The behavior of the rubber band is compared with both that of an ideal. Pdf theory of thermodynamic variables of rubber band heat. Polymeric rubberelastic material rem is in many ways analogous to ideal gases. Doing so will give us the generalized hookes law for homogenous, isotropic, elastic materials. The principle is one of the four fundamental postulates of macroscopic thermodynamics. In this paper, we introduce a rubber band experiment that uses maxwell relations to measure changes in entropy and internal energy. If the equation of state for a rubber band is given by where. To give some context, the question is asking which of the two formula give the correct entropy for a rubber band and why. If a rubber band stretched 3 cm when a 100g mass was attached to it, then how much would it stretch if two similar rubber bands were attached to the same masseven if put together.
Jan 04, 2018 the crosslinking property of polymers is vital to the bands elasticity. The band remains an unsung supergroup of the contemporary british folk rock scene of the 1990s, as its members went on to become award winning recording artists in their own right. Theory of thermodynamic variables of rubber band heat engine. Using rubberelastic materialideal gas analogies to teach. Currently i have not found a simple equation or chart that shows the relationship between the distances an elastic band. The flory theory of rubber elasticity has pointed out the rubber elasticity has primarily entropic origins. Equation 2 is the first law of thermodynamics is used to describe the rubber band heat engine system and equation 3 describes the work done by the system. So it is true that when we heat a rubber band it pulls, and this fact is definitely related to the fact that when we release the tension of it, it cools. The appropriateness of the standard equation of state of a rubber band is studied in an undergraduate laboratory experiment. Thus, the problem is equivalent to a rubber band impacting a rigid surface at speed v. F atll0 l0l2 where l0 10 cm is the original unstretched length, a 1. How would you go about measuring the proportionality constant k of a rubber band.
This should imply the entropy of the rubber band has decreased, but how does the entropy of the whole universe increase here. Equation were a british, young devonbased folk band formed in 1995, to combine the core talents of the lakeman brothers with kathryn roberts and kate rusby, later replaced for a spell by cara dillon. Entropy maximization, fundamental equations, intensive vs. In this paper, we describe laboratory and classroom exercises designed to obtain the fundamental equation of a rubber band by combining experiments and theory. Part i emphasizes specific rem examples including historical perspectives, concepts of action and size, equations of state, problem solving. Exploring the thermodynamics of a rubber band oregon state.
I think perhaps i need an equation of state of the band. The behavior of the rubber band is compared with both that of an ideal elastomer and that of an ideal gas, considering the generalized joules law as the ideality criterion. However, the same force applied to the longer band stretches it from 12 inches to 18 inches. Equation of state and molecular structure objective to determine the macroscopic thermodynamic equation of state of an elastomer, and relate it to its microscopic molecular properties. To determine the number of polymeric chains per unit volume in a rubber band. When i stretch a rubber band, the fibers straighten out causing lesser randomness and more order. Homework statement for a stretched rubber band, it is observed experimentally that the tension f is proportional to the temperature t if the. Separable equations including the logistic equation. Rubber band thermodynamics module 8 university of minnesota chemistry 4501. F force k spring constant d distance the spring constant is a number associated with the individual spring, and something you may need to. As an ideal gas, rubber band also has a thermodynamic variables, such as equation of state, heat capacity, carnot cycle, work, and efficiency. Since in xx goes below ln and stays below, it converges to. This may be used to good advantage as a supplementary system for teaching elementary thermodynamic concepts, equations of state, and the laws of thermodynamics.
A thermodynamic study of an isotropic rubber band under uniaxial stress is presented on the basis of its equation of state. Jan 27, 2016 rubber band thermodynamics module 8 university of minnesota chemistry 4501. Physics 110 lecture 1 pvt systems and equations of state. In the first part, a band is stretched at constant temperature. Introduction to statistical mechanics, david chandler exercise 1. The cooling effect means that it is an endothermic process d h0 so that td s is positive.
Gale rhodes department of chemistry university of southern maine portland, maine 041049300. Does this mean a rubber band gets colder on stretching. The calculation involves the probability of finding the system with a given distribution of molecular configurations. Thats the equation in its general form, but we can rewrite it more explicitly in terms of its components of x,y, and z. For the acceptable choice deduce the dependence of the tension, upon, and. It is a polymer that means that the rubber molecules are made of long chains of atoms. Consider a rubber band under tension, f, with length per. Find a general expression for the rate of change of cv with volume at constant t. The rubber band has lower entropy, is more orderd when stretched. Without this property, the rubber band would have no reason to tend towards a tangled state, since the entropy would be about the same in both states. By the above equation, the shorter and more elastic rubber band would actually have a lower elasticity coefficient in our example than the longer, but less elastic band. Equation of state of a rubber band physics stack exchange.
If a rubber band stretched 3 cm when a 100g mass was attached to it, then how much would it stretch if two similar rubber bands were attached to the same masseven if put together in parallel or alternatively if tied together in series. The crosslinking property of polymers is vital to the bands elasticity. And, in fact, if we apply a gas flame to a rubber band holding a weight, we will see that the band contracts abruptly fig. Introduction we are all familiar with the very useful properties of such objects as rubber bands, solid rubber balls. Rubber band recoil proceedings of the royal society a. A theoretical equation of state for a rubber band approximated by some. These postulates are the starting point of reasoning in thermodynamics and you can derive everything else if you start from here. Numerous laboratories and classroom demonstrations address how the tension of rubber bands increases with temperature, 16 or to measure mechanical properties of rubber bands at room temperature. Thus the entropy of the rubber band increases when it goes from the stretched state to the natural state. In this equation, the proportionality between shear stress and shear strain is known as the shear modulus of a material. The entropy change for the stretching of rubber is calculated by statistical methods, neglecting intermolecular attractions and deformation of bonds and bond angles. Equation of state not linear in energy or system size physics stack.
The third variable v or t, or p follows from the equation of state. Abstract a thermodynamic study of an isotropic rubber band under uniaxial stress is presented on the basis of its equation of state. Cheme 240, homework 2 solutions university of california. I have done part a, but i am having difficulties in part b when i proceed according to the book. At the moment all i have is the obvious f kt where k is the constant of proportionality. Could i approximate it as a spring, fkx, elastic energy 12kx 2. Cheme 240, homework 2 university of california, berkeley. Lets physics the bejesus out of rubber bands if you havent seen any of joergs videos from the slingshot channel, you are really missing out. Show that a corresponding equation exists for an ideal rubber band. Lets physics the bejesus out of rubber bands wired. Under tension, the molecules in a rubber band line up and the arrangement becomes much more ordered, lowering the entropy. For powerlifting, a fast easy way to calculate the amount of pressure in lbs.
To determine how the entropy of a rubber band changes as the rubber band is stretched. Fourth problem set for physics 846 statistical physics i. As an ideal gas, rubber band also has a thermodynamic variables, such as equation of state, heat capacity. Also, show this equation of state satisfies the gibbsduhem equation. The equation of state of a rubber band for which the relevant state variables are l the length of the band, f the restoring force of the band and t the absolute temperature is given by. An elastomer has rather unusual physical properties. Oct 31, 2006 when the front reaches the clamped end, the whole rubber band is strainfree and translates at speed v. A resource for teachers a script for classroom demonstration illustrating dg dh tds. As the rubber is stretched they begin to untangle themselves as shown in figure 1b. The procedure shows students how classical thermodynamics formalism can help to obtain empirical equations of state by constraining and guiding in the construction of the physical models for the system under investigation. To measure partial derivatives experimentally and test the validity of the cyclic rule of partial differentiation. This material may consist of stepbystep explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting.
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