Thermodynamics and the Bounce Charles E. Carraher, Jr. Florida Atlantic University, Boca Raton. FL 33432 Both science and philosophy ask two fundamental questions: what events may occur, and why? In science, these questions fall into the area of thermodynamics or "thermo". Thermodynamics deals with the flow of free energy and is succinctly summarized by the Laws of Thermodynamics: Zeroeth Low. If the temperature of A = Band of B = C, then the temperature of A = C. First Law. Energy is conserved in an isolated system. Second Low. The net, overall randomness of an isolated system increases in any change, AS > 0. Third Law. Free energy is the measure of the tendency of change to occur in a constant mass, pressure, and temperature system.
All forms of energy tend in time to he converted into heat. The spontaneous flow of energy from high-energy regions to low is directly perceptible: An ice cube feels cold to your touch because your body is a system of higher energy than the ice. Thus, some of your energy flows to the ice cube, leaving your hand colder. The probability factor and the tendency for systems to go
In such a constant n, P, T system as described above for the Third Law, the free energy change, AG, is described by the relationship, 4G=AH-T4S
where AH is the energy (enthalpy) change T is the absolute tem~erature.and A S is the order or randomness-related such as chemical reactions are thermodychange. namicallv soontaneous when AG is neeative in a constant n. P, T Contributions hv A H and A S mav hoth work toward a spontaneous change as in the case o f t h e formation of most nonsaturated solute-solvent combinations such as table salt (NaCI) or common sugar (sucrose) dissolving in water. Here energy is gained through the solvation, hydrate formation, or hvdroeen hondine hv " " the solute and water. Entronv (ran. domness) is increased since we are going from crystalline salt (suear) and Dure water structures to the more fluid. more disordered, hydrated forms. See Figure 1. Entroov and enthalov . . terms mav also work aeainst one ancgther.' This is thr r a w in man;. vinyl polykeri~atiuns where energy is given off, at, AH is highly nrgative and AS is nrgarivr (going irom a less ordered to a more ordered state,. F~xt~uiately. for the po1ymf.r chrmiit, the change in enthalpy is often larger than the TAScontr~l)utim, giving an orerall nrynrive Af:.Thus, hoth theentropy andenthalpy factors must he cwsidered when drscril~inga renction. S w 1:igure 2.
vents
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Figure 1. Sodium chloride dissolving in water.
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Figure 2. A vinyl polymerization (A
= H,C%HX].
Volume 64 Number 1 January 1987
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Figure 3. Rebounding of a mefa1 ball bearing Figure 5. Rebounding of a superball
be similar. When dropped onto a hard surface the balls hit the surface and rebound; but why? The rebound of the ball bearing is largely due to the deformation of metal bonds by the striking of the hard surface (Fig. 3). This collision pushes the metal atoms into a higher energy situation. The metal atoms then move back to the original, lower energy sites resulting in a push against the surface resulting in the "bounce". The metallic bonding that isdistorted by the impact is of the primary type, on the order of 100 kcallmol of iron atoms. We can eet a ballnark feel for the amount of energy available versus the amount of energy necessary to "move" the iron atoms as follows: , (1) Let us assume that theareaaffected is 1mm square and 0.1 mm atoms if Figure 4. Dropping a ball bearing results in disruption of about 1OZ0Fe me impact area is about 1 mmz with a permeation depm of about 0.1 mm.
spontaneously from ordered to less ordered, more random situations can be related to students through discussions of what typically occurs to their "cleaned up" room (a system of low probability). I t takes considerable effort and enerav to put a room in good order. However, after several daysrthe situation normally tends to go spontaneously to a more random, less ordered state. In our house we have a 3-year-old girl, Cara, who goes from room to room, quizzically looking into every box, drawer, under beds, etc.-and actually doing more than looking. In fact, Cara, "Attila the Honey", is the epitome of the Second Law. As scientists, we are aware that things are not always as they superficiallv (In fact. we have almost come to . amear. .. expect the unexpected and rationalize i t when it occurs.) We would like to convey to students that there are exdanations for events if they simply ask the right questions;make the correct observations, and have the proper knowledge. We know why balls bounce, don't we? Is the bounce of a ball related to energy or probability factors? The answer, of course. is "ves." In fact it denends on both. This deoendence can be ill;strated through' the following demonstration, which uses a metal ball bearing (I use one about the size of a golf ball) and a "superball". I also try to use balls of about the same weight so that the impact energies of the two balls will ~
44
Journal of Chemical Education
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deep, or 10-'0 m3. Each iron atom occupies a volume of about m3. This translates into about loZoatoms being directly impacted (Fig. 4). (2) How much energy ia required to move these 1OZ0iron atoms? Theattractive forces holding the iron atoms are about 8 X 10-10 Jlatom which translates into about 80 J holding these 1020 atoms. (3) The energy available from dropping a 50-g hall bearing 2 m is (50 g X 9.8 m/s2X 2 m), or (0.05 kgl(9.8 m/s2)(2m)= 0.98 kg m2/ s2 = 0.98 J. The "hound' does not involve much actual bond breakage, but rather involves distortion of the iron atoms for which the presence of about 1%of the bond energy (80J X 0.01 0.8 J) should be adequate to achieve this distortion. Thus, there is sufficientenergy to distort about loz0iron atoms.
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For the ball bearing there is little unoccupied or free volume so the applied force is used to distort the primary (metal) bonded iron atoms with little change in the overall order of the iron atoms. Energy is the principal driving force here. Polymers arc most tightly parked when thry are arranged in an ordered fashion such as a folded clothes line or thread on a spool. The "superball" is a semi-tough rubber that is solidified so that the polymer chains are arranged in a hiehlv disorganized, random manner. When the .'s;perball"'hi[s the surface, the decreased spare is largely srcommodated 11). a reorganization of the polymer chains into a more ordered, less probable configuration (Fig. 5). When the polymer chains return to their original, highly disorganized state, the "push" to occupy the original, predeformation volume is
translated into a push against the surface resulting in the "hounce". In this situation, probability is the major driving force in the bounce. While the energies holding the actual carbon and hydrogen together to form the polymer chain are of the same magnitude (but not the same type-i.e., metallic versus covalent bonding) as those holding the metal atoms together, the energies of importance here are associated with interchain attractive forces since there is sufficient free volume to allow whole chain segments to move into their free volumes. 'These interchain associations are of the order of 1-2 kcall mol of interaction (per -CH*unit for cross-linked polyethylene) or about 1% of that associated with the forces holding the iron atoms in place. On a numher-wise basis, many more polymer units can be affected by the impact. This is partially due to the ready availability of unoccupied space within the rubber hall. Thus, chain segments can, with relatively little energy, arrange themselves into a more tightly packed, volume-efficient space. Further, since the forces holding chains together are inversely proportional to distance (usually force = ll(distance)Z), the tendency toward achieving the more ordered orientation is assisted by energy forces. So, the polymer chains tend to react to the impactassociated volume decrease by formation of more ordered configurations that occupy lesser volumes. Thus, the impact energy does "work" in rearranging the less ordered chains into ordered chains (much as we must ask our children to do with their rooms) and, as such, is converted into an entropyassociated free energy component. Conversely in a metal, the atoms are already tightly packed so that further distortion of the metal atoms simply compounds the problem, thus making further distortion
more difficult so that energies required for further distortion approach primarv bond energies. This "distortion" enerev is different in magnitude fromthe "shock wave" energy. This shock wave energy allows metals t o dissipate energy throughout the entire hall hearing, which is on the order of 10"imes smaller than the distortion energies. Thus, while fewer metal atoms are affected through major space reassignments, all may share in the redistribution of the energy .. gained on impact. Some observant students may notice that the superhall bounces higher than the metal hall hearing when both are dropped from the same height. Several factors are in play. While chain-folding by the superhall is a more efficient means of storing free energy than is simple iron-lattice deformation, we should look further for the answer. In each case, the total free energy is conserved. The major factor contributing to extent of bounce appears to he related to the efficiency with which each material is able to store and return the imparted free energy. Metals are good conductors of heat. Thus, as the rigid, tightly fitting iron crystal grains a t the site of impact are deformed (thus storing free energy), some of the free energy is converted to heat and shock waves, which dissipate throughout the hall and the surroundings (as sound). Converselv, oreanic ~olvmers are noor conduc. " tors resulting in more &eniiou of the free energy (less sound and less heat conductivity) at the site of impact, allowing greater subsequent recovery of the free energy there. Thus, an apparently similar phenomenon, the "hounce", results from-two different free-energy contributors. his simple demonstration can he used to introduce the two freeenergy contributors, honding types, and the scientific method.
Volume 64
Number 1
January 1987
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