CubicSpline

A cubic spline is a piecewise cubic polynomial function that is continuous in value, first derivative and second derivative. The cubic spline fit underlying this web application is implemented as described in Numerical Recipes. The columns T (temperature), c_sat (heat capacity), and d²c_sat/dT² (second derivative of c_sat with temperature) correspond to the tabulated values described by x_i, y_i, and y′′_i in section 3.3 of the reference.

Between the minimum value in the table and the lower bound of the fit, heat capacities are assumed to be cubic in temperature (c_sat = aT³).

Please note that the equations described above are expressed in terms of heat capacity and not in the necessary integral form.