The thermodynamics of ideal-rubber elasticity

The thermod5mamic properties of an ideal rubber can be expressed in terms of the Helmholtz energy, A T,a,m). The exact differential of the Helmholtz energy for a closed system is then  

The force of extension is a thermodynamic function with exact differential  

For an ideal gas, the internal energy, U, is independent of volume. For an ideal rubber, the internal energy is independent of the elongation dll / = 0. The final necessary identity is obtained from Equation 

The force of extension is linearly proportional to temperature, with a slope that depends explicitly on the elongation. The actual value of the slope 

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