GENERAL ARTICLE Rubber as an Aid to Teach Thermodynamics

GENERAL ARTICLE

Rubber as an Aid to Teach Thermodynamics∗The Discovery by a Blind Scientist

Geethamma V G and Sampath V

Geethamma V G was aFulbright Fellow at

University of Illinois, USAand a Royal Society

International PostdoctoralFellow at Cavendish Lab,University of Cambridge,UK. She was also a Young

Scientist Awardee.

V Sampath is presently aProfessor of Metallurgicaland Materials Engg. at IITMadras. He holds a PhD

from IISc, Bengaluru and hasthree decades of research and

teaching experience. Hisfields of interest are: shape

memory alloys, smartmaterials, nano- and

composite materials, andstructure-property

correlation in materials.

The behaviour of rubber differs from that of conventionalmaterials. Rubber heats up on stretching and cools on re-traction. Also, stretched rubber shrinks on heating (ther-moelastic shrinkage) while a stretched metal elongates. Theelastic recovery of rubber is due to its tendency to maximizethe entropy. The same property also causes the thermoe-lastic shrinkage. Metallic materials possess energy elastic-ity, while ideal rubber possesses entropy elasticity. The ther-modynamic behaviour of rubber is similar to that of gaseousmaterials. Hence rubber can be used as an aid for teachingthermodynamics.

1. Gough–Joule Effect

John Gough was not born blind. But by a sheer quirk of fate, helost his eyesight due to smallpox before turning three. However,his senses of touch and hearing were intact, and he was bestowedwith a sharp inquisitive mind and adequate skills for experimen-tation. He tended to be philosophical too. John Dalton, a wellknown British scientist, who proposed the atomic theory, helpedGough by reading out to and writing for him. He had great admi-ration for Gough.

In 1805, Gough observed two important properties of rubber [1].Firstly, in a simple experiment, he sensed with his lips (lips beinga temperature sensitive part of the human body), a rise in temper-ature when a piece of uncrosslinked natural rubber was stretchedrapidly. He also discovered that the rubber cooled down rapidlyon retraction. In another experiment, a rubber band (suspended

∗DOI: https://doi.org/10.1007/s12045-019-0772-x

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Box 1. Gough–Joule Effect

1. Rubber warms on stretching and cools down on retraction.2. Stretched rubber shrinks on heating and elongates on cooling.

Experience Gough–Joule Effect!Take a piece of rubber with the dimensions 7 × 3 cm. Hold it loosely on the upper lip. Stretch it quickly tothe maximum extent possible, taking care not to break it. Your lip will feel the warmth. Then hold the stripaway from the lip for 5 seconds. Place it on the lip and release the force quickly; now your lip becomescold.

with a weight) was warmed. It was observed that the rubber bandKeywords

Gough–Joule effect, rubber, ther-

moelastic, entropy elasticity, adi-

abatic, isothermal, thermodynam-

ics, teaching aid, strain-induced

crystallisation, elastomer.

contracted thus raising the weight. Instead, if the length of therubber band was kept constant, the tension in the rubber increasedwith temperature. So he observed that stretched rubber contractedon heating and elongated on cooling.

About fifty years later, another scientist named James Joule con-firmed these observations with crosslinked natural rubber [2]. Thisbehaviour is observed in certain synthetic rubbers too. This phe-nomenon is known as Gough–Joule Effect (Box 1) [3]. Since thephenomenon involves a temperature change when a solid is sub-jected to stress, it is also known as thermoelastic (elastocaloric)property [4]. However, if the stress exceeds the elastic limit, it iscalled thermoplasticity. In other words, the thermal response ofan elastic material is thermoelasticity while the thermal responseof plastic is thermoplasticity.

RapidThe phenomenon ofshrinkage on heating and

expansion on cooling isa unique property of

stretched rubber. Thisbehaviour is in contrast

to that observed inconventional materials

which expand onheating.

deformation of metals also causes a change in tempera-ture. But it is only in the range of one Kelvin. However, thephenomenon of shrinkage on heating and expansion on cooling isa unique property of stretched rubber. This behaviour is in con-trast to that observed in conventional materials which expand onheating.

The increase in temperature during the deformation of rubber isnot fully offset by the decrease in temperature during its retrac-

218 RESONANCE | February 2019

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tion. So Gough–Joule effect is significant in certain practical ap-plications. Rubber products such as automobile tyres, bridge seg-ments, and vibration dampers are exposed to cyclic loading dur-ing their service life. Heat is generated in these rubber productsdue to the conversion of mechanical energy into heat (hysteresis).Hysteretic heat build-up represents a wastage of mechanical en-ergy. In addition, it leads to early damage to the product. Thetotal heat developed in a product is the sum of hysteretic heatand heat due to the thermoelastic effect. In many products, heatgenerated due to thermoelasticity is crucial. A familiar exampleis the wear and tear of automobile tyre as it undergoes severaldeformation-recovery cycles during its rotation.

2. Thermoelastic Inversion

In Gough–Joule effect, the The thermoelasticinversion occurs due tothe small butthermodynamicallysignificant changes ofvolume occurring with achange of temperature orthe application of aforce. This phenomenonis not shown by idealrubbers where thechange in volume isnegligible.

temperature of rubber increases con-siderably when it is stretched to large extensions. But for smallextensions (< 50%), a slight decrease in temperature is observed.This phenomenon is called thermoelastic inversion [5]. However,for small deformations, the temperature of rubber increases dur-ing compression and does not even change during shear or tor-sion. Also, generally materials exhibit a positive coefficient oflinear expansion. But for rubber, this coefficient changes frompositive to negative depending upon its extension. Stretched rub-ber shrinks on heating at fairly high extensions. At high elonga-tion, the force developed in stretched rubber is proportional to theabsolute temperature. But at low extensions (< 10%), stretchedrubber elongates on heating. It indicates decreased tension at hightemperature [6]. This phenomenon is also due to thermoelasticinversion.

The thermoelastic inversion is due to the small but thermodynam-ically significant changes of volume occurring with a change oftemperature or the application of a force. Hence this phenomenonis not shown by ideal rubbers where the change in volume is neg-ligible. In brief, the competition between energy effects and en-tropy effects in rubber at small and large extensions leads to ther-moelastic inversion.


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Figure 1. Isothermal andadiabatic processes.

3. The Secret Behind Gough–Joule Effect

In general, an object feels cold when heat flows from our skin tothe object. Conversely, it feels warm when heat flows from theobject to our skin. The stretched rubber strip feels warm becauseit liberates heat to our skin. Now let us see, how heat is developedin rubber during stretching.

The reason of Gough–Joule effect remained elusive for many yearsuntil Herman Staudinger, Kuhn and others propounded theoriesin the 1920s and 1930s [7–9]. The two fundamental requirementsfor a material to exhibit thermoelasticity are temperature changeand elasticity (reversibility). At first, consider the temperatureeffect. There are two reasons for this: adiabatic stretching andstrain-induced crystallisation.

TheIn an isothermal process,the system is in contact

with a reservoir at aconstant temperature,while in an adiabatic

process, the system isthermally insulated from

its surroundings.

temperature of a system increases or decreases dependingupon the nature of phenomenon occurring in the system. Let ussee the difference between isothermal and adiabatic processes. Inan isothermal process, the system is in contact with a reservoirat a constant temperature. Thermodynamically speaking, a reser-voir is a large entity which can transfer heat into or out of a systemwithout undergoing a change in temperature. Hence in an isother-mal process, the system either receives heat or loses heat so thatits temperature remains constant (Figure 1). The transformation


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is very slow in an isothermal process.

But in an adiabatic process, the system is thermally insulatedfrom its surroundings. The insulator can be rubber, plastic orwood. These materials have very low thermal conductivity andthe system neither gains heat nor loses heat from or to the sur-roundings. Hence though the system undergoes a process whichmay increase (or decrease) its temperature, heat is not emitted(or absorbed). In this process, energy is exchanged with the sur-roundings only as work. When the process is fast, it does nothave enough time for the transfer of energy as heat to or from thesystem. So when a material is deformed rapidly, the temperatureof the system is changed. The experiment mentioned in Box 1should be rapid so as to minimize heat transfer from the rubberstrip to the surroundings, and thus make the process adiabatic.

Normally Normally rubber isamorphous. But certaintypes of rubberscrystallise on faststretching due tostrain-inducedcrystallisation.Simultaneously, thetemperature of rubberrises due to the release oflatent heat ofcrystallisation.

rubber is amorphous. But certain types of rubbers crys-tallise on fast stretching due to strain-induced crystallisation. Thisproperty is discussed in detail later. Simultaneously, the temper-ature of rubber rises due to the release of latent heat of crystalli-sation. This explains why the lip feels warm as discussed earlier.The latent heat of crystallisation raises the temperature of rubberup to 10 K at 500% strain. But the adiabatic loss of its entropycan reach only 1 K at this strain. Hence Gough–Joule effect ismainly due to the latent heat of crystallisation. When the forceis released, rubber retracts to its original state becoming amor-phous again absorbing heat from the surroundings. This leads tothe sensation of lips getting cooled.

The second observation, viz., shrinkage-on-heating, can be ex-plained as follows. If heat is released during the stretching ofrubber, adding heat causes its contraction. The enhanced thermalenergy of rubber molecules increases the possibility of conforma-tional changes. This accelerates the recovery of rubber. Also, theelastic modulus of rubber is proportional to temperature due toits entropy elasticity. In order to understand this behaviour thor-oughly, it is essential to understand the structure of rubber.


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Box 2. When Does a Material Exhibit the Properties of Rubber?

• The material should be a high molecular weight polymer with an average molecularweight (M̄w) of 5 × 105 to 10 × 105 g/mol.

• On deformation, free rotation about the bonds provide high conformational possibilities.

• Long main chain facilitates inherent flexibility.

• No aromatic rings, no conjugate double bonds, no bulky side groups, no polar groups, nohydrogen bonding.

• Small cohesive energy density.

• Amorphous.

• Lightly crosslinked.

• Glass transition temperature (Tg) is below room temperature.

4. Structure of Rubber

RubberRubber is composed ofhigh molecular weight,

chainlike, polymermolecules. These aremany thousand times

larger than the lowmolecular weight

conventional molecules.

is composed of high molecular weight, chainlike, poly-mer molecules. These are many thousand times larger than thelow molecular weight conventional molecules. Weak Londonforces act as the intermolecular forces between uncrosslinked rub-ber molecules. But crosslinked rubber contains strong chemicalbonds. The atoms in the rubber chains (molecules) are in constantthermal vibration. The average molecular weight (M̄w) betweencrosslinks in vulcanised rubber is in the range of 5000–10000g/mol. A material should satisfy certain molecular requirementsin order to exhibit rubbery nature. These are summarized in Box2. For more details on this topic, go through our earlier article[10].

In the main chain of rubber, the C–C–C bond angle is fixed at109.5o. But atoms have the freedom of rotation about the singlebonds on the main chain and the side chains. Thus molecules


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possess many conformational possibilities in 3D space providingvariable shapes to rubber molecules. The chain segments tend tocoil up, instead of remaining linear. Hence, rubber moleculesare extremely flexible, highly coiled chains with an entangledand convoluted structure. Due to this random structure, it pos-sesses high entropy (disorder) in the normal state. This prop-erty along with the weak intermolecular forces allows rubber todeform greatly even under very small forces. However, as therubber molecules are coiled and entangled, rubber possesses lessflow and more stiffness.

5. Strain-Induced Crystallisation

Amorphous nature is one of the most important molecular re-quirements of rubber. Such a system has high entropy. But whenrubber is stretched, its molecules are oriented in the direction ofthe applied force. Thus, the system becomes crystalline, andits entropy is reduced (Figure 2). This phenomenon is knownas strain-induced crystallisation. The inter-chain and intra-chainforces which cause strain-induced crystallisation are not strong.Hence molecules regain the original state on releasing the appliedforce. This Two observations

support strain-inducedcrystallisation. When asample of unstretchedrubber sample is frozenand is subsequentlybroken, the pieces takeup irregular shape. But ifa stretched rubbersample is broken,parallel strands of fibrescan be seen in the brokenpieces. This dual natureof rubber can beobserved with the nakedeye.

property depends upon the structure and regularity ofthe repeating units of rubber molecules and has significance inpractical applications as it provides excellent mechanical proper-ties and good resistance to crack growth in rubber products. Nat-ural rubber, chloroprene rubber and polyisoprene rubber exhibitthis property [11].

How is this phenomenon confirmed? Two observations supportstrain-induced crystallisation. When a sample of unstretched rub-ber sample is frozen and is subsequently broken, the pieces takeup irregular shape. But if a stretched rubber sample is broken,parallel strands of fibres can be seen in the broken pieces. Thisdual nature of rubber can be observed with the naked eye.

The second observation pertains to the translucence of unstretchedrubber and the cloudy appearance of stretched rubber. Unfilledrubber is amorphous. It can be considered as a homogeneous


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Figure 2. Strain-inducedcrystallisation decreases theentropy of natural rubber.

medium without any obstacles which cause absorption or scat-tering. The transmission of light through the material is reason-ably good, and hence it appears translucent. When it is stretched,molecules are oriented in the direction of the applied force. Thuscrystallites are formed and, therefore, it becomes heterogeneous.Hence light is scattered, and rubber appears cloudy.

6. Thermodynamics in Engineering and Chemistry

The basic concept of thermodynamics is the transduction of heatinto work and work into heat. It means that heat is the energyin transit corresponding to a definite amount of work. The word‘thermodynamics’ has its origin in Greek: thermes meaning heat,and dynamikos meaning powerful or force [12].

OnIn Nature, relativemotion (of surfaces) is

converted to heat due tofriction. But the

conversion of heat intowork is not a natural

phenomenon.

rubbing our palms together, we can feel the warmth. Here me-chanical work/friction is converted into heat. But the heat gener-ated thereby cannot be converted back to work. In Nature, relativemotion (of surfaces) is converted to heat due to friction. But theconversion of heat into work is not a natural phenomenon. How-ever, a ‘heat engine’ transforms heat into work. Thermodynamicswas developed as a subject in the late 18th and early 19th cen-turies to support man’s necessity to extract work from heat usingheat engines [13].

But now thermodynamics is not limited to heat-work interconver-


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sion alone. It is used to explain different phenomena/processesin diverse fields, such as information science [14, 15], economics[16] and biology [17] apart from mechanical engineering, chem-ical engineering [18], materials science, physics, chemistry [19],food science, etc. Also, it is interesting to note that areas like‘human thermodynamics’ has emerged and evolved [20].

Though Though the basicconcepts ofthermodynamics are thesame in both engineeringand chemistry, there aredifferences. Onedifference is the signconventions for workand heat.

the basic concepts of thermodynamics are the same inboth engineering and chemistry, there are differences. One dif-ference is the sign conventions for work and heat. Work is de-fined as the action through a distance against an opposing force.It is the product of force and the distance to which the object ismoved/displaced. Engineers give priority to the work a systemcan do. For example, steam in a heat engine can move a piston.So in engineering (and physics), work is considered as positive(w>0) if it is done by the system. As a result, its internal energyfalls. Also, work is negative, if it is done on the system.

On the other hand, chemical systems (solids and liquids) do notundergo considerable change in volume during reactions. Henceno expansion work is observed in chemical systems, unlike gases.Chemists are more interested in energy changes associated withthe system rather than that with the surroundings. Hence in chem-istry, work done on the system is positive, and the work done bythe system is negative. This results in an increase in internal en-ergy as heat is transferred to the system as work. Heat gained bythe system from the surroundings (endothermic process) is posi-tive, whereas heat lost by the system to the surroundings (exother-mic process) is negative.

It is interesting but confusing at times that different authors dis-cuss the thermodynamics of rubber using both the conventions.This could be due to the interdisciplinary nature of polymer sci-ence and technology.

7. Elasticity of Metal and Rubber

Elasticity is the ability of a material to resist a deforming forceand to restore its original size and shape when the force is re-


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Figure 3. Rubber springand metal spring.

moved. The higher the resistance to deformation, the greater isthe elasticity of the material. A highly elastic material returnsquickly to its original shape when the force is removed. Bothmetallic materials and rubber are elastic in nature. But the rea-sons for their elastic behaviuor are different.

TwoSince rubber undergoesmuch higher reversible

deformations thanmetallic materials,

rubber can function athigh strains. Rubber canalso store elastic energyabout 150 times higher

than that of steel and canrelease most of this

energy on retraction.

parameters are used to measure the extent of elasticity – elas-tic limit and modulus. Elastic limit is the maximum stress that amaterial bears before it undergoes permanent deformation [21].The elastic limit of metal is higher than that of rubber. Modu-lus is the ratio of stress and strain. Metals undergo only a small(≈1%) reversible strain, even under very large forces. Rubber, onthe other hand, is the most easily deformable material. It can bestretched rapidly to very high elastic strains (500 to 1000%) evenunder small loads. No other material is comparable to rubber asfar as this property is concerned. Hence the modulus of elasticityof metal is higher than that of rubber. Also, on releasing the ap-plied forces, rubber retracts rapidly and almost completely, withminimum energy loss.

Since rubber undergoes much higher reversible deformations thanmetallic materials, rubber can function at high strains. Rubbercan also store elastic energy about 150 times higher than that ofsteel and can release most of this energy on retraction. Thereforerubber dissipates less energy as heat during deformation. It meansthat rubber possesses small hysteresis loss (heat build-up). Hencea rubber spring can be a solid block whereas a metal spring actsby bending or twisting a long slender coiled structure (Figure 3).

The deformation in metals can be of two types – plastic and elas-tic. Metals do not exhibit a change in volume during plastic defor-


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mation. But they show a definite change in volume during elasticdeformation. The Poissons ratio is a measure of volume changeduring deformation. The Poissons ratio of materials like water,which does not exhibit a volume change is 0.5. Similarly, thePoisson’s ratio of rubber is also about 0.5. It means that the vol-ume change of rubber is negligible during its deformation. Butthis ratio is about 0.35 for most of the metals.

Another important difference is the energy elasticity of metal andthe entropy elasticity of rubber. It is discussed in the next sec-tions.

8. Thermoelastic Experiment

Elasticity Elasticity andGough–Joule effect aredescribed by thethermoelasticexperiment. Thisexperiment describes theunique thermalbehaviour of rubbercompared to metals.

and Gough–Joule effect are described by the thermoe-lastic experiment. This experiment describes the unique thermalbehaviour of rubber compared to metals. A metal strip elongateson heating, while a piece of rubber shrinks. In the experiment,thin pieces of metal and rubber are stretched under a load (W)within their elastic limits. The load should be small so as to avoidpermanent deformation. Choose a rubber that is capable of crys-tallising on stretching.

In metals, the constituent atoms are held together in a 3D structureby the electrostatic attractive forces that exist between the positiveion core and the negative electron clouds. A metal strip elongateson loading (Figure 4), the application of force changes the sizeand shape of the atomic lattice. As a result, the internal energyof the system increases. This is an enthalpy (bond energy) effect.When the applied load is released, the lattice restores the originalstate by decreasing its internal energy. Hence the elasticity ofmetal is called energy-derived elasticity or energy elasticity.

When the stretched metal is heated, expansion occurs because ofthe increased oscillation of atoms about their equilibrium posi-tions. In other words, the effects resulting from the stretching andheating of the metal are attributed to the intermolecular potentialenergy.


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Figure 4. Thermoelasticexperiment: Stretched metalelongates on heating.

9. Entropy Elasticity of Rubber

RubberThe conformation ofrubber molecules

changes on deformation.But there is no change in

bond length or bondangle. However, if the

applied force is veryhigh, C–C bonds break

causing the breakage ofpiece of rubber.

elongates when a load W is applied to it (Figure 5). Asa result, its molecules are uncoiled, and the entangled structureis loosened. In the case of vulcanized rubber, chain segmentsuncoil till the crosslinks prevent uncoiling. The conformationof rubber molecules changes on deformation. But there is nochange in bond length or bond angle. However, if the appliedforce is very high, C–C bonds break causing the breakage of rub-ber piece. When a tensile load is applied, the rubber moleculesalign in the direction of force as mentioned earlier. The systembecomes crystalline, and its entropy is reduced (Figure 2). Thisis a reversible process. When the applied force is released, freerotation of atoms causes molecules to coil up again. This happensdue to the tendency of the system to maximize its entropy it hadin its undeformed state. Hence the elastic memory of rubber iscalled entropy-derived elasticity or entropy elasticity.

As neither bond stretching nor bond bending occurs during stretch-ing, the change in enthalpy of rubber is zero. If we were able tostretch the rubber molecules, the rubber would have got straight-ened out. But a completely linear structure will not be obtainedbecause the C–C–C bond angle is 109.5o and not 180o.

Thus metallic material possesses energy elasticity, while an idealrubber exhibits entropy elasticity. In order to be an ideal rubber,


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Figure 5. Thermoelasticexperiment: Stretched rub-ber shrinks on heating.

it should neither be uncrosslinked nor Metallic materialpossesses energyelasticity, while an idealrubber exhibits entropyelasticity. In order to bean ideal rubber, it shouldneither be uncrosslinkednor be highlycrosslinked; it should beoptimally crosslinked.

be highly crosslinked; itshould be optimally crosslinked. Also, the deformation of realrubbers involves a change in volume. Hence in real rubbers, theelasticity is not based on entropy alone, it includes a change ininternal energy also.

When stretched rubber is heated, molecules undergo chaotic move-ment, and thus a random state is formed. The enhanced thermalenergy of the chains increases the molecular conformation and ac-celerates its recovery. Hence under a constant load, rubber piecesshrink at high temperatures (Figure 5). In other words, the tensionin stretched rubber increases on heating. The shrinkage due to theentropy of rubber is much higher than the thermal expansion ofmetals. For example, a rubber band contracts reasonably whenheated under tension, but the elongation of a metal strip under atensile load is not visible to the naked eye.

10. Origin of Elastic Force in Rubber

The internal energy of a system is due to its potential and kineticenergy. It is difficult to physically measure the internal energy of asystem. But the change in internal energy (ΔU) of a system can becalculated from the initial and final values of the internal energy,i.e. Ufinal −Uinitial. According to the first law of thermodynamics,energy can neither be created nor be destroyed. Hence energychange of the system and the surroundings are related to each


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other asThe internal energy of asystem is due to its

potential and kineticenergy. It is difficult tophysically measure the

internal energy of asystem. But the change

in internal energy of asystem can be calculatedfrom the initial and final

values of the internalenergy.

follows.

ΔUsystem = −ΔUsurroundings

ΔUsystem + −ΔUsurroundings = 0 .

A small change in the internal energy (dU) of an isolated systemis due to two factors, i) heat exchange (dQ) between the systemand surroundings and ii) work done (dW) on the system or by thesystem. The first law of thermodynamics is represented by eitherof the following equations.

dU = dQ + dW (1)

or

dU = dQ − dW (2)

In (1), dU is the sum of total heat exchange into the system andthe work done on the system by its the surroundings. Here thework done increases the internal energy of the system. Whenwe use this equation, it means that work is done on the system.But in equation (2), dU of a closed system is equal to the heatsupplied to the system, minus the work done by the system on itssurroundings. These two equations are equivalent because,

Won the system = −Wby the system

Different authors use either (1) or (2) when the thermodynamicsof rubber is discussed [22, 23]. In this article, we follow (1). Thesecond law of thermodynamics states that for a reversible process,dQ is equal to the product of entropy change (dS ) and absolutetemperature (T).

dQ = TdS . (3)


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Consider Consider the stretchingof a rubber band under atensile force so as tocause a change in itslength. The workinvolved in stretching isa combination of workdone by the system andthe work done on thesystem.

the stretching of a rubber band under a tensile force ( f )so as to cause a change in its length, dL. The work involved instretching is a combination of work done by the system and thework done on the system. The work done by the system (pressure-volume explansion) is negative. It is due to the expansion of rub-ber against the atmosphere and is written as −PdV , where P is theexternal pressure and dV is the change in volume associated withelongation. But work done on the system (force-displacementwork) is positive, and is written as + f dL.

dW = −PdV + f dL . (4)

Ideal rubber is an incompressible material without a change involume. Hence the change in volume (of rubber network) on de-formation is negligible, except for swelling. Therefore PdV isconsidered as zero here. But in more detailed analysis of elastic-ity, this term cannot be neglected. Hence,

dW = f dL . (5)

Substituting equations (5) and (3) in (1), we get

dU = TdS + f dL, (6)

f dL = dU − TdS . (7)

By taking the partial derivatives of the above equation with re-spect to length at constant temperature and volume, we get,

f =(∂U∂L

)T,V− T

(∂S∂L

)T,V

. (8)

According to the above equation, a plot of force versus tempera-ture yields a straight line whose slope and intercept are

(∂S∂L

)T

and(∂U∂L

)T

respectively. The elongation occurs as a result of tensile

force involving only a change in the entropy. Hence(∂U∂L

)T,V

isnegligible. Therefore, the elastic force for an ideal rubber is,


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Figure 6. Thermoelas-tic experiment: Compressedgas expands on heating.

f = −T(∂S∂L

)T,V

. (9)

The negative sign indicates that the force acts in a direction thatis opposite to the increase in length. Also, it is clear that the forceis proportional to the absolute temperature under a constant strainbelow 350%. This is true for an approximate range of tempera-tures from 200 to 400K.

11. Behaviour of an Ideal Gas

Consider the behaviour of an ideal (perfect) gas. Its pressure isdue to the overall effect of impacts of atoms/molecules on thewalls of the container. Gas molecules have kinetic energy. Theinternal energy is the sum of the kinetic energies of the individualgas molecules.

A downward moving piston does work on a gas by compress-ing it. Gas molecules collide with the downward moving piston,and the pressure of the gas increases. This is caused neither bythe intermolecular potential energy nor by the individual molec-ular kinetic energy. But it is due to the fewer configurations ofmolecules possible in the reduced volume. The effect of chang-ing the volume of a gas at constant temperature is, therefore, ex-plained on the basis of entropy and not energy. In a compressed


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gas, the extent of deformation is given by the reciprocal volume,1V (Figure 6). Increase in deformation (decrease in volume) corre-sponds to decrease in entropy. Therefore the pressure of an idealgas is entropically derived.

Also, on increasing the temperature of a compressed gas, the mo-mentum of its molecules increases. Hence when the compressedgas is heated, it expands to attain a state of maximum entropy.Consequently, energy is exchanged with the surroundings in theform of work. This property is the basis of heat engines.

The equation of an ideal gas is obtained from (2).

dU = TdS − PdV. (10)

On rearranging the above equation,

PdV = TdS − dU. (11)

Differentiating the above equation with respect to volume,

P = T(∂S∂V

)T−

(∂U∂V

)T. (12)

Here, we see two components to pressure similar to that of rubber– one is due to entropy, and the other is due to internal energy.According to Joules law, internal energy change is zero for anideal gas. So the above equation becomes,

P = T(∂S∂V

)T. (13)

Unlike rubber,(∂S∂V

)T

is positive for an ideal gas. Hence pressureacts in the same direction as increasing volume.

12. Analogies Between Rubber and Gas

Ideal gas and ideal rubber appear and behave differently. For ex-ample, ideal rubber is an incompressible material, unlike gases.


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However, theirIdeal gas and idealrubber appear and

behave differently. Forexample, ideal rubber is

an incompressiblematerial, unlike gases.

However, theirthermodynamic and

molecular behaviour arestrikingly similar.

thermodynamic and molecular behaviour are strik-ingly similar.

During an adiabatic process, no heat is absorbed or liberated.This happens when the system is thermally insulated from thesurroundings. In a mechanical system, this is achieved by a gastaken in a thermally insulated cylinder confined by a piston. Rub-ber is an insulator. Hence no exchange of heat occurs across theboundary during stretching and retraction of rubber.

The stretching of an ideal rubber and the compression of an idealgas are similar. Both cases involve a work input (work is doneon the system) and a heat output. Adiabatic heating occurs whena gas is compressed (as in a diesel engine) due to work done onit by its surroundings. Similarly, adiabatic stretching of rubberincreases its temperature. But the case of rubber is more com-plicated. If crystallisation occurs during stretching, part of thetemperature increase is due to the latent heat of crystallisation.Adiabatic cooling occurs when the pressure of a gas is decreasedrapidly (expansion), causing it to do work on its surroundings.Similarly, rapid retraction of rubber causes a decrease in temper-ature.

The retractive force in rubber and decrease in pressure of gasare entropically derived. When rubber is stretched, its chain-like molecules uncoil, and its entropy decreases. Entropy-driven‘pulling back’ can be sensed directly by touch. The reverse hap-pens on contraction. Hence the retraction of rubber is sponta-neous similar to the free expansion of compressed gas. For bothgas and rubber, the total entropy change for the reversible pro-cess is positive or zero since these act as (temporarily) isolatedsystems.

Consider (8) for the elastic force in rubber and (12) for the pres-sure of a gas. In both cases there are two terms – one for the in-ternal energy and the other for entropy. At constant temperature,the pressure is independent of internal energy of ideal gas (13).In analogy with this, the elastic force is independent of internalenergy of an ideal rubber (9).


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For an ideal gas, dW = −Popposing dV . During expansion, gasdoes work on the surroundings. Hence, work is negative by con-vention [24]. But since rubber is an incompressible material, thework for rubber becomes + f dL. This equation is analogous tothe mechanical energy which is the product of force and distance.When rubber is stretched, work is done on the system and so it ispositive.

13. Rubber as a Teaching Aid for Thermodynamics

The laws of thermodynamics can be applied to all systems suchas solids, liquids and gases. If we change the temperature or pres-sure of solids and liquids, they do not undergo a noticeable changein their size; whereas the volume of a gas changes remarkably.Also, the use of real (non-ideal) gas leads to difficulties in solv-ing the equations of state. Hence in traditional physical chemistrytextbooks, an ideal gas is used as the material to discuss the lawsof thermodynamics [25, 26]. In mechanical/chemical engineeringbooks, generally, steam is used as the material.

But Entropy is a difficultthermodynamic conceptto teach. However,scientists have usedrubber to developeffective demonstrationmethods to introduceentropy. Rubber can beused as the workingsubstance in a heatengine, and rubber canalso be used for lecturedemonstration of CarnotCycle.

measuring/handling the gases need complex instruments andarrangements. Hence introductory lessons on thermodynamicsare usually done without any classroom demonstrations; begin-ners find thermodynamics difficult. Teaching the concepts of ther-modynamics, therefore, necessitates the use of other materials,which behave like gases. As discussed above, the thermodynamicand molecular behaviour of ideal gas and ideal rubber are similar.Also, rubber can be handled easily in classroom demonstrations.Hence rubber is an alternative to gas in teaching thermodynamics[27–30].

Entropy is a difficult thermodynamic concept to teach. However,scientists have used rubber to develop effective demonstrationmethods to introduce entropy [31–33]. The concept of heat en-gine has been discussed by Sarkar and Mondal [34], whereas uti-lization of rubber as the working substance in a heat engine hasbeen described by other scientists [35–38]. While Srinivasan [39]has described Carnot’s research, scientists [40, 41] have also dis-


GENERAL ARTICLE

cussed the lecture demonstration of the Carnot Cycle using rub-ber. The teaching and learning of thermodynamics can be madeeasier by developing systematic teaching methodologies utilizingrubber as a teaching aid. Reader, now it is your turn; create ateaching aid using rubber appropriate for your subject.

14. Acknowledgement

Geetha is thankful to Prof. E Terentjev in the University of Cam-bridge, UK for providing a chance to study the actuation proper-ties of rubber in his lab.

Suggested Reading

[1] J Gough, A Description of a Property of Caoutchouc or Indian rubber; WithSome Reflections on the Cause of the Elasticity of this Substance, Memoirs ofthe Literary and Philosophical Society of Manchester, Vol.1, p.288, 1805.

[2] J P Joule, On Some Thermodynamic Properties of Solids, Philosophical Trans-actions of the Royal Society of London, Vol149, p.91, 1859.

[3] M I Liff, Another Demo of the Unusual Thermal Properties of Rubber, ThePhysics Teacher, 48, October 2010.

[4] W Thomson (Lord Kelvin), On the Thermoelastic and Thermomagnetic Prop-erties of Matter, Transactions of the Royal Society of Edinburgh, Vol.20, p.57,1853.

[5] J Pellicer et al., Thermodynamics of Rubber Elasticity, J. Chem. Educ., Vol.78,No.2, p.263, 2001.

[6] L R G Treolar, The Elasticity and Related Properties of Rubber, Rep. Prog.Phys., Vol.36, p.755, 1973.

[7] B Schweizer and J Wauer, Atomistic Explanation of the Gough–Joule Effect,The Eur. Phys., J.-B, Vol.23, p.383, 2001.

[8] D Guyomar, et al., Elastocaloric Modelling of Natural Rubber, Appl. Therm.Eng., Vol.57, p.33, 2013.

[9] W Hu, Polymer Physics: A Molecular Approach, Springer Science & BusinessMedia, Technology & Engineering, 2012.

[10] V G Geethamma and S Thomas, Why Does a Rubber Ball Bounce?, Resonance,Vol.2, p.48, 1997.

[11] Y Nie, Z Gu, Y Wei, T Hao and Z Zhou, Features of Strain-Induced Crystal-lization of Natural Rubber Revealed by Experiments and Simulations, PolymerJournal, Vol.49, p.309, 2017.

[12] Peter Atkins, An Introduction to the Laws of Thermodynamics, Oxford Univer-sity Press, 2010.

[13] K P N Murthy, Josiah Willard Gibbs and his Ensembles, Resonance, p.12,2007.


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[14] J Machta, Entropy, Information, and Computation, Am. J. Phys., Vol.67,p.1074, 1999.

[15] N Gershenfeld, Signal Entropy and the Thermodynamics of Computation,IBM Systems J., Vol.35, Nos.3&4, 1996.

[16] G A Lozada, The Hotelling Rule for Entropy-Constrained Economic Growth,Ecological Economics, Vol.133, p.35, 2017.

[17] J B Udgaonkar, Entropy in Biology, p.61, September 2001.[18] V Kumaran, Josiah Willard Gibbs, Resonance, p.4, July 2007.[19] J C Binny, Entropy and the Direction of Natural Change, Resonance, p.82,

September 2001.[20] L Thims, Thermodynamics � Information Theory: Science’s Greatest Sokal

Affair, J. of Human Thermodynamics, Vol.8, No.1, 2012.[21] M Euler, Hooke’s Law and Material Science Projects: Exploring Energy and

Entropy Springs, Physics Education, Vol.43, No(1, pp.57–61, 2008.[22] D Roundy and M Rogers, Exploring the Thermodynamics of a Rubber band,

Am. J. Phys., Vol.81, No.1, 2013.[23] J Fried, Polymer Science and Technology, Prentice Hall of India, 1999.[24] B Smith, Using Rubber Elastic Material-Ideal Gas Analogies to Teach Intro-

ductory Thermodynamics, Part II: The Laws of Thermodynamics, J. Chem.Educ., Vol.79, p.1453, 2002.

[25] B Smith, Using Rubber Elastic Material-Ideal Gas Analogies to Teach Intro-ductory Thermodynamics, Part I: Equations of state, J. Chem. Educ., Vol.79,p.1444, 2002.

[26] A H Johnstone et al., Misconceptions in School Thermodynamics, Physics Ed-ucation, p.248, 1977.

[27] G Marx, J Ogborn and P Tasnadi, Rubber as a Medium for Teaching Thermo-dynamics, Eur. J. Phys., p.232, 1984.

[28] W C Galley, Mass-elastic Band Thermodynamics: A Visual Teaching Aid atthe Introductory Level, J. Chem. Educ., Vol.84, No.7, p.1147, 2007.

[29] G L Gilbert, Lecture Table Experimental Demonstration of Entropy, J. Chem.Educ., Vol.54, No.12, p.754, 1977.

[30] I Muller and P Strehlow, Rubber and Rubber Balloons: Paradigms of Ther-modynamics, Springer Science & Business Media, 2004.

[31] T Matsuo et al., Rubber Elasticity in the Introductory ThermodynamicsCourse, J. Thermal Analysis and Calorimetry, Vol.69, p.1015, 2002.

[32] T A Brzinski and K E Daniels, Burning Rubber: A Polymer Physics Lab forTeaching Entropy, American J. Physics, 2015.

[33] D Roundy et al., From Fear To Fun In Thermodynamics, PERC Proceedings,American Association of Physics Teachers, p.42, 2013.

[34] A Sarkar and S S Mondal, External and Internal Irreversibility: Heat Engineas an Example, Resonance, p.535, May 2018.

[35] S J Appleyard, Making Work: Demonstrating Thermodynamic Concepts withSolar-Powered Wax and Rubber Heat Engines, Phys. Educ., Vol.42, p.612,2007.

[36] E G Cox, A Heat Engine Run by Rubber, J. Chem. Educ., Vol.31, No.6, p.307,1954.


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[37] N Muharayu et al., Designing of Learning by Analogy on an Elastic Heat En-gine as an Enrichment Material in Senior High School, International Confer-ence on Advances in Education Technology, 2014.

Address for Correspondence

Geethamma V G

Department of Polymer

Engineering

University College of

Engineering

Thodupuzha, Kerala 685 587,

India.

Email:

[email protected]

Sampath V

Department of Metallurgical

and Materials Engineering

Indian Institute of Technology

Madras

Chennai 600 036, India.

Email: [email protected]

[38] N Muharayu et al., Theory of Thermodynamic Variables of Rubber Band HeatEngine, J. of physics, Vol.739, 2016.

[39] J Srinivasan, Sadi Carnot and the Second Law of Thermodynamics, Reso-nance, p.42, November 2001.

[40] J E Mark, Some Aspects of Rubber-like Elasticity Useful in Teaching BasicConcepts in Physical Chemistry, J. Chem. Educ., Vol.79, No.12, p.1437, 2002

[41] J G Mullen, G W Look and J Konkel, Thermodynamics of a Simple Rubber-band Heat Engine, Amer. J. of Phy., Vol.43, p.349, 1975.


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GENERAL ARTICLE Rubber as an Aid to Teach Thermodynamics