is reached, if one looks at the displacement of the manometer, one is able to measure the pressure exerted by the vapour at equilibrium. That would be your equilibrium vapour pressure. It is also often discussed as "saturation" vapour pressure because the gas phase is completely saturated with that molecule, i.e. no further increases in evaporation are possible.

The vapour pressure of a substance, therefore, describes how "volatile" it is. A gas which has a very high vapour pressure is more volatile, i.e. its tendency to be a gas exceeds its tendency to be a liquid. The saturation vapour pressure of a volatile anaesthetic agent at room temperature may be quite high. For example, for sevoflurane, the SVP value is 157 mmHg, and for desflurane it is 669 mmHg. In contrast, the saturation vapour pressure of something of lower volatility, like water, at room temperature and sea level is only about 18.6 mmHg.

The mention of room temperature and sea level is an important qualifier: saturation vapour pressure is influenced by both pressure and temperature. For example, at body temperature (i.e. in the lower airways) the SVP of water increases to about 47-48 mmHg. These relationships need to be discussed in greater detail, as one can envision a particularly nasty SAQ or viva based on these topics.

## Relationship of saturation vapour pressure and temperature

In short, as temperature increases, so does the vapour pressure. Increasing the energy of the molecules of the liquid by heating them allows more of those molecules to lift off from the surface of the liquid. This can be represented in the form of a graph:

Because of the fact that nothing in this world is ideal, the behaviour expected of an ideal gas is not seen experimentally, and the relationship between temperature and saturation vapour pressure is not linear. Rather, the pressure increases exponentially with temperature. This has implications for sealed containers, which are rather prone to exploding as the result of this phenomenon.

Anyway: here is a real-world example using water. At zero degrees, the saturation vapour pressure is zero because the liquid is frozen and no evaporation is taking place. As temperature increases, the saturation vapour pressure increases exponentially. At 100° C, the saturation vapour pressure is 760 mmHg, which also happens to be the boiling point of water.

This offers a nice segue into the discussion of what exactly a "boiling point" is. This is the temperature at which vapour pressure equals atmospheric pressure. Above this temperature, bubbles of vapour form within the liquid. Below this temperature evaporation takes place only from the surface.

Boiling is distinct from evaporation. Evaporation takes place from the liquid's surface; boiling is something which affects all of the mass of the liquid. As the temperature increases, the vapour pressure becomes high enough to form bubbles deep below the surface of the liquid (where the vapour pressure must overcome the combination of atmospheric pressure as well as the pressure from the column of liquid at depth).

## Relationship of boiling point and atmospheric pressure

From the above, it follows that pressure clearly influences the temperature at which a liquid will boil. The higher the ambient pressure, the higher the temperature at which the saturation vapour pressure will exceed the ambient pressure. If we descend into the Challenger Deep and stick a heating filament, out of our bathysphere, one would need to produce a very large amount of heat to create a bubble of steam.  Down at the bottom of a 1 km mine shaft, the boiling point of water is 104 C°.  Conversely, as pressure decreases, the boiling point temperature also decreases. On top of Mount Everest the boiling point of water is about 65 C°.

As you travel higher, you encounter a decreasing atmospheric pressure, and so the boiling point temperature continues to decrease. This goes on until you hit the Armstrong Limit, where body fluid boiling point temperature is the same as normal core body temperature. Water has a saturated vapour pressure of 47mmHg at body temperature (37°C); therefore at an atmospheric pressure of 47 mmHg any exposed body fluids will boil. Those lucky few who have been exposed to such conditions and survived to report on their experience describe the peculiar sensation of their saliva boiling just before they blacked out.

## Critical pressure and critical temperature

According to the IUPAC Gold Book:

The critical temperature is "that temperature, characteristic of each gas, above which it is not possible to liquefy a given gas."

The critical pressure of a gas is "the minimum pressure which would suffice to liquefy a substance at its critical temperature. Above the critical pressure, increasing the temperature will not cause a fluid to vaporize to give a two-phase system".

In short, for every gas, there should be some critical temperature above which that gas cannot be liquefied, no matter how much pressure is applied. The converse is the critical pressure: at any higher pressure, no vapour will form, and the gas will remain a liquid without evaporating.

To illustrate this, anaesthesia textbooks love to use nitrous oxide. As CICM examiners frequently have a background in anaesthesia, and given their propensity to plagiarise questions from the ANZCA exams, Australian ICU trainees should fully expect nitrous oxide to be examined in the CICM Part One, even though its relationship to routine Intensive Care practice is minimal.

Anyway. Observe, a mass of nitrous oxide at 40°C. Watch it calmly obey Boyle's law as we change the volume of its container.

As the volume increases, the pressure decreases in a smooth almost-linear relationship. At all stages in this process, nitrous oxide remains a gas. In fact, no additional pressure would force it to become a liquid at this temperature, because the temperature is above the critical temperature for nitrous oxide, which is 36.5°C.

Ok then, let us decrease the temperature to 36.5°C and do the same experiment.

Now, the graph has a weird knee in it. At the higher range of pressures, all of the nitrous oxide remains a liquid at this temperature, and there is no gas/vapour in the chamber. Then, at a certain pressure, boiling occurs and it becomes a gas. That pressure is the critical pressure of nitrous oxide: it is the minimum pressure required to liquify this gas at this temperature.  The critical pressure for nitrous oxide happens to be extremely high, about 73 atmospheres. Below the critical pressure, at this temperature, all of the nitrous oxide is gaseous and follows Boyle's law.

Now, let us lower the temperature to 20°C, essentially the room temperature in an operating theatre. As pressure drops, liquid nitrous oxide will evaporate and will separate into a liquid phase and a vapour phase. At 20°C, this occurs at a pressure of around 55 atmospheres. As the volume increases, the pressure will remain stable.

This may sound weird, but consider that this 55 bar pressure is the saturated vapour pressure of nitrous oxide at 20°C. If one keeps the temperature the same but increases the volume, more of the liquid will evaporate, leaving the pressure stable. This process will continue as volume increases, until all the liquid has evaporated. Only beyond that point will the nitrous oxide gas behave according to Boyle's law. Anaesthesia viva examiners love this factoid, because it has a practical application in the operating theatre. The tank of nitrous oxide supplied to the operating theatre will usually have a mixture of liquid and vapour inside, with a tank pressure of 55 barr. As gas is siphoned off, this pressure will remain unchanged until all of the liquid nitrous oxide has evaporated. As a result, in order to determine how much nitrous oxide is left, one would need to weigh the tank.

Typically, in textbooks concerned with the physics aspect of anaesthesia, these isotherms are all rolled into one graph, which usually looks like this:

At this stage it would be important for the hardcore physics nerd to point that there is a distinction drawn between the "gas" and "vapour" phases. The terms are not entirely synonymous. The word "vapour" is used to describe an evaporated substance which is below its critical temperature; i.e. its a gas which still has the option of becoming a liquid if the pressure rises. In contrast, the word "gas" is specifically used to describe a substance which is above its critical temperature, i.e. no matter what the pressure does it will never liquify. Thus, all water in the troposphere of the earth is by this definition a vapour, as the critical temperature for it is approximately 354°C.

A "gas" and a "vapour" state of any substance may have essentially identical physicochemical properties.

Strictly speaking the word 'gas' applies to a substance above its critical temperature while 'vapour' is the word used for a substance below its critical temperature.

From this graph, one can see that there is a point of minimum pressure and maximum temperature at which both a gaseous and a liquid phase of a given compound can coexist. This is the critical pointThe volume of space occupied by 1kg of a gas at its critical point is generally referred to as the specific critical volume, though this term is not found in the IUPAC Gold Book and therefore may represent some sort of heretical departure from normal physics nomenclature.

It is probably worth remembering some of these graphs, and being able to reproduce them on cue. For nitrous oxide specifically, these are all based on some work by Couch et al (1961), who measured these data empirically and plotted them on a pressure/volume graph (see below.

## Latent heat of vapourisation

With all this talk of boiling and isotherms,  logically, the next important thing to discuss is the amount of energy required to bring about the evaporation of a liquid. Energy needs to be invested in the liquid (as heat) which translates into more rapid molecular movement which is required for evaporation to occur. The amount of energy which is required for this is called the latent heat of vapourisation. Davis (1992) gives a definition of this term which is ready for exam regurgitation:

Specific latent heat is defined as the heat required to convert 1 kilogram of a substance from one phase to another at a given temperature (SI unit of specific latent heat Jkg-1).

Thus, in order to 1kg of water to become 1kg of steam at body temperature, 2.42 MJ is required to turn 1 kg water into 1 kg vapour. The lower the starting temperature, the greater the amount of latent heat required. This can be plotted on a graph of temperature vs. latent heat. To again borrow nitrous oxide as a handy example:

Thus, one can see that as temperature increases, the additional latent heat of vapourisation decreases, until it hits zero. The temperature at which it hits zero is the critical temperature of that liquid. Above that ambient temperature, no added latent heat is required to make the liquid into a vapour- it is spontaneously maintained as vapour already. Or rather, the term loses applicability because, in order for latent heat of vapourisation to be a meaningful term, there must be some liquid to evaporate, and beyond the critical temperature, the substance can't be liquified at any pressure.

Latent heat of vapourisation has some implications for the care of patients in the operating theatre, with its Siberian chill. For the patient, there is a significant energy investment required to maintain the humidity of inspired gases. The chapter from Davis (p. 132, from the 1995 edition) calculate that at a minute volume of 7L/min, the total heat loss from respiration (i.e.watts of energy used to heat enough water to humidify the inspired gas) is 12 W, which is about 15% of the total basal heat loss. This is working from the assumption that inspired gases are perfectly dry, i.e. the humidity is 0%.

Speaking of humidifying inspired gases:

## Absolute humidity and relative humidity

In chemistry, humidity is a term used to refer to the water content of a gas volume. It can be described in absolute or relative terms. This is probably unfairly anthropocentric, as other liquids don't have a special word to describe their vapour content; presumably, if the main life-giving fluid in one's biosphere was liquid methane, one would have a special term for that instead. Anyway;  to borrow the definitions from Davis (1995, p.146 of the 4th edition):

Absolute humidity is the mass of water vapour present in a given volume of air.

Relative humidity is the ratio of the mass of water vapour in a given volume of air to the mass required to saturate that given volume of air at the same temperature. It is usually expressed as a percentage.

The IUPAC gives a slightly different wording:

[Relative humidity is] "the ratio, often expressed as a percentage, of the partial pressure of water in the atmosphere at some observed temperature, to the saturation vapour pressure of pure water at this temperature."

This has some specific (potentially, viva-able) implications for the ICU and anaesthesia population. Let's say the absolute humidity of air at 20°C is something like 17g/m3, which represents a relative humidity of 100%. When warmed to body temperature, the absolute humidity remains the same (17g/m3. However, fully saturated air at 37°C actually contains 44g/m3. Thus, warming this air to body temperature reduces the relative humidity to 39%. Additional energy is expended on evaporating additional water so that the inspired gas reaches 100% humidity by the time it gets into the bronchi.

## Relationship of colligative properties and solute content

Though this is ostensibly the Respiratory System section, one thing follows naturally from another, and it would probably be amiss not to touch on the specific matter of solute content as an influence on boiling point (and freezing point, for that matter).

In short, the boiling point and freezing point, at any given pressure,  is influenced by the solutes dissolved in the liquid. Specifically, the boiling point and freezing point decrease proportionally to the molar concentration of solute dissolved in the liquid.

This freezing point depression is the property which governs the use of antifreeze in the cooling water of internal combustion engines. It also causes road ice to melt when salt is poured over it. Weirdly, the same concentration of solute depresses the freezing point by more degrees than it increases the boiling point.  For water, the lowest depressed freezing point seems to be around -18 C°. Some animals have ways of making their body fluids hyperosmolar, thereby surviving temperature excesses.

This has implications for body fluids, which have a tendency to have a bunch of solutes in them.  In a solution with multiple solutes, the vapour pressure will be depressed.  Each solute’s individual vapour pressure contributes to the total vapour pressure, in proportion to its mole fraction. The mole fraction is the proportion of the total molarity of solutes this solute contributes. So the more solutes you add, the lower the individual solute mole fraction and the lower the contributed vapour pressure.

That’s confusing. The bottom line is, the more solutes you add to a solution, the lower the vapour pressure, at any given temperature and pressure level.

## References

IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).

Hill, D. W. "Physics applied to anaesthesia VI: gases and vapours (2)." British journal of anaesthesia 38.9 (1966): 753-759.

Couch, Earl J., and K. A. Kobe. "Volumetric Behavior of Nitrous Oxide. Pressure-Volume Isotherms at High Pressures." Journal of Chemical and Engineering Data 6.2 (1961): 229-233.

Wilkes, Antony, and David Williams. "Measurement of humidity." Anaesthesia & Intensive Care Medicine 19.4 (2018): 198-201.

Thomas, Gary, and Stephen Stamatakis. "Physics of gases." Anaesthesia & Intensive Care Medicine 10.1 (2009): 48-51.

Gupta, Ben. "Gases and Vapours" Anaesthesia 15.2 (2012).