Reversible adiabatic extension

This effect can be examined further by studying the reversible adiabatic extension of an elastomer. Although this experiment is more easily carried out imder conditions of constant pressure rather than constant volume, it is best to derive the relevant equations for constant voliune. For this reason, we will consider first the Helmholtz function for the system, i.e.. 

This shows that for a rapid reversible adiabatic extension when (dfldT)jp is positive, the temperature of the elastomer increases. The equation also tells us that the elastomer will contract, not expand, on heating. 

For statistically independent systems, the property S is extensive, it is invariant during all reversible adiabatic processes, and it increases during all irreversible adiabatic processes. 

By extension, the equality also applies to an adiabatic process that is conducted quasi-statically (i.e., to a reversible adiabatic process) because such process is infinitesimally away from equilibrium at all times. The two results in eqs. (d.i) and (d.2) can be combined into the single condition. 

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