1. An apparatus for extracorporeal treatment of blood comprising: a preparation line having one end connected to an inlet of a secondary chamber of a treatment unit and configured to convey fresh treatment liquid to the secondary chamber, the fresh treatment liquid presenting a characteristic (Cd in ) which is one selected from the group of: conductivity in the fresh treatment liquid, and concentration of at least one substance in the fresh treatment liquid; a spent dialysate line having one end connected to an outlet of said secondary chamber and configured to remove spent liquid from the secondary chamber, the spent liquid presenting a characteristic (Cd out ) which is one selected from the group of: conductivity in the spent liquid, and concentration of at least one substance in the spent liquid; and a control unit configured for commanding execution of a task for determination of a parameter indicative of the effectiveness of the extracorporeal blood treatment, said task comprising the following steps: receiving at least one prescription baseline (Cd set ) for the characteristic (Cd in ) in the fresh treatment liquid; causing fresh treatment liquid to flow in the preparation line to the secondary chamber with the characteristic being at said prescription baseline (Cd set ); causing spent liquid to flow out of the secondary chamber into the spent dialysate line; receiving at least one parametric mathematical model which puts into relation the characteristic (Cd in ) in the fresh treatment liquid with the characteristic (Cd out ) in the spent liquid, said parametric mathematical model presenting a prefixed number of free parameters; causing an upstream variation of the value of the characteristic (Cd in ) in the fresh treatment liquid with respect to said prescription baseline (Cd set ) thereby causing a corresponding and timely delayed downstream variation of the same characteristic (Cd out ) in the spent liquid flowing in the spent dialysate line; measuring a plurality of values taken by a reference portion of said downstream variation of the characteristic (Cd out ) in the spent liquid, said reference portion having duration shorter than the entire duration of the downstream variation; estimating said free parameters of the at least one parametric mathematical model by means of said reference portion measured values and identifying one single characteristic mathematical model which puts into relation the characteristic (Cd in ) in the fresh treatment liquid with the characteristic (Cd out ) in the spent liquid; and computing at least one value of a parameter indicative of the effectiveness of the extracorporeal blood treatment by using said characteristic mathematical model and one or more values taken by the characteristic (Cd in ) in the fresh treatment liquid.