Using the Carnot cycle to determine changes of the phase transition temperature

The Clausius-Clapeyron relation and its analogs in other first-order phase transitions, such as type-I superconductors, are derived using very elementary methods, without appealing to the more advanced concepts of entropy or Gibbs free energy. reasoning is based on Kelvin's formulation second law thermodynamics, should be accessible high school students. After recalling some basic facts about Carnot cycle, we present two different systems that undergo discontinuous transitions (ice/water normal/superconductor), construct engines exploit properties these produce work. In each case, show if transition temperature $T_tr$ were independent parameters, pressure magnetic field, it would possible violate principle, i.e., a perpetuum mobile kind. Since proposed cyclic processes can realized reversibly limit infinitesimal changes temperature, their efficiencies must equal an ordinary cycle. We immediately obtain equation form $dT /dX = f(T, X)$, which governs how with parameter $X$.