Terrance B. Tripp University of Maine at Presque Isle Presque Isle, 04769
I I
TextbcwkErt~~ 126: ,
The Definition of Heat
The topic of energetics has received increasing attention in the eeneral chemistrv curriculum in recent vears in part because it is the basis oielementary t h e ~ m o d ~ a m iacisd in nart hecause of the oresent social awareness of "enerw". The concept of heat is h&c to an understanding of energy-Gansfer and elementarv thermodvnamics. Unfortunately, many students approarh the study of srience with a complete misunderstandine. of the concept of heat. This misunderstanding will be reinforced if any bne of a large number of available general chemistry textbooks is consulted. The data in Table 1result from a random sampling of first level college chemistry textbooks published during the past ten years and reveal that the concept of heat is presented either incorrectly or superficially in most cases. The generally accepted qualitative definition of heat is: Heat is energy transferred from one system to another solely by virtue of a difference in temperature (1-10). The most common misconceptions regarding heat relate to the idea that it is something which is a component of a system. For example, statements like "a system a t high temperature has a lot of heat" or "a hot ohject has more heat than a cold ohject" are common and incorrect as noted (11-12). In reality heat appears only a t the boundary of a system as energy is being transferred because of a temperature difference between the system and the surroundings. In order to he meaningful and measurable, heat must be defined quantitatively. The definition must he hased on a precise statement of theFirst Law of Thermodynamics in one of its several forms (9, 13-17). Consider a closed system, at rest, at constant elevation, in the absence of electric or magnetic fields and characterized by well-defmed thermodynamic states. svstem is isolated from the surroundines in such - The a way as to ailow only work to be done on or hy thk system. There is no heat and the svstem is adiahatic. Let the svstem he changed from an equilibrium state 1to another state 2 by the nerformance of work defined in thermodvnamics as a process whose only effect external to the system could he the raisine of a weieht (18). The First Law guarantees the existence of a state Function, internal en erg,^, and identifies the change in this function as Here Wad is called the adiahatic work. If the system is not a t rest or is moved in a force field, terms must he added to the left side of eqn. (1) to account for changes in potential andlor kinetic energy. Wad will then equal the change in the total energy of the system. For example, a system raised in a gravitational field will experience an increase in gravitational potential energy achieved by a transfer of energy as work. This process is not coupled to processes which affect the internal energy of the system and the internal energy remains constant Suggestions of material suitable for this column and guest columns suitable for publication directly should be sent with as many details as possible, and particularly with reference to modern textbooks, to W. H. Eberhardt, School of Chemistry, Georgia Institute of Technology, Atlanta, Georgia 30332. Since the .ouroose . of this column is to urevent the suread and ront~nua~ion of errvrs and not thr e\,aluationof individuni texts, t h ~ sources of errors diarusr~dwill not he cited. In order to he prebtntcd. an rrr,.r n,wt u~rtrrin at lrnst t w u indrpendtnt recent ~landnrd books. 782 / Journal of ChemicalEducation
Summary of the Treatment of the Concept of Heat in Recent First Lewl College Chemistry Textbooks Number of First Level Treatment of H a s t Concept
College Chemistry Textbooks
Correct Definition Incorrect Definition Unclear Presentation
NO Definition
(19). The present development requires that only processes which change the internal enerw of the svstem be considFor the same change in state of a system under nonadiabatic conditions, the work will not be equal to the change in internal energy; i.e. AE12f W (nonadiabatic process)
A quantity of energy Q is also transferred across the houndary of the system and is defined and computed as
Q = AElz - W (nonadiahaticprocess)
(12)
This energy, transferred hy processes other than work, is heat. Combining eqns. (1) and (2) gives
Q = Wed-W a n d we see that the energy transferred as heat is equal to the difference between the actual work and the work required to achieve the same change in state adiabatically. In this approach, it is evident that the fundamental measure of energy is work (20). Other approaches are possihle using different formulations of the First Law hut this one is related immediately and precisely to the modern practice of calorimetry hased on electrical measurements and avoids circuitoua reasoning hased on heat as a directly measurable quantity. The mechanisms of energy transfer as heat are conduction, convection, and radiation. Heat conduction occurs when two narts of a material suhstance are maintained at different iemperatures. The circulation of a fluid across a temperature eradient produces heat conduction. Svstems may emit and khsurb e~kctruma~netic radiation and ;he rudiaribn emitted hv a hodv hv virtue of its temperature is thermal radiation. The net &eigy flow to or from-a system as thermal radiation is heat (21). Confusion about the measurement of heat is often the hasic source of misunderstanding. The quantity of energy transferred as heat is measured with on;of a wide varie& of calorimeters. Most of the terminology associated wkh these measurements was develooed hefore the notion of heat related to work was developed an2 much confusion about heat can he traced to this source. Therefore. it is valuable to examine several calorimetric techniques in order to clarify the nature of these measurements (22) and the terminology appropriate to each. The constant-volume. adiabatic calorimeter (see f i w e . nart a) operates on the that the thermal co&uct&ity from the surmundines can be reduced essentially to zero (23). Thus, any pr~~ceks nccurrlng within the system is charartt&rd hy AE = 0.Enerm transferred as heat frum n sample or sub. &tern containedbithin the calorimeter, flows to the hody of
TEMPERATURE
VOWYE ENERG
SOMKE
WKET
SUBSTANCE
G1P
ILE
EKRB SOURCE
IT*
JACIET
Differenttypr of calorimeters: a) adiabatic calorimeter, b) isothermal c a b rimeter; c) microcalorimeter.
chanee of the calorimetric fluids has been determined, suhsequent additions of energy to the calorimeter, either as heat or work. can he evaluated from the volume change of the system. 1 t is instructive to note that with this calorimeter, energy transferred to the system as heat does not produce a change in the temperature of the calorimeter, hut the temnerature of the process is restricted to that of the phase equilibrium. With the two calorimeters just described, it should be realized that the energy transferred will be classified as heat or work depending upon how the system is defined. For example, if a current is passed through an electrical resistor placed inside a calorimeter and the resistor is considered part of the system, the energy transferred will he classified as work. On the other hand, if the resistor is not included in the system, the enerw transfer will be classified as heat. Neither the adiahatic or the isothermal calorimeter measures heat directlv. Thev detect a chanee in the enerav state of the calorimeter*andwhether this e n e k change wascaused bv heat or work is determined bv the desien - of the exwriment. In contrast, microcalorimeters (see figure, part c) are based on a nrincinle which allows a direct measure of enerw flow as heat 729). ~icrocalorimetersare designed to retain the sample in a cavity which is surrounded by as many as one thousand thermocouples arranged in such a way as to detect the difference in temperature between the inner and outer walls of the cavity. This difference in temperature is related to the rate of energy flow across the cavity walls as the temperature of the entire assemblage is increased and integration of this rate over time vields the total enerw transferred to or from the cavity nr heat. -. --. -. The principal error which appears in many introductory chernistm textbooks relates to statements which imdv either --~~--directly or indirectly that systems "have" heat. ~h:ls>otion, of course. is a carrv over of the semantics of the old caloric theory which are n i t consistent with the present concept of heat. Misconceptions are manifest in several ways: (a) confusion of heat with temperature; (h) identification of heat with the kinetic enerw of the molecules: (c) i m o r o ~ e interpretar tion of historicarkxperiments and id) "se of words whi'ch becloud the orohlem. ~ r e ~ u e ntextbook tl~ authors state that heat and temperature are not the same thing and then subsequently imply that a system a t high temperature has more heat than at low temperature or that "heat must have been added" if the temperature of a system increases. I t should he clear that, althoueh a temperature difference must exist for energy to be transf&ed as beat, the temperature of a system dies not represent heat. A system does not have heat any more than it has work. Sometimes heat is confused with the kinetic energy of the molecules in a system. For example, statements like "heat is the random motion of the molecules" are common. In reality, this molecular kinetic energy is part of the internal energy of a system and, under suitable conditions, can he increased or deireased by a transfer of energy as heat or work, or indeed, hv some other change internal to the system which involves no transfer to the surroundines. The averaee kinetic enerev ... of the moleculei ran be related w the temperlrture of a system h\, kinetic theow armmenti and is called bv some authors (XI, 31) the thermal energy of the system. his form of energy should never he confused with heat. As part of the discussion of heat, some authors refer to the classical experiments of Count Rumford and Joule. Unfortunately, many times the significance of these experiments is interpreted incorrectly. For example, the cannon-boring experiments reported by Count Rumford are frequently quoted to support the notion of the conversion of work into heat. In reality, energy as work was transferred to the cannon under essentiallv adiahatic conditions thereby causing the temperature of the system (cannon and chips) Gincreaser g he only time heat was involved was during the subsequent ~
the calorimeter and increases the internal energy of this subsvstem. This change in internal enerw . of the calorimetric sul~iystemisawumpanied by an increase in temperature. It is assumed that the change in internal energy of thecalorimn therhange in itjtemperature. eter body is related uniq& t 'I'hus, a simple indirect measure of the increase in the internal energy of the calorimeter is available (24). Since the whole svstem is adiabatic, we see by eqn. (1)that the same change in internal energy can he achieved by transferring energy to the calorimeter as wurk. In principle then, thecnlurimeter is calibrated hy performing known amount of work on the calorimeter and noting the change in internal energyas indicated hv the chanee in temoerature. Once the relationship between temperatire change and internal energy change h& been established. subseauent enerev transfers either as heat or work, to or from the caiorimeter, &nhe measured by noting the temnerature variation onlv. ~ e t h b d sof calibrating the calorimeter lead directly to choice of enerev units. The standard unit of enerw is the absolute joule defined as the work done when the point of apolication of one newton is displaced a distance of one meter In the direction of the force (25)and is represented for practical use bv the enermex~endedin one second by an absolute ampere in-an absol;ie ohm (26). Before the relitionship hetween heat and work was understood, another energy quantity, the thermal or wet calorie, was defined and used extensivelv when measuring heat (27). I t was defined as "the amount oi energv whirh must he transferred wnplicitly as heat I to raise the remperature uf one gram of water #medegree wntrierade". - - ~ -- ~ -- ~ , for ~ examnle. ~ ~ , from ~ 14.5 ~ to 15 So(: (271.Herause the calorie appears extensively in the chemical literature, the chemical communitv has been reluctant to chanee from this unit of energy. Consequently, the so-called "dry" calorie is now defined as 1 calorie (thermochemical) = 4.184 (exactly) absolute joules (28). This number, 4.184, often referred to as the mechanical equivalent of heat, should be recognized for what it is: the conversion fador between energy units in calories and joules in the same sense that the number 2.54 (exactly) is the conversion factor between inches and centimeters. The isothermal calorimeter (see fimue, - ..part h) contains two phases of a pure substance in equilibrium, e.g., a liquid in equilibrium with its solid phase, and energy transferred to or from the system results in a change in the relative quantity of the two phases (23). Very often water at its freezing point is used as the operating fluid; the device is known as an ice calorimeter. The freezing or melting Drocess is a result of a change in the enthalpy orthe system due to a transfer of enerav to or from the calorimeter. The calorimeter is normally designed to permit the measurement of any change in thk volume of the svstem and this volume change is used as a measure of the ekhalpy change which has occurred as a result of an energy transfer. The energy equivalent of the volume change of the system is determined by measuring the amount of electrical work required to achieve the same change in state. Once the relationship between energy change a i d volume ~
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Volume 53. Number 12 December 1976 / 783
transfer of energy from the hot cannon and chips t o the surroundings. Many authors, including Count Rumford, confuse heat with temperature and conclude that because the cannon became hot, heat energywas involved or "heat was generated". The significance of Count Rumford's ohsemations, of course, is that they disproved the caloric concept of heat. Joule's experiments concerned the measurement of the "mechanical equivalent of heat." As noted earlier this number is simply the conversion factor between energy units in d o r i e s and energy units in joules. Some authors imply or conclude that in Joule's paddle wheel experiments (32)energy transferred to the system as work was "converted to heat" because the temperature of the system increased. Actually, Joule measured the quantity of energy, added to the system as work, required to produce a change in state of the calorimeter as indicated by a change in temperature. No heat was involved in the process since there was no temperature difference between the paddle wheel and the water (17).The quantity of energy, added as heat in units of calories, needed to achieve the same change in state was also determined. The data were then used to evaluate the conversion factor between energy units in calories and energy units in joules; the so-called mechanical equivalent of heat. Descriptions of this experiment which appear in introductory textbooks should he very careful not to imply that Joule studied a process whereby work was converted to heat. He simply examined a process for changing the energy state of a system using work and another process for achieving the same change in energystate using heat and compared the two. Probably the greatest source of confusion about the concept of heat centers around the semantics used in discussing the topic. For example, "heating an object" is common parlance. It should he realized that the process of heating implies increasing the temperature of a system. This can he achieved by transfeming energy to the system as heat or work. Unfortunately, there tends to be a correlation by students, and regrettably some textbook authors, between the words heating and heat. Thus, the conclusion is drawn that if an object is heated, heat must he "added" to it thereby producing a system which has "more heat," a meaningless deduction. I n a more subtle case, phase changes are characterized by latent heats. ex.. the htent heat of vawrization. Such phrases tend to implyihat beat is contained in a system. Although precise statements can be made utilizing these terms, reference to the enthalpy of vaporization avoids confusion about the term heat and the implications of heat content. Even here, there is ambiguity since the term really implies an enthalpy change. The statement "conversion of heat to work" leads to confusion about the nature of heat. This terminology derived from the study of heat engines and, as eloquently pointed out by Guggenheim (33), must be used with extreme caution. A uniquely defined conversion of heat to work is accomplished only in a process where aE = 0.In practice, this condition is most often realized in a cyclic process, of which the heat engine is an example. In this case, a portion of the energy transferred to the system as heat, and temporarily increasing the internal energy of the system, is transferred out again as work. The conversion process in reality is simply a change in the mode of energy transfer. In processes where AE # 0, the terminology "conversion of heat into work" is meaningless (33). The term heat capacity is a source of semantic confusion and one of those unfortunate misnomers which exist in thermodynamics (34).The term implies that a system has a capacity of possessing heat and tends to perpetuate the most common misconception about heat. Heat capacities are, in fact, energy capacities. For example, the quantity C,, the heat capacity at constant volume, is in reality the temperature dependence of the internal energy of a system at constant volume (35-40);that is
784 / Jwrnal of Chemical Education
C, = (aElaT),
While this temperature dependence can he measured b y adding energy to a system as heat, i t should he realized that work or a combination of heat and work can be utilized to achieve the same result. To conclude, heat is the name assigned to energy as it is transferred across the houndary of a system by virtue of a difference in temperature. Quantitatively, it is the difference between the adiabatic and nonadiabatic work required to achieve a given change in state of a system. Heat, like work, is energy in transfer. I t is not a property of the system, i t is of a transitory nature, which should never he considered as something identifiable within a system. The successful teaching of the concept of heat will be accomplished if a clear definition of the system, the surroundings and the boundary is presented followed by an emphasis on the necessity of a temperature difference between the system and the surroundings and the associated transfer of energy across this boundary. The author wishes tn acknowledge with thanks Prof. W. H. Eherhardt for his valuable sueeestions and comments durinethe preparation of this manuscript. -u
(41 Sheehan. W F."Phyaical ChemiaVy." 2nd Ed.. Allyn and Bacon, Inc.. Baton, Mass., 1970. p. 86. (51 Smith, N. 0.."Chemical Thcnndynsmie%." Reinhold Publishing Cirp., New York, 1967. p. 2. 161 Van Wylen. G. J.."Thermdynamio."6th Ed., John Wilcy andSons.Nw Yurk, 1959. p. 59. 171 Wesar. J., "Basic C h w r i d T h e e d y n a m i o . " W. A anjamin lnc, New York, 1366, p. 23. (81 Worthin8.A. G..and Halliday. D.,"Hcat," John Wiley and Sons, New York. 1948.p. 102. I91 Zlmmky,M. W.."Hcat and&nndynamiol,"5thEd., M f f i n w - H i l l b k Compmy, New York. 1918, p. 78. I101 Trihus. M.. "Thermostatirs and Thermodvnamicr." D. Van Noatrand Co.. Inc.. ~ r , n n m nhem . JPM,. 190.p 139 tilt A d m s A '.and Hdmne.I: D."Fundammlal8ofThceodynamtca."Harpor.nd H ~ t h c r aUcu . York IS42.p M. 1121 ~ ~J . A ~t . O U ~~.I n ~ f h~c m o d . m m r r s . ~ ~ ~ ~ n i s d r ~ ~ ~ r b ~wi s t hhai nr ne .~M~~ ~.
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(13) Ref. i121, p. 163. PubliahingCo.Lfd.. New (14) Adkin8.C. J. "EquilibtiumThemodynamiol."Mffi~av-Hill York. N.Y.. 1966.p. 33. (15) Holman, J. P., "Thermdynamio." 2nd Ed., MeGraw-Hill Bmk Co., NOWYork, 1969.
" dfi ...
116) 2emsnsky.M. W., J.CHEM.EDUC.,Sl.572 (1974). I171 Csnagaratna, S. G.. Amsr J.Physics., 37.679 (1969). 118) Ref. (121, p. 121. 1191 Rcf. 1131.0.162. 1201 Ref (3). pr30. 1211 Ref. 191. p. 101. (221 Bridgeman,P. W.."The NatvreofThermdynamio." Peter Smith.Gloumrter. Msas., 1969.p. 28. 1231 . . Calvort. E.. andPrnr H.."RecentPnmm in Mi~mcalmcaldme~."TheMmMiIImCa. New ~ o ; k . 1963, 5.' 1241 Ref. 1141. 0.85. , .~~ (251 M & I ~ , ' K A ~ International T~~ SystemofUnit*."2ndRev..Seienfifieand Technical Information Offirr. NASA. Washington. D.C.. 1973, p. 4. 1261 b i d , F.D.."Fundamcntal Measurement*and Comtant*ofScienm and Technnlagy: The Chemical Rubber Co.. Cleveland. Ohio. Chan 10. 127) Ref. (261, Chap. 9. (251 Ref. 1251, p. 11. 1291 Ref. 1231. Chao.4. imi ~ e i15i: t p.4i. 131) Ceste1lon.G. W.."PhysidChemiW." 2nd Ed..Addison-Wal~yPvbliahingC~,mpany, Reading, Ma-.. 1971, p. 96. 1321 Partington,J. R.."AnAduaneed Treatise on Physical Chemiatry,"Longmans, Green and Co., Ltd., London, 1949, Vol 1, p 138. 1331 Guggonhein. E. A,, "Thcrmodynamic8.). 5th Ed..North Holland Publishing Co.. Amsterdam. 1967,~.12. (34) Re( (31, p.85. (35) Msmn, S. H.. and Lmdo, J . B., "Fundamentala of Phyaical Chemistry." MacMillan Publishing Co., lnc. NOWYork, 1974. p. 251. I361 Ref. 1311, p. 120. I371 Ref. 191. p.85. (381 Hataomuilm, G. H.. and K ~ n e n . J H.,"PrmeiplasofGeneral . Thermodynamio:Johnb Wiley and Sons, he.. New York, 1965, p. 65. 1391 Ref. 1151, p.50. 1401 Ref. (121, p. 186.
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