Isochoric heat capacities (c(v)) of methanol, ethanol, and 1-propanol and binary mixtures of water with each of these alkanols were measured in the temperature range from 280 to 420 K and at pressures up to 30 MPa. The measurements were carried out on liquid-phase samples with a twin-cell type adiabatic calorimeter. Liquid densities were also reported in this work on the basis of the mass of the sample and the volume of the calorimetric cell. The experimental expanded uncertainty (with a coverage factor k = 2) of temperature measurements is +/-13 mK, and that of pressure measurements is +/-8 kPa. The expanded relative uncertainty for isochoric heat capacity is estimated to be +/-2.2% for the liquid-phase measurements, and for density it is +/-0.16%. The behavior of c(v) is anomolous, indicating that alkanol + water mixtures are strongly associated due to the influence of hydrogen bonds.