Relative humidity (RH) and temperature (T) data from an RH&T sensor like the DHT22 can be used to compute not only absolute humidity AH but also dewpoint temperature TD

There has been a fair amount of interest in my formula which computes AH from measured RH and T, since it adds value to the output of RH&T sensors. To further extend this value, I have developed another formula which computes dewpoint temperature TD from measured RH and T.

Formula for computing dewpoint temperature TD

In this formula (P Mander 2017) the measured temperature T and the computed dewpoint temperature TD are expressed in degrees Celsius, and the measured relative humidity RH is expressed in %

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– – – –

Strategy for computing TD from RH and T

1. The dewpoint temperature TD is defined in the following relation where RH is expressed in %

2. To obtain values for Psat, we can use the Bolton formula[REF, eq.10] which generates saturated vapor pressure Psat (hectopascals) as a function of temperature T (Celsius)

These formulas are stated to be accurate to within 0.1% over the temperature range –30°C to +35°C

3. Substituting in the first equation yields

Taking logarithms


Separating TD terms on one side yields

– – – –

Spreadsheet formula for computing TD from RH and T

1) Set up data entry cells for RH in % and T in degrees Celsius.

2) Depending on whether your spreadsheet uses a full point (.) or comma (,) for the decimal separator, copy the appropriate formula below and paste it into the computation cell for TD.

Formula for TD (decimal separator = .)


Formula for TD (decimal separator = ,)


3) Replace T and RH in the formula with the respective cell references. (see comment)

Your spreadsheet is now complete. Enter values for RH and T, and the TD computation cell will return the dewpoint temperature. If an object whose temperature is at or below this temperature is present in the local space, the thermodynamic conditions are satisfied for water vapor to condense (or freeze if TD is below 0°C) on the surface of the object.

– – – –

© P Mander August 2017

From the perspective of classical thermodynamics, osmosis has a rather unclassical history. Part of the reason for this, I suspect, is that osmosis was originally categorised under the heading of biology. I can remember witnessing the first practical demonstration of osmosis in a biology class, the phenomenon being explained in terms of pores (think invisible holes) in the membrane that were big enough to let water molecules through, but not big enough to let sucrose molecules through. It was just like a kitchen sieve, we were told. It lets the fine flour pass through but not clumps. This was very much the method of biology in my day, explaining things in terms of imagined mechanism and analogy.

And it wasn’t just in my day. In 1883, JH van ‘t Hoff, an able theoretician and one of the founders of the new discipline of physical chemistry, became suddenly convinced that solutions and gases obeyed the same fundamental law, pv = RT. Imagined mechanism swiftly followed. In van ‘t Hoff’s interpretation, osmotic pressure depended on the impact of solute molecules against the semipermeable membrane because solvent molecules, being present on both sides of the membrane through which they could freely pass, did not enter into consideration.

It all seemed very plausible, especially when van ‘t Hoff used the osmotic pressure measurements of the German botanist Wilhelm Pfeffer to compute the value of R in what became known as the van ‘t Hoff equation


where Π is the osmotic pressure, and found that the calculated value for R was almost identical with the familiar gas constant. There really did seem to be a parallelism between the properties of solutions and gases.


JH van ‘t Hoff (1852-1911)

The first sign that there was anything amiss with the so-called gaseous theory of solutions came in 1891 when van ‘t Hoff’s close colleague Wilhelm Ostwald produced unassailable proof that osmotic pressure is independent of the nature of the membrane. This meant that hypothetical arguments as to the cause of osmotic pressure, such as van ‘t Hoff had used as the basis of his theory, were inadmissible.

A year later, in 1892, van ‘t Hoff changed his stance by declaring that the mechanism of osmosis was unimportant. But this did not affect the validity of his osmotic pressure equation ΠV = RT. After all, it had been shown to be in close agreement with experimental data for very dilute solutions.

It would be decades – the 1930s in fact – before the van ‘t Hoff equation’s formal identity with the ideal gas equation was shown to be coincidental, and that the proper thermodynamic explanation of osmotic pressure lay elsewhere.

But long before the 1930s, even before Wilhelm Pfeffer began his osmotic pressure experiments upon which van ‘t Hoff subsequently based his ideas, someone had already published a thermodynamically exact rationale for osmosis that did not rely on any hypothesis as to cause.

That someone was the American physicist Josiah Willard Gibbs. The year was 1875.


J. Willard Gibbs (1839-1903)

– – – –

Osmosis without mechanism

It is a remarkable feature of Gibbs’ On the Equilibrium of Heterogeneous Substances that having introduced the concept of chemical potential, he first considers osmotic forces before moving on to the fundamental equations for which the work is chiefly known. The reason is Gibbs’ insistence on logical order of presentation. The discussion of chemical potential immediately involves equations of condition, among whose different causes are what Gibbs calls a diaphragm, i.e. a semipermeable membrane. Hence the early appearance of the following section


In equation 77, Gibbs presents a new way of understanding osmotic pressure. He makes no hypotheses about how a semipermeable membrane might work, but simply states the equations of condition which follow from the presence of such a membrane in the kind of system he describes.

This frees osmosis from considerations of mechanism, and explains it solely in terms of differences in chemical potential in components which can pass the diaphragm while other components cannot.

In order to achieve equilibrium between say a solution and its solvent, where only the solvent can pass the diaphragm, the chemical potential of the solvent in the fluid on both sides of the membrane must be the same. This necessitates applying additional pressure to the solution to increase the chemical potential of the solvent in the solution so it equals that of the pure solvent, temperature remaining constant. At equilibrium, the resulting difference in pressure across the membrane is the osmotic pressure.

Note that increasing the pressure always increases the chemical potential since


is always positive (V1 is the partial molar volume of the solvent in the solution).

– – – –

Europe fails to notice (almost)

Gibbs published On the Equilibrium of Heterogeneous Substances in Transactions of the Connecticut Academy. Choosing such an obscure journal (seen from a European perspective) clearly would not attract much attention across the pond, but Gibbs had a secret weapon. He had a mailing list of the world’s greatest scientists to which he sent reprints of his papers.

One of the names on that list was James Clerk Maxwell, who instantly appreciated Gibbs’ work and began to promote it in Europe. On Wednesday 24 May 1876, the year that ‘Equilibrium’ was first published, Maxwell gave an address at the South Kensington Conferences in London on the subject of Gibbs’ development of the doctrine of available energy on the basis of his new concept of the chemical potentials of the constituent substances. But the audience did not share Maxwell’s enthusiasm, or in all likelihood share his grasp of Gibbs’ ideas. When Maxwell tragically died three years later, Gibbs’ powerful ideas lost their only real champion in Europe.

It was not until 1891 that interest in Gibbs masterwork would resurface through the agency of Wilhelm Ostwald, who together with van ‘t Hoff and Arrhenius were the founders of the modern school of physical chemistry.


Wilhelm Ostwald (1853-1932) He not only translated Gibbs’ masterwork into German, but also produced a profound proof – worthy of Sadi Carnot himself – that osmotic pressure must be independent of the nature of the semipermeable membrane.

Although perhaps overshadowed by his colleagues, Ostwald had a talent for sensing the direction that the future would take and was also a shrewd judge of intellect – he instinctively felt that there were hidden treasures in Gibbs’ magnum opus. After spending an entire year translating ‘Equilibrium’ into German, Ostwald wrote to Gibbs:

“The translation of your main work is nearly complete and I cannot resist repeating here my amazement. If you had published this work over a longer period of time in separate essays in an accessible journal, you would now be regarded as by far the greatest thermodynamicist since Clausius – not only in the small circle of those conversant with your work, but universally—and as one who frequently goes far beyond him in the certainty and scope of your physical judgment. The German translation, hopefully, will more secure for it the general recognition it deserves.”

The following year – 1892 – another respected scientist sent a letter to Gibbs regarding ‘Equilibrium’. This time it was the British physicist, Lord Rayleigh, who asked Gibbs:

“Have you ever thought of bringing out a new edition of, or a treatise founded upon, your “Equilibrium of Het. Substances.” The original version though now attracting the attention it deserves, is too condensed and too difficult for most, I might say all, readers. The result is that as has happened to myself, the idea is not grasped until the subject has come up in one’s own mind more or less independently.”

Rayleigh was probably just being diplomatic when he remarked that Gibbs’ treatise was ‘now attracting the attention it deserves’. The plain fact is that nobody gave it any attention at all. Gibbs and his explanation of osmosis in terms of chemical potential was passed over, while European and especially British theoretical work centered on the more familiar and more easily understood concept of vapor pressure.

– – – –

Gibbs tries again

Although van ‘t Hoff’s osmotic pressure equation ΠV = RT soon gained the status of a law, the gaseous theory that lay behind it remained clouded in controversy. In particular, van ‘t Hoff’s deduction of the proportionality between osmotic pressure and concentration was an analogy rather than a proof, since it made use of hypothetical considerations as to the cause of osmotic pressure. Following Ostwald’s proof that these were inadmissible, the gaseous theory began to look hollow. A better theory was needed.


Lord Kelvin (1824-1907) and Lord Rayleigh (1842-1919)

This was provided in 1896 by the British physicist, Lord Rayleigh, whose proof was free of hypothesis but did make use of Avogadro’s law, thereby continuing to assert a parallelism between the properties of solutions and gases. Heavyweight opposition to this soon materialized from the redoubtable Lord Kelvin. In a letter to Nature (21 January 1897) he charged that the application of Avogadro’s law to solutions had “manifestly no theoretical foundation at present” and further contended that

“No molecular theory can, for sugar or common salt or alcohol, dissolved in water, tell us what is the true osmotic pressure against a membrane permeable to water only, without taking into account laws quite unknown to us at present regarding the three sets of mutual attractions or repulsions: (1) between the molecules of the dissolved substance; (2) between the molecules of water; (3) between the molecules of the dissolved substance and the molecules of water.”

Lord Kelvin’s letter in Nature elicited a prompt response from none other than Josiah Willard Gibbs in America. Twenty-one years had now passed since James Clerk Maxwell first tried to interest Europe in the concept of chemical potentials. In Kelvin’s letter, with its feisty attack on the gaseous theory, Gibbs saw the opportunity to try again.

In his letter to Nature (18 March 1897), Gibbs opined that “Lord Kelvin’s very interesting problem concerning molecules which differ only in their power of passing a diaphragm, seems only to require for its solution the relation between density and pressure”, and highlighted the advantage of using his potentials to express van ‘t Hoff’s law:

“It will be convenient to use certain quantities which may be called the potentials of the solvent and of the solutum, the term being thus defined: – In any sensibly homogeneous mass, the potential of any independently variable component substance is the differential coefficient of the thermodynamic energy of the mass taken with respect to that component, the entropy and volume of the mass and the quantities of its other components remaining constant. The advantage of using such potentials in the theory of semi-permeable diaphragms consists partly in the convenient form of the condition of equilibrium, the potential for any substance to which a diaphragm is freely permeable having the same value on both sides of the diaphragm, and partly in our ability to express van’t Hoff law as a relation between the quantities characterizing the state of the solution, without reference to any experimental arrangement.”

But once again, Gibbs and his chemical potentials failed to garner interest in Europe. His timing was also unfortunate, since British experimental research into osmosis was soon to be stimulated by the aristocrat-turned-scientist Lord Berkeley, and this in turn would stimulate a new band of British theoreticians, including AW Porter and HL Callendar, who would base their theoretical efforts firmly on vapor pressure.

– – – –

Things Come Full Circle

As the new century dawned, van ‘t Hoff cemented his reputation with the award of the very first Nobel Prize for Chemistry “in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions”.

The osmotic pressure law was held in high esteem, and despite Lord Kelvin’s protestations, Britain was well disposed towards the Gaseous Theory of Solutions. The idea circulating at the time was that the refinements of the ideal gas law that had been shown to apply to real gases, could equally well be applied to more concentrated solutions. As Lord Berkeley put it in the introduction to a paper communicated to the Royal Society in London in May 1904:

“The following work was undertaken with a view to obtaining data for the tentative application of van der Waals’ equation to concentrated solutions. It is evidently probable that if the ordinary gas equation be applicable to dilute solutions, then that of van der Waals, or one of analogous form, should apply to concentrated solutions – that is, to solutions having large osmotic pressures.”

Lord Berkeley’s landmark experimental studies on the osmotic pressure of concentrated solutions called renewed attention to the subject among theorists, who now had some fresh and very accurate data to work with. Alfred Porter at University College London attempted to make a more complete theory by considering the compressibility of a solution to which osmotic pressure was applied, while Hugh Callendar at Imperial College London combined the vapor pressure interpretation of osmosis with the hypothesis that osmosis could be described as vapor passing through a large number of fine capillaries in the semipermeable membrane. This was in 1908.


H L Callendar (1863-1930)

So seventeen years after Wilhelm Ostwald conclusively proved that hypothetical arguments as to the cause of osmotic pressure were inadmissible, things came full circle with hypothetical arguments once more being advanced as to the cause of osmotic pressure.

And as for Gibbs, his ideas were as far away as ever from British and European Science. The osmosis papers of both Porter (1907) and Callendar (1908) are substantial in referenced content, but nowhere do either of them make any mention of Gibbs or his explanation of osmosis on the basis of chemical potentials.

There is a special irony in this, since in Callendar’s case at least, the scientific papers of J Willard Gibbs were presumably close at hand. Perhaps even on his office bookshelf. Because that copy of Gibbs’ works shown in the header photo of this post – it’s a 1906 first edition – was Hugh Callendar’s personal copy, which he signed on the front endpaper.


Hugh Callendar’s signature on the endpaper of his personal copy of Gibbs’ Scientific Papers, Volume 1, Thermodynamics.

– – – –


Throughout this post, I have made repeated references to that inspired piece of thinking by Wilhelm Ostwald which conclusively demonstrated that osmotic pressure must be independent of the nature of the membrane.

Ostwald’s reasoning is so lucid and compelling, that one wonders why it didn’t put an end to speculation on osmotic mechanisms. But it didn’t, and hasn’t, and probably won’t.

Here is how Ostwald presented the argument in his own Lehrbuch der allgemeinen Chemie (1891). Enjoy.


“… it may be stated with certainty that the amount of pressure is independent of the nature of the membrane, provided that the membrane is not permeable by the dissolved substance. To understand this, let it be supposed that two separating partitions, A and B, formed of different membranes, are placed in a cylinder (fig. 17). Let the space between the membranes contain a solution and let there be pure water in the space at the ends of the cylinder. Let the membrane A show a higher pressure, P, and the membrane B show a smaller pressure, p. At the outset, water will pass through both membranes into the inner space until the pressure p is attained, when the passage of water through B will cease, but the passage through A will continue. As soon as the pressure in the inner space has been thus increased above p, water will be pressed out through B. The pressure can never reach the value P; water must enter continuously through A, while a finite difference of pressures is maintained. If this were realised we should have a machine capable of performing infinite work, which is impossible. A similar demonstration holds good if p>P ; it is, therefore, necessary that P=p; in other words, it follows necessarily that osmotic pressure is independent of the nature of the membrane.”

(English translation by Matthew Pattison Muir)

– – – –

P Mander July 2015

Radon gas levels in indoor spaces are known to fluctuate considerably, so continuous monitoring is necessary to compute long-term averages. This particular radon detector, which uses continuous air sampling coupled to algorithm-based alpha spectrometry, is designed to do this job and has gained good reviews on Amazon. It is made in Norway by Corentium AS.

My unit has been in continuous operation since October 2015. Although the short-term average figure goes up and down from day to day, and to a lesser extent from week to week (the display shows alternating 1-day and 7-day figures), the long-term average figure is really quite steady.

I was thinking about this the other day, and it occurred to me that since the long-term figure varies so little in a month’s turning, I could use it to estimate the entry rate of radon gas into the enclosed space where the device is located.

– – – –

Formula for computing entry rate

1. Units in becquerels per cubic meter (Bq/m3)

If the device is showing a steady long-term average figure (n) and the enclosed space has a volume of v cubic meters, the entry rate of radon gas is computed as follows:
Entry rate = 8.78nv attomoles per month
For example, if n = 79 and v = 5
Entry rate = 8.78 × 79 × 5 = 3468 attomoles per month
(1 attomole = 10-18 moles)

2. Units in picocuries per litre (pCi/L)

If the device is showing a steady long-term average figure (n) and the enclosed space has a volume of v cubic meters, the entry rate of radon gas is computed as follows:
Entry rate = 324.74nv attomoles per month
For example, if n = 4.64 and v = 5
Entry rate = 324.74 × 4.64 × 5 = 7534 attomoles per month
(1 attomole = 10-18 moles)

– – – –

Explanatory notes
First I should clarify what I mean by entry rate. Radon is a gas that seeps into enclosed spaces through conduits, joints and cracks; it is also exhaled by diffusion through surfaces. Having infiltrated the space, some of the radon will escape, either through back-diffusion or infiltration into adjacent spaces. Without knowing the rates of ingress and escape, one can conclude that a steady long-term average figure on the detector, which implies a steady concentration of radon in the enclosed space, indicates equilibrium between the rate of radon ingress on the one hand, and the rate of radon escape and decay on the other. In other words at equilibrium

Defining entry rate as the difference between ingress rate and escape rate, we have

Given the premise that the concentration of radon gas in the enclosed space is steady, the decay rate can be taken as constant since it is determined solely by the concentration – i.e. the number of radon atoms present in a given volume. So a steady long-term average on the detector means that the entry rate, as here defined, is also constant.

Radon is a very dense gas, almost 8 times as dense as air, and this tempts many to think that radon accumulates at the bottom of an enclosed space. This is not what happens. Like any gas, radon exhibits the phenomenon of diffusion – which is the tendency of a substance to spread uniformly throughout the space available to it. What the density of a gas does affect is the rate at which the gas diffuses. But given sufficient time to reach a state of equilibrium, it can be assumed that the concentration of radon gas will be uniform throughout the enclosed space.

– – – –

Assigning a unit of time
So far I have said nothing concerning the unit of time to be applied in relation to the foregoing rate equation. Now we can address this issue, which constitutes the novelty of the computation scheme.

— Let the unit of time by which rate is measured be set equal to the half-life of the isotope (Rn-222) of which radon gas is largely composed.

Let the entry rate of radon gas into a previously radon-free bounded space be x atoms per unit of time corresponding to the half-life of Rn-222. At the end of the first half-life period, x/2 atoms will have decayed (via α emission) while x/2 atoms remain. At the end of the second half-life period, the first x atoms will have decayed to x/4 while the second x atoms will have decayed to x/2. At the end of the third half-life period, the first x atoms will have decayed to x/8 and the second x atoms to x/4, while the third x atoms will have decayed to x/2 … and so on according to the following scheme

This process forms an absolutely convergent geometric series in which the number of radon atoms remaining in the space after n half-life periods will be

The conclusion is reached that if the entry rate of radon gas into a previously radon-free bounded space is x radon atoms in the unit of time corresponding to the half-life of Rn-222, the number of radon atoms in this space will over successive half-lives approach a steady-state value of x.

Assuming diffusion throughout the space, a steady state value of x should be realized in little more than a month since when n = 8 (equivalent to 30.6 days) the series sum is 99.6% of x.

– – – –

Computing entry rate
Given a steady long-term average figure on the detector, which implies a steady concentration of radon gas throughout the bounded space, the number of radon atoms in this space can be estimated as follows.

For decay rates measured in becquerels per cubic meter (Bq/m3)
Let the long-term average figure on the detector, measured in decays per second per cubic meter be n, and let the bounded space be v cubic meters.
In the half-life of Rn-222 (3.8235 days) the number of decays in volume v will be n × v × 330,350
This equals x/2 where x is the steady state population of radon atoms in volume v
Therefore x = n × v × 660,701 radon atoms
By the theorem, x is also the number of radon atoms entering the bounded space in a unit of time equal to the half-life of the isotope (Rn-222) of which radon gas is largely composed – 3.8235 days. The magnitude 8x is therefore the number of radon atoms entering the space in a month (8 x 3.8235 = 30.6). Dividing 8x by the Avogadro number converts the number of radon atoms into moles of radon gas:
Entry rate (moles of radon gas per month) = 8 × n × v × 660,701 / (6.022 x 10^23)

The entry rate of radon gas ≅ 8.78nv attomoles per month
(1 attomole = 10-18 moles)

For decay rates measured in picocuries per litre (pCi/L)
Let the long-term average figure on the detector, measured in picocuries per litre be n, and let the bounded space be v cubic meters.

The entry rate of radon gas ≅ 324.74nv attomoles per month
(1 attomole = 10-18 moles)

– – – –

Please note that the theorem on which the above calculations are based is untested. Until the theorem has been tested and the accuracy of results obtained with it has been determined, the calculation of entry rate as herein defined can only be regarded as a theoretical prediction and should be viewed accordingly.

P Mander May 2017

– – – –

William Nicholson and Anthony Carlisle

May 1800: Carlisle (left) and Nicholson discover electrolysis

The two previous posts on this blog concerning the leaking of details about the newly-invented Voltaic pile to Anthony Carlisle and William Nicholson, and their subsequent discovery of electrolysis, are more about the path of temptation and birth of electrochemistry than about classical thermodynamics. In fact there was no thermodynamic content at all.

So by way of steering this set of posts back on track, I thought I would apply contemporary thermodynamic knowledge to Carlisle and Nicholson’s 18th century activities, in order to give another perspective to their famous experiments.

– – – –

The Voltaic pile


Z = zinc, A = silver

In thermodynamic terms, Alessandro Volta’s fabulous invention – an early form of battery – is a system capable of performing additional work other than pressure-volume work. The extra capability can be incorporated into the fundamental equation of thermodynamics by adding a further generalised force-displacement term: the intensive variable is the electrical potential E, whose conjugate extensive variable is the charge Q moved across that potential




At constant temperature and pressure, the left hand side identifies with dG. For an appreciable difference therefore


where E is the electromotive force of the cell, Q is the charge moved across the potential, and ΔGrxn is the free energy change of the reaction taking place in the battery.

For one mole of reaction, Q = nF where n is the number of moles of electrons transferred per mole of reaction, and F is the total charge on a mole of electrons, otherwise known as the Faraday. For a reaction to occur spontaneously at constant temperature and pressure, ΔGrxn must be negative and so the EMF must be positive. Under standard conditions therefore


The redox reaction which took place in the Voltaic pile constructed by Carlisle and Nicholson was


ΔG0rxn for this reaction is –146.7 kJ/mole, and n=2, giving an EMF of 0.762 volts.

We know from Nicholson’s published paper that their first Voltaic pile consisted of “17 half crowns, with a like number of pieces of zinc”. We also know that Volta’s method of constructing the pile – which Carlisle and Nicholson followed – resulted in the uppermost and lowest discs acting merely as conductors for the adjoining discs. Thus there were not 17, but 16 cells in Carlisle and Nicholson’s first Voltaic pile, giving a total EMF of 12.192 volts.

– – – –

External work

On May 1st, 1800, Carlisle and Nicholson set up their Voltaic pile, gave themselves an obligatory electric shock, and then began experiments with an electrometer which showed “that the action of the instrument was freely transmitted through the usual conductors of electricity, but stopped by glass and other non-conductors.”

Electrical contact with the pile was assisted by placing a drop of water on the uppermost disc, and it was this action which opened the path to discovery. Nicholson records in his paper that at an early stage in these experiments, “Mr. Carlisle observed a disengagement of gas round the touching wire. This gas, though very minute in quantity, evidently seemed to me to have the smell afforded by hydrogen”.

The fact that gas was formed “round the touching wire” indicates that the contact was intermittent: when the wire was in contact with the water drop but not the zinc disc, a miniature electrolytic cell was formed and hydrogen gas was evolved at the wire cathode, while at the anode the zinc conductor was immediately oxidised as soon as the oxygen gas was formed.

In thermodynamic terms, the electrochemical cells in the pile were being used to do external work on the electrolytic cell in which the decomposition of water took place


ΔG0rxn for this reaction is +237.2 kJ/mole. So it can be seen that the external work done by the pile consists of driving what is in effect the combustion of hydrogen in a backwards direction to recover the reactants.

– – – –


Carlisle and Nicholson were intuitive physical chemists. They knew that water was composed of two gases, hydrogen and oxygen, so when bubbles which smelled of hydrogen were observed in their first experiment, it immediately set them thinking. Nicholson wrote of being “led by our reasoning on the first appearance of hydrogen to expect a decomposition of water.”


William Nicholson (1753-1815)

Nicholson used the term decomposition, so it seems safe to assume they formed the notion that just as water is composed from its constituent gases, it can be decomposed to recover them. That is a powerful conception, the idea that the combustion of hydrogen is a reversible process.

Whether Carlisle and Nicholson extended this thought to other chemical reactions, or even to chemical reactions in general, we do not know. But their demonstration of reversibility, beneath which the principle of chemical equilibrium lies, was an achievement of perhaps even greater moment than the discovery of electrolysis by which they achieved it.


Anthony Carlisle (1768-1840)

– – – –

Redox reactions

Carlisle and Nicholson’s discovery of electrolysis was made possible by the fact that the decomposition of water into hydrogen and oxygen is a redox reaction. In fact every reaction that takes place in an electrolytic cell is a redox reaction, with oxidation taking place at the anode and reduction taking place at the cathode. The overall electrolytic reaction is thus divided into two half-reactions. In the case of the electrolysis of water, we have


These combined half-reactions are not spontaneous. To facilitate this redox process requires EQ work, which in Carlisle and Nicholson’s case was supplied by the Voltaic pile.

Redox reactions also take place in every voltaic cell, with oxidation at the anode and reduction at the cathode. The difference is that the combined half-reactions are spontaneous, thereby making the cell capable of performing EQ work.

The spontaneous redox reactions in voltaic cells, and the non-spontaneous redox reactions in electrolytic cells, can best be understood by looking at a table of standard oxidation potentials arranged in descending order, such as the one shown below. Using such a list, the EMF of the cell is calculated by subtracting the cathode potential from the anode potential.

[Note that if you use a table of standard reduction potentials, the signs are reversed and the EMF of the cell is calculated by subtracting the anode potential from the cathode potential.]

For voltaic cells, the half-reaction taking place left-to-right at the anode (oxidation) appears higher in the list than the half-reaction taking place right-to-left at the cathode (reduction). The EMF of the cell is positive, and so ΔG will be negative, meaning that the cell reaction is spontaneous and thus capable of performing EQ work.

The situation is reversed for electrolytic cells. The half-reaction taking place left-to-right at the anode (oxidation) appears lower in the list than the half-reaction taking place right-to-left at the cathode (reduction). The EMF of the cell is negative, and so ΔG will be positive, meaning that the cell reaction is non-spontaneous and that EQ work must be performed on the cell to facilitate electrolysis.

The half-reactions of Carlisle and Nicholson’s Voltaic pile, and their platinum-electrode electrolytic cell, are indicated in the table below.


Table of standard oxidation potentials

– – – –

The advent of the fuel cell

Anthony Carlisle and William Nicholson

If Carlisle and Nicholson had disconnected their platinum-wire electrolytic cell after bubbles of hydrogen and oxygen had formed on the respective electrodes, and then connected an electrometer across the wires, they would have added yet another momentous discovery to that of electrolysis. They would have discovered the fuel cell.

From a thermodynamic perspective, it is a fairly straightforward matter to comprehend. Under ordinary temperature and pressure conditions, the decomposition of water is a non-spontaneous process; work is required to drive the reaction shown below in the non-spontaneous direction. This work was provided by the Voltaic pile, the effect of which was to increase the Gibbs free energy of the reaction system.


Upon disconnection of the Voltaic pile, and the substitution of a circuit wire, the reaction would spontaneously proceed in the reverse direction, decreasing the Gibbs free energy of the reaction system. This system would be capable of performing EQ work.

The reversal of reaction direction transforms the electrolytic cell into a voltaic cell, whose arrangement can be written

H2(g)/Pt | electrolyte | Pt/O2(g)

As can be seen from the above table, the EMF of this voltaic cell is 1.229 volts. We know it today as the hydrogen fuel cell.

Carlisle and Nicholson most surely created the first fuel cell in May 1800. They just didn’t apprehend it, nor did they operate it as a voltaic cell – at least we have no record that they did. So we must classify Carlisle and Nicholson’s fuel cell as an overlooked actuality; an unnoticed birth.

It would take another 42 years before a barrister from the city of Swansea in Wales, William Robert Grove QC, developed the first operational fuel cell, whose essential design features can clearly be traced back to Carlisle and Nicholson’s original.

– – – –

Mouse-over link to the original papers mentioned in this post

Nicholson’s paper (begins on page 179)

– – – –

P Mander September 2015

CarnotCycle would like to say thank you to everyone who has visited this blog since its inception in August 2012.

Thermodynamics may be a niche topic on WordPress, but it’s a powerful subject with global appeal. CarnotCycle’s country statistics show that thermodynamics interests many, many people. They come to this blog from all over the world, and they keep coming.

It’s wonderful to see all this activity, but perhaps not so surprising. After all, thermodynamics has played – and continues to play – a major role in shaping our world. It can be a difficult subject, but time spent learning about thermodynamics is never wasted. It enriches knowledge and empowers the mind.

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