Divemaster theory rewards one habit: rebuild every fact as a two-step problem you can solve on paper. Gas laws, absolute pressure, and residual nitrogen are often studied as separate facts, but supervision work demands chaining depth, pressure, absorbed gas, and planning limits into one coherent decision. Work the scenarios below with a pencil, score yourself against the rubric, and treat every simplified number here as a teaching device. Always plan real dives with the official tables your NAUI course uses, and confirm course and exam administrative details with NAUI directly at naui.org.
Gauge Versus Absolute Pressure: The First Link in Every Chain
Every depth-based calculation starts with absolute pressure, not gauge pressure. Train the habit of adding the surface atmosphere as a separate written step before applying any gas law, because one skipped atmosphere corrupts every number that follows.
Water adds one atmosphere for every ten metres, so a dive to 20 metres means 2 ata of water plus 1 ata of air, totalling 3 ata absolute. Write that conversion on paper as its own line even when it feels obvious. In a chained problem the absolute-pressure figure feeds consumption rates, partial pressures, and volume changes, so an error here multiplies rather than stays contained. Make the formula explicit: absolute pressure equals one plus depth divided by ten, in metric.
Self-check: convert 0, 10, 20, 30, and 40 metres and confirm you get 1, 2, 3, 4, and 5 ata. Notice that doubling depth from 10 to 20 metres does not double absolute pressure, because the surface atmosphere stays fixed at one atmosphere. If any conversion takes longer than a breath, drill it until it is automatic, since hesitation on this first step slows every chained problem built on top of it.
Boyle's Law in Two-Step Problems: Depth Changes and Gas Supply
Boyle's law relates absolute pressure and gas volume inversely. Divemaster-level problems rarely stop at the formula; they chain a volume or consumption change into reserve planning, so solve and label both steps.
Worked scenario: a diver's surface consumption rate is 2 bar per minute. At 30 metres the absolute pressure is 4 ata, so consumption becomes 8 bar per minute, and 20 minutes of bottom time uses 160 bar. The mistake: a buddy plans the same dive with 6 bar per minute, treating 30 metres as 3 ata. The plan predicts 120 bar used, leaving 40 bar less reserve than reality demands. Why it matters: reserve math is a chain, and its first link is absolute pressure.
The same law appears as a volume question. A lift bag holding 30 litres at the surface holds 10 litres at 20 metres, because 3 ata compresses the gas to a third of its surface volume. A plausible mistake is inverting the ratio, multiplying by 3 instead of dividing, or using gauge pressure and dividing by 2. Anchor the direction: pressure up, volume down. Write the ratio with units attached and the direction becomes hard to flip.
Dalton's Law and Partial Pressures: Finding a Working Depth Limit
Dalton's law states that each gas in a mixture contributes its fraction of the total absolute pressure. That single sentence supports two chains: depth to partial pressure, and a partial-pressure limit back to a maximum depth.
Arithmetic example, not a limit recommendation: air at 40 metres sits at 5 ata absolute, so the oxygen partial pressure is 0.21 times 5, or 1.05 ata. For a 32 percent mix at 30 metres, it is 0.32 times 4, or 1.28 ata. The plausible mistake is multiplying the fraction by depth in metres directly, which produces a meaningless number because depth is not pressure. Convert to absolute pressure first, every time.
The reverse chain asks: given a partial-pressure ceiling from your course materials, what depth is the limit? Divide the ceiling by the gas fraction to get maximum absolute pressure, subtract one atmosphere, and multiply by ten for metres. Practise both directions until the division feels as natural as the multiplication, because leadership-level problems ask you to work backwards from a limit to a depth, not only forwards.
Repetitive Diving on Paper: Residual Nitrogen Time Done in Order
Repetitive-dive planning chains three lookups in strict order: pressure group after dive one, residual nitrogen time after the surface interval, adjusted bottom time for dive two. The order is the skill.
Worked scenario: dive one to 18 metres for 30 minutes, a one-hour surface interval, then dive two planned to 12 metres for 25 minutes. The mistake: checking dive two against its limit using 25 minutes alone, ignoring nitrogen still dissolved from dive one. The better decision: read the pressure group at the end of dive one, convert it through the interval table into residual nitrogen time, add that to 25 minutes, and compare the total with the 12-metre limit. That added time can push a plan that looked comfortable over the line on paper.
Why it matters: this is the same chaining habit as the gas problems, with a result from one lookup becoming the input to the next. Letter designations, interval ranges, and limit values differ between table families, so drill with the exact tables your NAUI course uses; the transferable part is the sequence, not the numbers. A simplified teaching table is fine for learning the order, but never plan a real dive with one.
Which Gas Law Is the Question Actually Testing?
Boyle, Dalton, and Henry each describe a different link: pressure versus volume, fraction times absolute pressure, and dissolved gas driven by the surrounding partial pressure. Naming the link first tells you the formula and the direction.
Identification drill: the words volume, space, or consumption point to Boyle; fraction, percent, or partial pressure point to Dalton; tissue, dissolved, or surface interval point to Henry. Underline the keyword before touching a formula. In mixed problems, such as computing consumption at depth during a repetitive dive, both Boyle and table logic appear in sequence, and the keyword map keeps the steps from blurring together.
Henry's law is the conceptual bridge between physics and the tables: it explains why nitrogen keeps dissolving at depth and why a surface interval cannot erase the load instantly. Treat it as the reason residual nitrogen time exists rather than a calculation tool, and be ready to state the relationship in one sentence. Understanding that bridge turns the repetitive-dive procedure from memorised steps into a logical chain.
| Concept | Relationship it describes | Typical two-step use | Direction of work |
|---|---|---|---|
| Boyle's law | Absolute pressure versus gas volume | Depth change, then volume or consumption change | Start from the surface value, divide by the new ata |
| Dalton's law | Gas fraction times absolute pressure equals partial pressure | Depth to partial pressure, or a limit back to maximum depth | Both directions |
| Henry's law | Dissolved gas follows the surrounding partial pressure | Explains on-gassing at depth and off-gassing during intervals | Conceptual; drives the tables |
| Charles's law | Temperature effects on gas pressure and volume | Fill and storage temperature caveats | Usually a qualitative note |
Role Boundaries: Supervision Decisions That Chain Back to Theory
Leadership scenarios test whether planning theory and responsibility connect: assisting versus conducting training, and enforcing limits set by the tables and the dive plan rather than by improvisation.
A useful paper distinction: divemasters supervise certified divers and assist instructors with logistics, briefings, and in-water control, while evaluating student skill performance and teaching new skills belongs to the instructor role. When a scenario mixes both, name who does what before answering anything else. That single naming step prevents answers that quietly assign instructional decisions to a supervising diver who is not conducting the class.
Scenario to trace: during a supervised dive, a certified diver wants to extend beyond the planned profile. The chain: re-check no-decompression status with the tables, re-estimate gas reserves using absolute pressure, then respond within the supervision plan rather than improvising. The physics and the responsibility questions are the same skill viewed from two sides, which is why role scenarios repay being solved with the tables open. For the precise scope of the NAUI divemaster role, rely on your course materials and naui.org.
A Drill Sequence and Self-Check Rubric for Chained Problems
Build fluency with a fixed sequence: single conversions, two-step chains, full repetitive plans, then role scenarios. Score each attempt against a rubric so improvement is observable rather than felt.
Exercise: write five problems of your own, one Boyle volume change, one consumption chain, one partial-pressure question in each direction, one two-dive plan, and one role scenario, then trade sets with a study partner and solve theirs the next day. Expected observation: within a few sessions you start writing the absolute-pressure line automatically before finishing the problem statement, and your errors shift from wrong formulas to misplaced units, which is the sign the chain has formed.
Adaptable sequence: spend the first stretch on conversions until instant, the next on two-step chains, then on repetitive plans with your course tables, and finish with mixed timed sets. Readiness checks: you convert any standard depth to absolute pressure without hesitation, you state each law in one sentence, you complete a two-dive plan cold without notes, and your rubric scores hold at full marks across a whole mixed set.
- Absolute-pressure line written before any other work (1 point)
- Law identified by name in one sentence (1 point)
- Units carried through every line and attached to the final answer (1 point)
- Table order correct: dive, group, interval, residual time, adjusted time (1 point)
- Final answer sanity-checked against a rough estimate (1 point)
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.