  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.

Soft Condensed Matter;Statistical Mechanics