Using heat capacity and compressibility to choose among two-state models of liquid water

We extend to heat capacity Cp the model of Vedamuthu, Singh, and Robinson (J. Phys. Chem. 1994, 98, 2222). This model and that of Bartell (J. Phys. Chem. B 1997, 101, 7573) fit successfully, even in the supercooled region, the temperature dependence of Cp, volume, and isothermal compressibility kappa(T). The Robinson model is superior for kappa(T). Tanaka's model (J. Chem. Phys. 2000, 112, 799) fails for C(p) even after correction of a derivational error. All three models assume that the liquid consists of low-density component 1 and high-density component 2. We conclude that Robinson's tactics, ignoring the intercomponent equilibrium constant and determining compositions solely from volumes, yield the most reliable compositions and individual-component properties. Our fits of the Robinson model to C(p) yield at 0 degrees C H(2) - H(1) of (135 +/- 35) J/g, H(1) - H(ice) of 0.8DeltaH(fus), and C(2) - C(1) of (0.1 +/- 0.7) J/K.g. The enthalpy difference between the components is largely responsible for the rapid change of C(p) at the lowest supercooled temperatures. We propose an adjustment to Speedy and Angell's (J. Chem. Phys. 1976, 65, 851) experimental values of kappa(T) for supercooled water.