Question

Consider the following observation: A rubber band is stretched under tension (at least 0.5 cm wide) and then touched to the Upper lip and found to be warm. Then the rubber band is relaxed and stretched a second time and held under tension for several seconds. The rubber band is relaxed and touched to the upper lip and found to have a cooling effect. Analyze these two observation using delta G = Delta H - T delta S for the enthalpy, entropy and free energy changes.

Answer 1

Hi,

Entropy change (stretching and contracting at constant T):

Heat is produced in the rubber band as it is stretched. If we stretch slowly in air at room temperaure, we have a reversible, isothermal process with q< 0 (heat is lost to the surroundings). Then ?Sstretch = qrev/T <0 in the stretching process. Since entropy is a state function, ?Scontract = qrev/T >0 for the reverse process of slowly allowing the rubber band to contract. The rubber band has lower entropy, (is more orderd) when stretched. Under tension, the molecules in a rubber band line up and the arrangement becomes much more ordered, lowering the entropy. The criterion for spontaneity for an isolated system is ?Ssys >0. Suppose the system is the rubber band and the air in a large room. Therefore, if a constraint keeping the rubber band stretched is removed, it will spontaneously contract, with ?Ssys, contract   >0

Enhalpy change (with heat source):

There is another "PV"-like term in the enthalpy, namely    "-FD", where Fis the force and Dis the distance . The "-" sign is there because the force is taken to be positive (as is the pressure) but the force of the rubber band is in the opposite direction of the force on a piston, pulling in instead of pushing out. Thus

H=E + PV - FD