We obtain an expression for the second derivative of the line in a PT diagram denoting a first-order phase transition for a pure hydrostatic system. Our result goes beyond the classical Clausius–Clapeyron equation, which provides only the first derivative of the pressure with respect to the temperature along the transition line. We present two pedagogical derivations suitable for an undergraduate thermodynamics class; the first one uses derivatives of the entropy while the second one uses derivatives of the enthalpy. The final expression for the second derivative involves only standard thermodynamic quantities such as the specific heats, the isothermal compressibilities, and the coefficients of thermal expansion of the two phases at the transition line. As an illustration, we compute the second derivatives of the freezing and vaporization lines of water at atmospheric pressure, and show that at this pressure the freezing line is concave down (negative second derivative) while the vaporization line is concave up (positive second derivative).

Not even the use of the most sensitive of modern films has brought about a reduction of the dose administered to patients in Spain. Only digital systems, it seems, will bring about reduction in this dose.

The introduction of legislation has resulted in a gradual improvement in dental radiology practices.

There has been a gradual improvement in dental radiology practices; however, the incorporation of digital systems has not resulted in all the benefits hoped for, and mistakes are frequent. Besides the physical parameters that have been established, anatomical and clinical image quality criteria should be established to convince dentists of the real benefits of incorporating quality guarantee procedures in their practices.

No abstract