the use and misuse of the laws of thermodynamics 28176

8/11/2019 The Use and Misuse of the Laws of Thermodynamics 28176

1/7

cannot ever remember having sold ahook, hu t once burned one. It was a text-book ofthermodynamics. have felt a little guilty aboutthat ever since, but only because the particular hookthat so incensed me at the time was in fact not muchworse than nearly all the others in its field. Thermo-dynamics is incredibly badly presented, for the mostpart by people who do not understand it. The usualundergraduate course consists more of pretentiouspseudo-philosophy than of anything relevant to experi-mental science. It is hardly surprising that the under-graduate's gorge rises when he is never told what

thermodynamics is, or what it is not, or what it is for;or when he rightly suspects that the arguments pre-sented to him are fallacious, or as he would say: Youcan prove anything you like by thermodynanlics ;or when he is asked as he often is to calculate the resultsof impossible experiments on imaginary substances.

One of t he sources of this muddle is the misguidedcompulsion most teachers feel to try to introducethermodynamics historically.' Unless th e teacherha8 himself done research on the history, his account iscertain to he grossly inaccurate or grossly incomplete ormost probably hoth. Why for example does he neverintroduce the first and second laws in the order in whichthey were originally formulated, namely the second

before the first? Why, for another example, does hisusual account of Carnot's cycle hear so little relationto Carnot's own exposition? But even if the teacher ofthermodynamics were a competent historian therewould he little to be said for introducing thermody-namics historically. The history of thermodynamicsis in fact a much more difficult subject th en thermody-namics itself and much less well understood.

Whatever part Carnot's cycle may have played inthe history of thermodynamics, its use in undergraduatecourses wastes time; unnecessarily introduces consider-able conceptual difficulties; hides and obscures theintroduction of the new, and in thermodynamics all-important, physical quantity called temperature;

and worst, is often used, by way of a stealthy assump-tion of precisely th at which it is proposed to prove, toseem to deduce the second law from the f irst .= More-over neither Gibhs in the 1870s nor an y of the authors ofthe best modern trea tments found it necessary to makeuse of Carnot's cycle.

M 1 McGlashan

University of Exeter

Exeter, England

EDITOR'S NOTE: This article is bmed upon the InauguralLecture by Professor McGlashan on January 18, 1965 followinghis appointment to the first chair of Physical Chemistry in theUniversity of Exeter.

The Use and Misuse of the

LUWSof Thermodynamics

GUQGENHEIM, . A,, Bullet of the Institute of Physics,June 1955.

Another source of pedagogic muddle is the widely-held misconception that thermodynamics approachesclosely th e ideal of a purely deductive science, deduciblelike Euclidean geometry from a small number of axiomswhich can he expressed in words, though muchprogress has been made toward the axiomatization ofthermodynamic^ ^ the mathematical structure has

still not been completely separated from the physicalcontent. Bu t none of th at need concern the under-graduate. Provided tha t having made our entry, wethen rely quite formally on deduction, we may chooseto enter th e subject a t any level of sophistication, justas we commonly choose to introduce mechanics tostudents for the first time through Newton's lawsof motion rather th an through th e principle of leastaction. A rare undergraduate may some day want tointerest himself in the logical foundations of thermo-dynamics. I n the meantime he will come to no harmwhile he listens to us teaching the others, and him, howto use thermodynamics in his chemistry. At leastin this university I hope that thermodynamics willalways he taught as par t of an experimental science andnever as muddled metaphysics nor bogus history.

Now what is thermodynamics? One way of answer-ing tha t question is by a comparison of thermodynamicswith mechanics. I n mechanics one deals with three

independent basic quantit ies: mass, length, and time.In electromechanics, by which mean mechanics pluselectricity and magnetism, t ha t number i s expanded tofour: mass, length, time, and electric current. Thermo-dynamics includes the whole of electromechanics hut

Briefly,

A U = w + pAssume that a substance exists for which simultaneously:

1) : P V = nRT

and 2): dU = CvdT

i.e., (Za): (aU/aV), = and (2b ): (aUlbT)v = Cv = C v ( 7 )

Thn:

q/T = dU/Y w/T

= Cv(T)dT/T nRdV/V (P. P)dV/T

so that when P. = P, that is to say when the expansion is re-versible,

prer/T = Cv(T)dT/T nRdVIV

Therefore for the reversible expansion of a substance defined byhoth 1) and Z), p/T depends only on the initial and find tem-peratures, and an the initial and final volumes, and so for aclosed cycle Z(q/T) = 0.

3 LANDSBERG, . T. , Thermod~amics, IntersciencePublishers, s division of John Wiley Sons, New York, 1961.

6 / Journal of Chemical Education


2/7


3/7

where we have assumed tha t a ny work is pressure (P)volume V ) work,' where T is called the thermodynamictemperature and is here introduced for the first timealong with S which is called the entropy, and where ,Ais called the chemical potential of the substance i andn, is th e amount of th at substance, and we havesummed over all substances present.

Of these quantit ies P and V can be measured byordinary mechanical methods and n, by ordinary chem-ical methods. Bu t are T, and pr completely andindependently defined by this equation? They are if,and only if, we can derive from the equation a recipefor the measurement of each. We find th at we canderive recipes for measuring ratios of thermodynamictemperatures T, by means of a special kind of ther-mometer called a gas thermometer, and for measuringdifferences of entropy or of chemical potential by meansof electromechanical, thermometric, and calorimetricmeasurements.

It turns out t o he convenient to make some new defini-tions:

H = U + P V A = U - T S G = H - T S

where H is the enthdpy which we mentioned earlier,A is called the Helmholtz function or the Helmholtzfree energy, and G is called the Gibhs function.

We can for convenience use these new definitions totransform our fundamental equation to a ny of t hefollowing:

dHDL VadPCI + TcdSm + Z dnie

These equations, though convenient, of course con-tain nothing new. We might note in passing, however,th at the quantit y called energy in textbooks ofphysics, such as th e energy E Q21/2eAof charginga condenser is actually a change in free energy and notof energy. The free energy turns out to be the thermo-dynamic analogue of the electromechanical potentialenergy, and is both a more familiar and less complicatedquantity th an t he energy U

We must now complete our sta tement of t he secondlaw. Any body can be regarded as being made up ofone or more phases. We must now distinguish betweensuch a body which is in internal equilibrium and onewhich is not. If th e body consists of a cup of water witha spoonful of sugar lying at the bottom it is not in in-ternal equilibrium because, without any help from us,the sugar will dissolve in the water. If one part of abody is hot and another cold, the body is not in internalequilibrium because, without any help from us, the hotpart will cool and the cold part will warm up. If thebody consists of a beaker containing a solution ofacidified permangauate a t room temperature to whichan excess of a solution of an oxalate has just been addedthen the body is not in internal equilibrium because,without any help from us, a chemical reaction will occurand go on until virtually all the permauganate has beenreduced to manganous ion.8

If other kinds of work are involved, we merely include theappropriate electrom echanical work terms z dX along with PdV.

228 Journal o f hemical Education

The second part of our statement of the second lawis th at for any body consisting of one or more phases,when the body is isolated from its surroundings, thatis to say when U and V are held constant, then theentropy S of t he whole body either increases or re-mains constant according to whether the body as awhole is not, or is, in interna l equilibrium. Expressedin symbols we the n have for the second part of our sta te-ment of the second law:

dS( Z',dSm) ( U and V constant) (2b)Equations (2a) and (2b) together with equation 1)

for the first law contain the whole of thermodynamics;the rest is easy algebra.

From equation (2h) we can immediately derive a setof other inequalities. I n particular

d S >, H and P constant)

dA ( T a nd V constant)

dG T nd P constant)

Of these, t he la st is the most useful because most of our. experiments are in fact done a t more or less constant

temperature and pressure.

Flow oh Heat Work Matter

Resulting from gra dient of:

Temperature ressure Chemicalpotentiai

Th en al ly conducting Mova ble wall lpirtan Wa ll permeobie towaii the substance i

Figure l o Figure b Figure l c

From equations (I), (2a), and (2b), we can also derivethe criteria of thermal, mechanical, and material equilib-rium. If two part s of a body separated by a thermallyconducting wall have different temperatures (Fig. la)then heat will flow spontaneously from the part withthe higher T to t he pa rt with the lower T. If two partsof a hody separated by a movable wall or piston havedifferent pressures (Fig. l b then work will flow spon-taneously from the part with the higher P to the partwith the lower P If two parts of a body separatedby a wall permeable to the substance i have differentchemical potentials of t he substance i (Fig. lc) thenthe substance i will flow from the part with higher ,A

the use and misuse of the laws of thermodynamics 28176

Documents