FE Other Disciplines Safety, Health, and Environment Practice Problems

The current FE Other Disciplines specification assigns 6-9 of the 110 exam questions to Safety, Health, and Environment. Form A contains 6 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

Personal sampling over a single 8-hour shift records a solvent vapor concentration of 180 ppm for 2.0 h, 95 ppm for 3.5 h, and 40 ppm for the remaining 2.5 h. The 8-hour time-weighted average exposure is most nearly:

(A)87 ppm
(B)99 ppm
(C)105 ppm
(D)126 ppm

Show worked solution

Answer: (B)

Weighted by duration over the full 8 h shift, the three intervals average about 99 ppm.

A time-weighted average charges each measured concentration for the fraction of the shift over which it persisted, so the three intervals enter as a duration-weighted sum, not as a plain average of concentrations.

TWA = \frac{\sum C _{i} T _{i}}{\sum T _{i}}

Every interval belongs in the numerator, including the low-concentration period, since the denominator is the full 8 h shift.

TWA = \frac{( 2.0 ) ( 180 ) + ( 3.5 ) ( 95 ) + ( 2.5 ) ( 40 )}{8.0} = \frac{792.5}{8.0}

TWA = 99.1 ppm

FE Reference Handbook — Safety, Health, and Environment: Industrial Hygiene, Time-Weighted Average Exposure

Why the other choices appear

(A)Drops the 2.5 h at 40 ppm from the numerator while retaining 8.0 h in the denominator: 692.5/8.0 = 86.6 ppm.
(C)Averages the three concentrations without duration weighting: (180+95+40)/3 = 105 ppm.
(D)Treats the 40 ppm period as non-exposure and divides the remaining 692.5 ppm-h by only 5.5 h of exposure: 126 ppm.