Why cumulative analysis can be more precise: in surface-area determination from sieve data, cumulative analysis avoids what simplifying assumption inherent to differential analysis?

Introduction / Context:
Calculating surface area from sieve analyses requires assigning representative sizes to fractions. Differential analysis treats each cut as uniform, which can introduce bias—especially when distributions within a cut are broad. Cumulative analysis mitigates this by integrating across cuts.

Given Data / Assumptions:

• Sieve test generates mass retained between consecutive apertures.
• Surface area depends strongly on fine sizes.
• Seeking more precise estimate without over-simplifying each fraction.

Concept / Approach:
Differential analysis approximates each fraction by a single representative size, effectively assuming equality within the band. Cumulative methods work with cumulative undersize or oversize distributions, reducing sensitivity to the internal spread within each fraction and thereby improving precision for area-related metrics.

Step-by-Step Solution:
Recognize the problematic assumption: uniform size within a fraction.Adopt cumulative curves: integrate contributions across particle sizes.Result: better capture of fines’ influence on total surface area.

Verification / Alternative check:
Comparisons with laser diffraction (which resolves sub-fraction distributions) typically show cumulative-based estimates align better than differential single-size approximations.

Why Other Options Are Wrong:
(a) describes the differential method’s assumption, not why cumulative is better.(b) screening “effectiveness” is unrelated to the analytical method chosen.(d) incorrect because (c) is correct.

Common Pitfalls:
Assigning the arithmetic mean of aperture sizes as the “representative” without considering distribution skewness leads to area underestimation.

Final Answer:
assumption that all particles in a single fraction are equal in size, is not needed.