The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is the tension in the rubber band, and $\text{L}$ is the length of the rubber band.
Which one of the following relations is $\text{CORRECT}$:
- $\tau =\left ( \frac{\partial U}{\partial S} \right )_{L}$
- $\left ( \frac{\partial T}{\partial L} \right )_{S}=\left ( \frac{\partial \tau }{\partial S} \right )_{L}$
- $\left ( \frac{\partial T}{\partial s} \right )_{L}=\left ( \frac{\partial \tau }{\partial L} \right )_{S}$
- $T=\left ( \frac{\partial U}{\partial S} \right )_{\tau}$