We report the first excess volumes measured at constant temperature and pressure for a contrasted binary mixture, methane + n-tetracosane, using high-pressure mercury-free equipment made of two piston cells equipped with sapphire windows. These measurements have been performed at 374.05 +/- 0.5 K, between 20 and 110 MPa, at four concentrations. Excess volumes at constant temperature and pressure between methane and n-tetracosane were found to be negative (-2 to -18% of the mixture volume). Saturation pressures were also obtained for the same system without sampling, using the phase rule together with phase volume measurements. Consistent results have been obtained in a large concentration range, with saturation pressures up to 85 MPa. In a second step, we analyse these results with the Peng-Robinson and Soave-Redlich-Kwong equations of state. A quadratic mixing rule on the covolume is required to get a satisfactory description of the excess volumes, without worsening the prediction of the saturation pressures. The binary interaction parameter in this mixing rule has been found to be virtually the same with both equations of state. Provided volumetric data and vapour-liquid data are used together, the interaction parameters on the covolume and on the attraction term are not correlated, These conclusions should extend to most equations of state with the Van der Waals repulsion term.