W. H. Eberhardt
Georgia lnst~tuteof Technology Atlanta, Georgia 30332
Two Lecture Experiments in Elementary Thermodynamics
T h e two lecture experiments described in this paper have been designed on the following premises. 1) Thermodynamics is a formalism intended for the interpretation of experiments; therefore, it is most desirable that lecture presentations include actual examples which should he as quantitative as possible within the constraints imposed by the lecture environment. 2) The laws of thermodynamics should he stated in operational language in a logical fashion; measurements of energy changes are generally made in terms of a n electrical operation and most commonly inside an adiabatic boundary. These notions and techniques should he used early and often in the introductory course. 3) Electrical measurements, batteries, and electrochemical cells are quite familiar to students, generally much more so than paddle-wheels, expanding gases, etc., and not only provide a simple and accurate quantitative experimental approach, but also tie in quite readily with the students' experience and intwest. The first experiment is a calorimetric measurement of 'the enthalpy of vaporization of CH2CI2and is designed t o illustrate the First Law, the definitions of work and heat, and the concepts of adiabatic and diathermic boundaries. The second experiment involves charging and discharging an electrical cell a t measured rates and is designcd t o illustrate the Second Law, the notions of reversible and irreversible processes, and the inequality determining the sense of a real process. Both experiments depend on the existence of suitable instruments t o measure and display electrical voltage and current. Our voltage measurements were made on a display meter constructed from a surplus Brown Recorder. The servo-mechanism was used t o drive a ten-turn heli-pot coupled with a string t o a traveling pointer with an excursion of 40 in. The input t o the servo-mechanism was designed around a single operational amplifier, Analogue Devices, Inc., Number 115A, in a feedback circu~twhich provided full-scale sensitivity in ranges of 0.001,0.01,0.1, 1.0, and 10.0V, and also, coupled with a pH meter, a scale ranging from 0 t o 10 pH units. Supported in part by a grant from the National Science Foundation. Presented at the American Chemical Society Meeting, September 10,1969. W. R., KELLEY,J. C., GIDDEN,R., AND EIIER'BARNARD, HAKDT. W. H.. J. CHILM. EDUC..45.206 (1968). , , In'this experiment an electrical ground-loop existed which coupled the recorder and power supply. Small, discontinuous jumps are evident when the electrical energy is turned on and off, but do not complicate the analysis significantly.
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Other approaches t o the display of electrical potentials are possible and range from a simple projectiontype meter t o the very elegant device dcscrihed by W. R. Barnard, et al.' The Heat of Vaporization of Methylene ChlarideA Calorimetric Experiment
I n this experiment a measured volume of CH2C12is introduced into a sample bulb immersed in water inside a clear Dewar flask. The temperature of the water is monitored by a thermistor probe (Yellow Springs Instrument Company Telethermometer) and displayed on the lecture meter using the 10 mv full-scale range. I n addition, a strip-chart recorder (Bausch and Lomb VOM-5) was used in parallel with the display meter t o provide a permanent record of the dependence of temperature on time. The system is assembled with the CH2C12in the sample bulb and the temperature allowed t o attain a constant value. A stopcock connecting the sample bulb t o a water-aspirator pump is opened and the liquid evaporated. The temperature of the calorimeter fluid falls during this process and again attains a constant value when all the liquid has evaporated. The pumping is discontinued and electrical energy is added until the thermometer indicates that the calorimeter has returned to its original temperature. Figure 1 presents a stripchart record of this p r o c e s ~ . ~
Vaporization time
.-
-
Heating
Figure 1 . Recorder troce of the variation of temperohre with time. The recorder full-scals range i s 0-10 mV m d corresponds to approximately 6'C; the time span indicated i s approximately 8 min.
The process is conceptually simple, perhaps deceptively so, but permits two forms of analysis as sketched in Figure 2. I n the first, the system is chosen as everything within the adiabatic walls. Obviously, the heat, Q, is zero; the total work done by the system on the surroundings is the p - V work plus the electrical work or W = p,AV - &it, where p, is the pressure exerted by the surroundings on the system; G, the electrical voltage; i, the current; and t , the time that electrical work was done on the system. If the evaporation is done a t a modest rate so that equilibrium of liquid and vapor can he assumed, the p - V work is described adequately by
Figure 2. Andyris of the vaporization experiment. Two approaches ore indicated. I f the entire colorimeter is considered 0 %the system, (3 = 0, W = p.AV &it and AHuan = &it. If only the sample is considered os the syskm, only p - V work i s done and Q' is the chongo in enthdpy.of colorimeter during vaporirotion. This enthdpy change is determined to be h e &if during the heating procerr
it is bard t o describe accurately and also raises some stimulating considerations. As the experiment is geuerally reported from research laboratories, the vaporization is carried out slowly with concurrent addition of electrical energy to maintain the temperature constant and t o approach quasi-static conditions as nearly as possible. An interesting extension of the experiment can be devised using the dependence of the vapor pressure on temperature. This experiment is relatively easy to perform because of the high vapor pressure of CH,Cl, a t room temperature and provides a simple but elegant illustration of the relation between direct thermal measurements and relations derived from basic thermodynamic considerations.
+
quasi-static conditions and the electrical energy added is just the enthalpy of vaporization. Alternately, if the system is chosen as just the sample itself and the remainder of the contents of the calorimeter are defiued as surroundings, the state of the surroundings is described completely by the temperature and is the same before and after the experiment. Thus, the electrical energy added t o warm the calorimeter fluid represents the change in enthalpy of the surroundings during the evaporation. The energy is transported across the boundary between the sample and the calorimeter as heat, Q'; the same p - V work is done by the gas on expanding, but no other work is involved. The result implies that AH for the surroundings is zero, the heat lost by the fluid is just equal to the electrical work added to restore the calorimeter to its original state, and the heat flowing into the sample is the enthalpy of vaporization. For our experiments, the calorimeter fluid was 400 ml of water, and a sample of 10-15 ml of CHzClzprovided an adequate temperature drop. Some boiling chips were required to maintain smooth evaporation. Heating times ranged from 120 to 180 sec with a power input of 1.0 A at about 40 V. The measured enthalpy of vaporization ranged from 6600 to 7200 cal/mole compared with the reported value of 6820 cal/mole at 30°C.3 'l'hr priucipnl s o ~ ofk erpor nppenwd to bc the drift i l l hrt.+ l i n t s ~tttrihutrdto lack u i :~di:ib:tticityof t l ~ cvulorimeter. One of the challenges of the experiment rests on the various approximations implied in the treatment of the data. For example, the fluid is pumped out of the calorimeter, and, therefore, the contents of the calorimeter change during the experiment. The electrical energy is required to warm only the calorimeter, not the sample itself. The question arises: what is the magnitude, or even the sign, of this error? Since the molar heat capacity of the gas is approximately half that of the liquid, 12.2 versus 23.9 cal/mole°K, respectively, the heat of vaporization changes with temperature by an amount comparable with the change in enthalpy of the liquid. The analysis leads to some interesting results. A more complex question concerns the work actually done by the gas expanding from the sample bulb. Since this process is not really a quasi-static one,
Figure 3. Schematic diogrom of the sell m d external circuit. The display voltmeter operates on o w1.0 V scale; the ammeter on a *2.5 mA scale.
The Voltage of a n Electrochemical Cell
The experiment is outlined schematically in Figure 3. A large H-cell is used; it embodies one electrode of Ag, AgNOa (0.2 F), the other electrode of Cu, Cu(NO& (0.2 F), and the junction glass-wool saturated with 0.2 F KNOa. The voltage of the cell is measured as a function of the current passed through it from an external source using two l'/z-V dry-cells supplying a variable potentiometer. The cell voltage is measured with the display multimeter described above using the full scale range of 1.0 V. The input impedance of the meter, lo5 ohms, is large compared with that of the cell, approximately 150 ohms, and the loading introduced by connecting the meter directly across the cell is negligible. The current passing through the cell is measured with a display milliammeter constructed from the works of a meter with range +2.5 mA mounted on the stage of an overhead projector. The experiment consists of measuring the voltage of the cell with no current, with a range of currents corresponding to discharge of the cell, and again with a range of currents corresponding to charging of the cell. The results are plotted as in Figure 4. The experiment may be analyzed in different Tvays. I n one, a certain amount of chemical reaction is considered to occur during the discharge of the cell at a chosen current for an appropriate length of time. The external circuit is then adjusted to provide the same charging current for the same time so that the same amount of chemical reaction is carried out, but in the opposite direction. The cell is assumed to operate isoa
"LandolGBijrnstein Tabellen," (6th Ed.), Springer-Verlag.
1961, Vol. 4,p. 292.
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cal. For a current of 1.5 mA, the discharging voltage is 0.24 V, the charging voltage 0.66 V. For the process discharging a t 1.5 rnA AG = -19,800 < -0.24 X 2 X 23,060 = -11,000 c d Similarly, for the charging process, i.e., reduction of CuZ+
Figure 4. Voltage -9 a function of current for charging and dirchmging the cell. The difference behveen these raltoges corresponding b a chosen current reprerents the irreversibility or entropy generotion ossocioted with o cyclical process conducted at a r o k determined by thot current. The limit of i = 0 corresponds to reverribility with no entropy creation or "lost WO*."
thermally and a t constant pressure so that, at the end of this experiment, the cell has been returned to its original state. The experiment shows that for the full cycle the electrical work done by the cell is less than that done on it to restore it to its original state. The difference . AW =
(WChBr.. - Wdlsohsrm)
=
(Vcharga - Vdia.hsr& X i X t = TAS;,,, represents the amount of work converted into heat in the surroundings and is a measure of the entropy created during the process. Only in the case of i = 0 are the two voltages the same and equal to the cell potential. Under these conditions, the reaction is "reversible" and the entropy production is zero. Alternately, the inequality representing the Second Law may be demonstrated. Thus, for a chosen amount of cell reaction, the change in Gibbs Energy, AG, is related to the work done by AGS - V X i X t
where the inequality determines the sense of the spontaneous process and the equality corresponds to equilibrium or reversible conditions identified as the limit of i = 0. Thus, from the zero-current potential, 0.43 V, the AG for oxidation of one mole of copper is - 19,800
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The overall cycle results in the conversion of electrical energy into heat of 19,400 cal per mole of copper. The change in enthalpy for the reaction may be computed approximately from tabulated values of the cnthalpy of formation of the ions in their standard states and is -35,220 cal. The corresponding entropy change is -50.9 cal/OI
