A high pressure calorimetric experiment to validate the liquid-liquid critical point hypothesis in water

An experimental proposal to test the existence of a liquid-liquid critical point in water, based on high pressure calorimetric measurements, is presented on this paper. Considering the existence of an intramolecular correlation in the water molecule we show how the response of the specific heat at high pressure is different depending on the existence, or not, of the second critical point. If the liquid-liquid critical point hypothesis is true there must be a maximum in the specific heat at some temperature $T>T_{H}$ for any pressure $P>P_{c}$ (being $T_{H}$ the homogeneous nucleation temperature and $P_{c}$ the pressure of the second critical point). This maximum does not appear for the singularity free scenario.