The heat capacity of the binary liquid mixture triethylamine-water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent alpha was determined to be 0.107+/-0.006, consistent with theoretical predictions. When alpha was fixed at 0.11 to determine various amplitudes consistently, our values of A(+) and A(-) agreed with a previous heat capacity measurement, but the value of A(+) was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A(+)/A(-)=0.56+/-0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid-vapor systems, The correction to scaling amplitude ratio D+/D-=0.5+/-0.1 was half of that predicted. As a result of several more precise theoretical calculations and experimental determinations, the two-scale-factor universality ratio X, which we found to be 0.019+/-0.003, now is consistent among experiments and theories. A new "universal" amplitude ratio R(BCr)(+/-) involving the amplitudes for the specific heat was tested. Our determination of R(BCr)(+)=-0.5+/-0.1 and R(BCr)(-)=-1.1+/-0.1 is smaller in magnitude than predicted and is the first such determination in a binary fluid mixture.