The fundamental thermodynamic relation for a rubber band is given by dU = TdS + τdL, where T is the absolute temperature, S is the entropy, τ is the tension in the rubber band, and L is the length of the rubber band. Which one of the following relations is CORRECT:
1
\(\left(\dfrac{\partial T}{\partial L}\right)_S = \left(\dfrac{\partial \tau}{\partial S}\right)_L\)
2
\(\tau = \left(\dfrac{\partial U}{\partial S}\right)_L\)
3
\(T=\left(\dfrac{\partial U}{\partial S}\right)_\tau\)
4
\(\left(\dfrac{\partial T}{\partial S}\right)_L = \left( \dfrac{\partial \tau}{\partial L}\right)_S\)