Reconstructing adiabats

We give an explicit method for calculating the equations of state of a thermodynamical substance from the following information: in the calibrated case, the system of isotherms and a single adiabat, in the uncalibrated one, the same but with two adiabats. For simple examples the entropy function can be computed explicitly from this material but it involves steps (solution of non-linear equations and an integration) which will usually require numerical methods for their implementation.