A rubber band is composed of a "bundle" of polymers, which form very long linear molecules or chains of simpler molecular units called monomers. These molecules can coil or unfold depending on the temperature and applied tension, giving these systems their elastic properties. The simplest equations of state for a system like this are given by:
[ U = cL_0T quad (5) ]
[ au = bT frac{L - L_0}{L_1 - L_0} quad (6) ]
Where ( c ) and ( b ) are constants, ( au ) represents the tension applied to the band at its elastic limit, ( L_0 ) is the length of the unstretched band, and ( L_1 ) represents the limit length of the band to which it can stretch without losing its elastic properties.
From equations (5) and (6), obtain the fundamental relationship of the rubber band.