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## Homework Statement

The equation of state for a rubber band with temperature T is [itex]\mathcal{F}=aT\left[\frac{L}{L_0}-\left(\frac{L_0}{L}\right)^2\right][/itex]

Where [itex]\mathcal{F}[/itex] is the tension, L is the stretched length and L_0 is the unstretched length

a) Write the Central Equation for the rubber band

b) Derive the energy equation for the rubber band [itex]\left(\frac{\partial U}{\partial L}\right)_T[/itex]

c) Show that U is a function of T only

## Homework Equations

[itex] dU=dQ+dW[/itex]

[itex] dU=\left(\frac{\partial U}{\partial T}\right)_LdT +\left(\frac{\partial U}{\partial L}\right)_TdL [/itex]

## The Attempt at a Solution

a) For the central equation some variant of [itex] dU=TdS+\mathcal{F}dL [/itex] I pressume?

b) Comparing the two relevant equations [itex]\left(\frac{\partial U}{\partial L}\right)_T=\mathcal{F} [/itex] ?

c)No real idea how to show this