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Within the framework of linear viscoelasticity this paper deals with the elaboration of a procedure for testing whether a given relaxation function is compatible with thermodynamics. In order to avoid any difficulty concerning the indeterminacy of the free energy functional, the second law is stated through the Clausius property for approximately-cyclic processes. Then, by considering sinusoidal strain tensor evolutions, it is shown that the statement of the second law is equivalent to a condition which, in essence, expresses the non-negativeness of the loss modulus. This means that, in order to test for compatibility with thermodynamics, it is enough to examine what happens in sinusoidal processes.

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