Memo To: Ms. Liticia Salter, Instructor From: Mahmudul Alam, Mohammad Sirajudeen Date: April 17, 2007 Subject: Transmittal Memo In response to your prompt, we have performed the rubber band experiment in a team and our main objective was to study and observe the change of entropy of the rubber band both in the stretched and relaxed state. Our report analyses the change of entropy both from the perspective of molecular orderliness and the energy degradation. The report also provides an explanation for why the rubber band contracts when it is exposed to heat. Our area of satisfaction was the outcome of the experiment, because it completely agreed with the theoretical explanation. As for the hair dryer, we borrowed it from a barber working in a men s saloon. Initially, we had a difficulty in convincing the barber that we are going to use it for an experiment, but finally we managed it. Please review and respond to our report at your earliest convenience. 1
Abstract The report presents the change of entropy in a rubber band both from the perspective of molecular orderliness and energy degradation. Rubber is an elastic hydrocarbon polymer, which unlike other substances contracts when exposed to heat because of its unique atomic structure. However, the outcome of the experiment, which mainly comprises two simple tests, demonstrated that like the other materials, the change of entropy in a rubber band also completely agrees with the theoretical explanation of entropy. Introduction The report discusses an experiment which was performed to observe and study the change of entropy in a rubber band both in relaxed and stretched state. The objective of this experiment was to determine whether the outcome holds the theory of entropy, and to provide with an explanation why the rubber band contracts if it is heated. This report contains the procedure and result of the experiment, including an analysis and a discussion of the result. Theory Entropy in a closed thermodynamic system is defined as a quantitative measure of the amount of thermal energy which is unavailable to do any work. In other words it is the measure of thermal energy which is given out or absorbed during a reaction. Entropy is actually the indicator of unavailable form of energy. For instance, let us assume a system, which is comprised of a hot body and a cold body. If somehow the hot body and the cold body come in contact, then according to the second law of thermodynamics, heat will automatically flow from the hot body to the cold body, and this thermal energy could be transformed into mechanical energy or work by a heat engine. Once the system reaches the equilibrium state, the energy of the system, according to the first law of thermodynamics and the law of energy conservation, will remain same, but then the energy cannot be used to do work any more. Although the energy is never destroyed, it tends to degrade from the useful form to the useless one, and entropy is the measurement of this degradation. Page 2
Entropy is also defined by the amount of disorder or randomness of a system. In the previous example, the system before reaching its equilibrium point was ordered, because the faster and more active molecules of hot body were easily separable from the less active molecules of cold body. This orderliness is destroyed at the equilibrium stage because at that point, molecules of hot body cannot be separated easily from that of cold body. With the increase in disorder, the amount of available form of energy decreases, and therefore, the messier the system, the higher the entropy. If a system absorbs or releases an amount of change in entropy is Δ Q heat energy in T temperature, then the ΔQ ΔS = T Δ Q or, Sfinal S initial = (1) T Apparatus For this experiment, we used the following apparatus: 4-5 rubber bands (in unstressed state, the rubber bands are 7 mm width and 28 cm long) a hair dryer a meter stick ( 1 m long) a hammer (weight approximately 1.25 kg) The rubber bands were provided by the instructor, while one of the team members had the hammer in his house. As for the hair dryer and the meter stick, we borrowed it from a local men s saloon and the Texas A & M University at Qatar Library (TAMUQ-L) respectively. Procedure We performed this experiment in an air-conditioned room, where the rubber bands were kept in for several hours. The experiment consists of two different types of tests, and we carried out both of the tests with more than one rubber band to come up with as precise result as possible. Page 3
Procedure of Test-1: The procedure of the Test-1 is quite straightforward, since it involves stretching and shrinking only. First, one of the team members held an unstressed rubber band in his forehead to feel the temperature of the rubber band, and it was felt little bit cooler than the room temperature. Placing his thumbs at each ends of the rubber band, he then quickly stretched the rubber band to its maximum, and immediately pressed it against his forehead to determine the temperature change of the rubber band. As the next step, he then suddenly released the rubber band, and again checked the temperature when the rubber band returned to its normal length. He repeated the test several times until he felt confident about the result. To make sure that the obtained results were correct, the other team member repeated the above mentioned procedure with another rubber band. Procedure of Test 2: The basic set-up for Test2- was also quite easy and pretty clear cut. First, we hung a rubber band vertically from a hook embedded in a concrete wall, and suspended a weight from the other end of it so that the rubber band remained in a linear, upright position, parallel to the surface of the wall. As for the weight, we used a 1.25 kg hammer, because we found that it does not surpass the elasticity limit of the rubber band. Next, we plugged in the hair dryer, and while it was warming up, we measured the length of the stretched rubber band under room temperature with the meter stick. Finally, we heated the rubber band by exposing it to the hot, warm air of the hair dryer, and recorded the final length of the rubber band. While heating, the hair dryer was kept 15 cm apart from the dangling rubber band. The figure on the following page introduces a schematic diagram of the basic set up of the Test 2. Page 4
Figure 1: The Schematic Diagram of the Test 2 apparatus arrangement Experimental Data The following table shows the results of Test-1: The State of the Rubber Band The Temperature felt Neither Stretched nor Contracted A little bit cooler than the room temperature After quickly Stretched Warm After Contracted Cool Table 1: The result of Test 1 Page 5
The results of Test-2 have been tabulated in the following table: Rubber Length before Length After Change in the Band Heating (cm) Heating (cm) Length (cm) Rubber Band 1 30 27 3 Rubber Band 2 30. 5 27.4 3.1 Rubber Band 3 31.5 28.7 2.8 Table 2: The data recorded from the Test 2 Analysis The result of this small experiment very closely supported every aspect of the scientific theory of entropy. Theoretically, the entropy was supposed to increase during the relaxation of the rubber band, and from the experiment we also found that the entropy increased during the relaxation process. The vice-versa was also true, and the discussion section further analyses and interprets this result in a narrative and elaborative way. Discussion of the Result: First, for the sake of explanation, let us assume that the temperature before and after the stretch of the rubber is T1 and T2. After stretching the rubber, we felt that it became warmer, which definitely says that in this process the rubber released a specific amount of heat Page 6
energy. Assuming that this specific amount of energy is Q joules, the change in entropy is ΔQ ΔQ, and this is a negative amount because here T2 > T1. The negative quantity is a T T 1 2 proof that the entropy decreases when the rubber band is stretched. After contraction, we found that the rubber band feels cool, and this means that it sucked an amount of heat energy from the heat detector-our forehead, and from the surrounding atmosphere as well. If T1 and T2 is the temperature of the rubber band before and after the contraction, Q is the amount of heat that is sucked up by the band, then the change of entropy in this case is ΔQ ΔQ T T 1 2, which is positive because T1>T2. The positive quantity is the indication that the entropy increases when the rubber band is released from its stretched position. The whole phenomena of expanding or contracting of the rubber band is a reversible process, but the phenomena include a spontaneous (contraction) and a non-spontaneous (expansion) process. The Second Law of Thermodynamics says that for any spontaneous process, the overall change in the entropy must be greater than or equal zero, which means the change, should be positive. Our rubber band experiment exactly demonstrated the similar result. During the relaxation, which is spontaneous process, the heat was absorbed, and the entropy increased. On the other hand, during the expansion, which is a non-spontaneous process, the heat energy was released, and the entropy increased. This change in entropy in the rubber band can also be explained even if entropy is taken as the measurement of the orderliness of something. In this situation, entropy will be the determinant of the orderliness of the molecules present in the rubber band. The loosely fitted chains or strings of molecules of the rubber band try to line up when the rubber band is stretched. Because of this being lined up, the disorder decreases, and the entropy on the other hand increases. Similarly, the opposite things occur when the rubber band is released fro its stretched position, and the entropy goes up. Unlike other substances, the rubber contracts when it is heated, and it can be explained from its atomic structure too. The rubber consists of chains or strings of very large, threadlike Page 7
molecules, these molecules move very dynamically in their respective chain when the rubber is heated. Because of the motion of the molecules at the middle of the chain, the ends of the chains are drawn closer and closer, which eventually forces the stretched rubber band to contract. The similarity between the Test-1 and Test-2 is that in both cases the rubber band contracts because of absorbing heat. In test one, the rubber band absorbs heat from the surrounding, and from the heat-detector, our lips, whereas in the second test it absorbs heat from the hot air of the hair dryer. However, in the second test, the rubber band contracts more because it absorbs more heat from the hot air. Conclusion: In the conclusion, we can say that although the contraction of the rubber band due to heat seemed unusual considering other materials expand because of heating, the atomic structure of the rubber showed us that this actually happens to comply with the theory of entropy. Appendices: The modulus of elasticity plays a great role in elasticity limit of any material, and therefore the modulus of elasticity was an important factor in determining the weight of the hammer. The following is a brief discussion about the elasticity limit, and it is directly copied and pasted from the following website: <http://hsc.csu.edu.au/engineering_studies/glossary/2296/index.html> Modulus of Elasticity: Rate of change of strain here is presented as a function of stress. The slope of the straight line is a portion of a stress-strain diagram. Tangent modulus of elasticity is the slope of the stress-strain diagram at any point. Secant modulus of elasticity is stress divided by strain at any given value of stress or strain. It also is called stress-strain ratio. Page 8
Figure 2: Modulus of Elasticity Graph Moduli of elasticity in tension and compression are approximately equal and are known as Young's modulus. Reference Seeley, M.S., Postgraduate physics student, Cambridge, UK. Why do rubber bands contract when heated instead of expanding? Website accessed and information retrieved on April 16, 2007.<http://www.physlink.com/education/AskExperts/ae478.cfm> Unknown Author. Entropy, Definition and much more from Answers.com. Website accessed and information retrieved on April 16, 2007. <http://www.answers.com/main/ntquery?s=entropy> Unknown Author. Entropy, Wikipedia, the free Encyclopedia. Website accessed and information retrieved on April 16, 2007.<http://en.wikipedia.org/wiki/Entropy> Unknown Author.Modulus of Elesticity. Website accessed and information retrieved on April 16, 2007.<http://hsc.csu.edu.au/engineering_studies/glossary/2296/index.html> Unknown Author.Dead Load. Website accessed and information retrieved on April 16, 2007.<http://en.wikipedia.org/wiki/Dead_load> Unknown Author.Entropy. Website accessed and information retrieved on April 16, 2007. <http://en.wikipedia.org/wiki/entropy> Page 9
Unknown Author.Order and Disorder. Website accessed and information retrieved on April 16, 2007.<http://en.wikipedia.org/wiki/Entropy_%28order_and_disorder%29> Unknown Author.Rubber band. Website accessed and information retrieved on April 16, 2007.<http://en.wikipedia.org/wiki/Rubber_Band> Page 10