Safety, Health, and Environment

A. Industrial hygiene

Industrial Hygiene and Exposure Limits

PEL, TLV, and IDLH; dose-response and LD50/LC50 toxicology; the additive rule for chemical mixtures; and radiation half-life — the quantitative core of FE-OTH safety.

Industrial hygiene is where the FE Other Disciplines exam turns vague 'safety' into something you can compute. The Safety chapter of the FE Reference Handbook gives you exposure limits, dose-response curves, lethal-dose data, and a mixture rule — and the exam rewards anyone who knows the difference between a hazard (the inherent capacity to harm) and a risk (hazard combined with the probability or exposure that someone actually meets it). The handbook states this directly as

\text{Risk}=\text{Hazard}\times\text{Exposure}

, and almost every numeric question in this area is really asking you to quantify the exposure side of that product. Get the definitions and the additive rule straight and you bank these points fast.

PEL, TLV, and IDLH — three limits, three sources

Three exposure limits appear over and over. The Permissible Exposure Limit (PEL) is OSHA's legally enforceable ceiling, usually expressed as an 8-hour time-weighted average (TWA). The Threshold Limit Value (TLV) is the ACGIH's recommended limit — the handbook defines TLV as the highest dose (in ppm by volume in the atmosphere) the body can detoxify with no detectable effect. IDLH (Immediately Dangerous to Life or Health) is NIOSH's concentration above which a 30-minute exposure could cause death or irreversible harm or prevent escape. PELs and TLVs govern routine 8-hour exposure; IDLH governs escape and respirator selection. They come from different bodies and are not interchangeable, though the SDS lists both PEL and TLV in Section 8.

\text{Risk} = \text{Hazard} \times \text{Exposure}

Time-weighted average exposure

A worker rarely sits in one constant concentration. The 8-hour TWA averages each measured concentration over the fraction of the shift it lasted, then compares the result to the PEL. If the workday is shorter or longer than 8 hours, you still normalize to an 8-hour basis. The exam loves a problem where two of three intervals are below the limit but the weighted average creeps over it — read for the duration of each interval, not just the peak.

\text{TWA} = \dfrac{\sum_i C_i\,t_i}{8\ \text{h}}

Dose-response, LD50, and LC50

Toxicology is built on the dose-response curve, which the handbook plots as toxic response (percent of a test population showing an effect or dying) against the logarithm of dose in

\text{mg/(kg}\cdot\text{day)}

. The curve's anchor point is the

LD_{50}

— the median lethal single dose expected to kill 50% of a test group, normalized per kilogram of body weight, usually by oral or skin exposure. Its inhalation cousin is the

LC_{50}

, the median lethal airborne concentration over a 1- or 4-hour exposure. A smaller

LD_{50}

means a more toxic chemical: botulinum toxin sits near

0.00001\ \text{mg/kg}

while table salt is around

4{,}000\ \text{mg/kg}

. To turn an

LD_{50}

into an absolute lethal dose, multiply by body weight.

D_{\text{lethal}} = LD_{50}\times \text{(body weight)}

Carcinogens versus noncarcinogens

The handbook treats these two classes with different math, and the exam expects you to know why. Carcinogens are modeled with a no-threshold, linear-at-low-dose curve: any exposure carries some incremental risk, computed as

\text{Risk}=CDI\times CSF

(chronic daily intake times cancer slope factor). EPA considers an acceptable added cancer risk to be

10^{-4}

to

10^{-6}

. Noncarcinogens, by contrast, have a threshold — the NOAEL (No Observable Adverse Effect Level) — below which no harm occurs. Their risk is captured by the hazard index

HI = CDI/RfD

, where

RfD

is the reference dose; an

HI>1.0

flags a possible adverse effect.

\text{Risk}_{\text{cancer}} = CDI\times CSF, \qquad HI = \dfrac{CDI}{RfD}

Mixtures of exposures — the additive rule

When a worker breathes several substances with similar (e.g., additive) toxic action, OSHA treats the exposure as additive: you do NOT compare each chemical to its own limit in isolation. Instead, sum the ratio of each measured concentration to its own limit. If the sum exceeds 1, the combined exposure is over the limit even when every individual chemical is under its own PEL. This is the single most-tested calculation in this area. The handbook gives the analogous Le Chatelier additive form for flammability; the toxicity version uses the same structure with PEL or TLV in the denominator.

E_{\text{mix}} = \sum_i \dfrac{C_i}{L_i} \;\le\; 1 \quad(\text{acceptable})

Radiation exposure and half-life

Ionizing-radiation problems on the FE reduce to exponential decay. A radioactive source's activity (and the dose rate it produces) falls by half every half-life

T_{1/2}

. You can work it with the discrete halving form or the continuous form using the decay constant

\lambda=\ln 2/T_{1/2}

. Shielding and distance also matter — dose rate from a point source falls off as inverse-square — but the half-life calculation is the one the exam asks numerically. Remember radiation dose is cumulative: ALARA (As Low As Reasonably Achievable) governs occupational practice.

A(t) = A_0\left(\tfrac{1}{2}\right)^{t/T_{1/2}} = A_0\,e^{-\lambda t}, \qquad \lambda = \dfrac{\ln 2}{T_{1/2}}

Biohazards and the hierarchy of evaluation

Biological agents — bacteria, viruses, molds, toxic yeasts, bloodborne pathogens — are hazards in exactly the handbook's sense: an inherent capacity to cause illness whose risk scales with exposure. The handbook notes that organic vapors and dusts from grain handling often carry toxic molds and yeasts and have low oxygen content, combining a biohazard with an asphyxiation hazard. Biosafety levels (BSL-1 through BSL-4) escalate containment with the agent's severity. The control logic mirrors chemical hygiene: recognize, evaluate, then control, always preferring engineering controls over PPE.

\text{Risk}_{\text{bio}} = \text{Pathogenicity}\times \text{Exposure}

Exam strategy

Memorize the three limit definitions and their issuing bodies (PEL = OSHA, legal; TLV = ACGIH,

\text{ppm}

, 'detoxify without effect'; IDLH = NIOSH, 30-min escape). For any multi-chemical problem, default to the additive rule

\sum C_i/L_i

and check against 1 — a sum of

1.3

means

30\%

over the limit. For LD50 problems, watch the per-kilogram units and multiply by body weight to get an absolute dose. For radiation, count half-lives:

t/T_{1/2}=3

means one-eighth remains. And never confuse hazard with risk — the exam writes distractors that swap them.

Key equations

Risk definition

\text{Risk} = \text{Hazard}\times\text{Exposure}

Handbook Safety chapter. Hazard is the inherent capacity to harm; exposure (or probability) is the chance of contact. Distinguishing the two is the most-tested conceptual point.

8-hour time-weighted average

\text{TWA} = \dfrac{C_1 t_1 + C_2 t_2 + \cdots}{8\ \text{h}}

$C_i$ = concentration during interval $i$ (ppm or mg/m³), $t_i$ = duration (h). Compare to the 8-h PEL.

Additive mixture rule

E_{\text{mix}} = \sum_i \dfrac{C_i}{L_i}

$C_i$ = measured concentration of component $i$ , $L_i$ = its PEL or TLV. $E_{\text{mix}}>1$ means the combined exposure exceeds the limit even if each component is individually compliant (additive-toxicity assumption).

Equivalent mixture limit

L_{\text{mix}} = \dfrac{\sum_i C_i}{\sum_i (C_i/L_i)}

The single limit a mixture of total concentration $\sum C_i$ would have under the additive rule; useful for reporting a combined PEL.

Lethal dose from LD50

D_{\text{lethal}} = LD_{50}\,(\text{mg/kg})\times m\,(\text{kg})

Converts a per-kilogram median lethal dose into an absolute dose (mg) for a body of mass $m$ . Smaller $LD_{50}$ = more toxic.

Carcinogen incremental risk

\text{Risk} = CDI\times CSF

$CDI$ = chronic daily intake [mg/(kg·day)], $CSF$ = cancer slope factor [(mg/(kg·day))⁻¹]. EPA acceptable range $10^{-4}$ to $10^{-6}$ . No-threshold, linear-at-low-dose model.

Noncarcinogen hazard index

HI = \dfrac{CDI}{RfD}

$RfD$ = reference dose, a chronic daily dose with no adverse effect. $HI>1.0$ indicates possible harm. Threshold model (NOAEL-based).

Reference dose from NOAEL

RfD = \dfrac{NOAEL}{UF}

$NOAEL$ = no-observable-adverse-effect level [mg/(kg·day)], $UF$ = total uncertainty factor for animal-to-human extrapolation.

Radioactive decay (halving form)

A(t) = A_0\left(\tfrac{1}{2}\right)^{t/T_{1/2}}

$A_0$ = initial activity or dose rate, $T_{1/2}$ = half-life. $t/T_{1/2}=n$ leaves a fraction $2^{-n}$ .

Decay constant

\lambda = \dfrac{\ln 2}{T_{1/2}} = \dfrac{0.693}{T_{1/2}}

Continuous-decay rate; $A(t)=A_0 e^{-\lambda t}$ . Units are inverse time, matching $t$ .

Inverse-square dose falloff

\dfrac{\dot D_2}{\dot D_1} = \left(\dfrac{r_1}{r_2}\right)^2

Point-source dose rate $\dot D$ falls with the square of distance $r$ ; doubling distance quarters the dose rate.

Worked examples

Additive exposure to a solvent mixture

Problem. A worker is exposed simultaneously to three solvents with additive toxicity. Measured 8-h TWA concentrations and their PELs are: solvent A, $60\ \text{ppm}$ (PEL $100\ \text{ppm}$ ); solvent B, $30\ \text{ppm}$ (PEL $50\ \text{ppm}$ ); solvent C, $25\ \text{ppm}$ (PEL $200\ \text{ppm}$ ). Is the combined exposure acceptable, and what is the equivalent mixture limit?

Solution. Apply the additive rule.

E_{\text{mix}}=\dfrac{60}{100}+\dfrac{30}{50}+\dfrac{25}{200}=0.600+0.600+0.125=1.325

. Since

1.325>1

, the combined exposure EXCEEDS the limit — by about

33\%

— even though every single solvent is below its own PEL. Equivalent mixture limit: total concentration

\sum C_i = 60+30+25 = 115\ \text{ppm}

, so

L_{\text{mix}}=\dfrac{115}{1.325}=86.8\ \text{ppm}

. The actual

115\ \text{ppm}

is above this, confirming non-compliance. Sanity check: each ratio is dimensionless and the largest contributors (A and B) each use

60\%

of their allowance, so summing must exceed 1. Answer: NOT acceptable;

E_{\text{mix}}=1.33

,

L_{\text{mix}}=86.8\ \text{ppm}

.

E_{\text{mix}} = \dfrac{60}{100}+\dfrac{30}{50}+\dfrac{25}{200} = 1.33 > 1

Radioactive source decay over a month

Problem. An iodine-131 source used in a tracer study has an initial activity of $400\ \text{MBq}$ . Its half-life is $8.02\ \text{days}$ . What activity remains after $30\ \text{days}$ , and what fraction of the original is that?

Solution. Number of half-lives:

n=t/T_{1/2}=30/8.02=3.74

.

A=A_0\left(\tfrac12\right)^{3.74}=400\times 2^{-3.74}=400\times 0.0748=29.9\ \text{MBq}

. Fraction remaining

=0.0748

, about

7.5\%

. Check with the continuous form:

\lambda=0.693/8.02=0.0864\ \text{day}^{-1}

, so

A=400\,e^{-0.0864\times30}=400\,e^{-2.593}=29.9\ \text{MBq}

— agrees. Sanity:

30\ \text{days}

is between 3 and 4 half-lives, so the answer must fall between

400/8=50

and

400/16=25\ \text{MBq}

, and

29.9

does. Answer:

29.9\ \text{MBq}

(

7.48\%

remaining).

A = 400\left(\tfrac{1}{2}\right)^{30/8.02} = 29.9\ \text{MBq}

Lethal dose from an LD50

Problem. Strychnine has an oral $LD_{50}$ of about $2\ \text{mg/kg}$ . Estimate the median lethal single dose for a $70\ \text{kg}$ adult, and compare its relative toxicity to ethanol ( $LD_{50}\approx 10{,}000\ \text{mg/kg}$ ).

Solution. Median lethal dose

= LD_{50}\times m = 2\ \text{mg/kg}\times 70\ \text{kg}=140\ \text{mg}

. Relative toxicity: a smaller

LD_{50}

means more toxic.

\dfrac{10{,}000}{2}=5000

, so strychnine is roughly

5000\times

more toxic than ethanol on a per-mass basis. Sanity check: units cancel to mg, and

140\ \text{mg}

is a tiny fraction of a gram — consistent with a potent poison. Answer:

\approx 140\ \text{mg}

; strychnine is about

5{,}000

times more toxic than ethanol.

D_{\text{lethal}} = 2\ \tfrac{\text{mg}}{\text{kg}}\times 70\ \text{kg} = 140\ \text{mg}

Common pitfalls

•Confusing hazard with risk. A capped, labeled drum of a deadly toxin is a high hazard but low risk; the exam swaps these terms in distractors. Risk = Hazard × Exposure.
•Comparing each chemical to its own limit and declaring 'all below PEL, so compliant.' For additive toxicity you MUST sum the ratios; a mixture sum of 1.3 is non-compliant even with every component under its individual PEL.
•Treating PEL, TLV, and IDLH as the same number. PEL is OSHA legal limit, TLV is ACGIH recommendation, IDLH is the NIOSH 30-minute escape concentration — different sources, different purposes.
•Forgetting that a SMALLER LD50 means MORE toxic. Candidates rank toxicity backwards because larger numbers feel 'bigger/worse.'
•Dropping the per-kilogram basis of LD50/LC50. Multiply by body weight to get an absolute dose; an LD50 alone is mg per kg, not mg.
•Using the threshold (NOAEL/RfD) model for a carcinogen. Carcinogens use the no-threshold linear model Risk = CDI × CSF; noncarcinogens use HI = CDI/RfD.
•Mixing up half-life and decay-constant forms, or using t/T₁/₂ in the exponential e⁻ˡᵗ. Use λ = ln2/T₁/₂ with the e form, or 2^−t/T directly — never both.

References

NCEES FE Reference Handbook — Safety
OSHA 29 CFR 1910.1000 — Air Contaminants (PELs and the mixture formula)
ACGIH — Threshold Limit Values (TLVs) and Biological Exposure Indices — Source of the recommended TLV limits referenced on the SDS.

B. Basic safety equipment

Basic Safety Equipment

Pressure-relief valves and rupture disks, emergency shutoffs, the fire triangle and extinguisher classes A–K, and the hierarchy of controls that ranks engineering above PPE.