Rubber bands! Consider the process where a stretched rubber band is released and converted to a

relaxed rubber band. Let's call the displacement of the rubber band $x,$ where $x$ is zero for the relaxed

state and positive for the stretched state. For sign conventions here, both the restoring force $f$ and

the displacement $x$ are defined as positive. $($From Prof. Munira Khalil CHEM $452$ materials.$)$

ii$.$ Using the definition $G=H-TS,$ express the force in terms of enthalpic and entropic contributions. You should get the following.$f=(\frac{\text{d}\text{e}\text{l}\text{H}}{\text{d}\text{e}\text{l}\text{x}}{)}_{T,P}-T(\frac{\text{d}\text{e}\text{l}\text{S}}{\text{d}\text{e}\text{l}\text{x}}{)}_{T,P}$

iii. Using a Maxwell relation, show the following relationship. $(\frac{\text{d}\text{e}\text{l}\text{S}}{\text{d}\text{e}\text{l}\text{x}}{)}_{T,P}=-(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{T}}{)}_{x,P}$

iv$.$ Use the data given in the table to calculate the following in correct units. $(\frac{\text{d}\text{e}\text{l}\text{S}}{\text{d}\text{e}\text{l}\text{x}}{)}_{T,P}$