The Devil’s in the Delta


  • William L. Luyben Lehigh University


Students frequently confuse and incorrectly apply the several “deltas” that are used in chemical engineering. The deltas come in three different flavors: “out minus in”, “big minus little” and “now versus then.”

The first applies to a change in a stream property as the stream flows through a process. For example, the “ΔH” in an energy balance around a unit is the difference between the enthalpies of the streams leaving and the enthalpies of the streams entering.

The second delta is a driving force difference. In heat transfer, it is “hot temperature minus cold temperature.” In mass transfer, it is “large chemical potential minus small chemical potential.” The chemical potentials can be partial pressures, molar or mass concentrations, mole fractions or activities. The third delta indicates the change in a variable with time. For example, in a batch reactor the ΔCA means the change in concentration of component A over some time period between t = t1 and t = t2. The delta in time is Δt = t2 – t1.

Although the distinctions among these various deltas and their appropriate application should be obvious and fundamental, students frequently use the wrong delta. This note is intended to provide a friendly suggestion to professors that they remind their students of the need to be careful in applying deltas.

Author Biography

William L. Luyben, Lehigh University

William L. Luyben earned degrees in chemical engineering from Penn State (B.S., 1955) and Delaware (Ph.D., 1963). His industrial experience includes four years with Exxon, four years with DuPont, and four decades of consulting with chemical and petroleum companies. He has taught at Lehigh University since 1967 and has participated in the development of several innovative undergraduate courses. He has authored 10 textbooks.