Maxwell Relations: Thermodynamics of a Rubber Band Physical Sciences Department, College of Science, Pamantasan ng Lungsod ng Maynila General Luna St., Intramuros, Manila Abstract— This experiment aimed to apply the Maxwell Relations to study the thermodynamics of a rubber band. From the calculated values and thermodynamic parameters, it was found out that temperature strongly influences the mechanical properties of rubber bands. Keywords— Thermodynamics, Maxwell Relations, Entropy, Enthalpy, Work, Change I. INTRODUCTION Rubber belongs to a class of macromolecular substances, called elastic polymers that have the rather unusual characteristic of being able to recover their original shape following a very large deformation. In order for a material to exhibit rubberlike elasticity, three conditions must be met: (1) the material must consist of polymeric chains, (2) the chains must be joined into a network structure, (3) the chains must have a high degree of flexibility. In natural rubber and in many types of synthetic rubber the network structure is present because the rubber is vulcanized, meaning that the individual linear strands of the polymer are cross-linked via S-S bonds to form a three-dimensional structure: A study of the properties of rubber provides an excellent illustration of several of the concepts of thermodynamics, including the mathematics of partial derivatives, the Maxwell relations, and the molecular interpretation of entropy. We will determine how the entropy of a rubber band changes as it is stretched. (Dowling) Thermodynamics provides us with relationships among different properties of a material. For rubber bands we are most interested in the relationships among the tension or restoring force, f, the length, L, the entropy, S, and the temperature, T. One interesting question raised by the above picture of the molecular structure of rubber has to do with the entropy of the material. The thermodynamic identity of a rubber band is  =  +  where T is the temperature, τ is the tension, U is the internal energy of the rubber band, S is its entropy, and L is its length. This relation follows naturally from the First Law of Thermodynamics combined with the definition of work as the dot product of force and displacement. We could use the differential relation given in Eq. (1), but since we are working at constant T, the Helmholtz free energy F provides a more useful starting point  =  −  The corresponding Maxwell relation −( ∂ S ∂ L )  =( ∂ τ ∂ T )  Tells us that we can determine how entropy changes with length at fixed temperature by measuring how the tension changes with temperature at fixed length. At the same time, measurement of the tension reveals how the free energy varies with isothermal changes in length =( ∂ F ∂ L )  Thus, measurements of τ and (∂τ / ∂T)  as a function of length, allow us to find Q, W, ∆F, ∆S, and ultimately ∆U by integration. (Brown) II. METHODOLOGY A. Effect of Initial Length of the Stretched Rubber on its Tension Figure 1 shows a photo and a schematic of the experimental setup. A rubber band was stretched from a hook in a stopper at the bottom of a glass tube to a chain connected to a force meter at the top of the tube. This setup allows the rubber band to be completely submerged when the tube is filled with water. It also allows students to quickly alter the length of the rubber band by changing which link of the chain is hooked onto the force meter. During the experiment, the temperature was adjusted by pouring water into the tube. They then measured tension as a function of rubber band length for different water temperatures. The water was emptied out of the top of the tube; so that water was efficiently poured and (1) (2) (3) (4)