Understanding Boyle`s Law in Physics IDC Dive Theory
Updated: Aug 20
Boyle`s law states, "If temperature remains constant, both volume and density of a gas are affected in proportion to the atmospheric pressure and inversely to each other."
Sir Roberto Boyle
Sir Roberto Boyle was a devout seventeenth-century Irish scientist, and his work was greatly influenced by Torricelli. Evangelista Torricelli was a student of Galileo (whose work Boyle also studied) and is best known for inventing the Barometer. While Torricelli determined the pressure of the atmosphere, Boyle aimed to discover what happened to volumes of air when the pressure changed. In 1662 he formulated Boyles Law.
But that is not his only contribution to diving. In 1670 he was the first person to document decompression sickness. He placed a viper (one of his many experiments with animals) in a vacuum jar and decreased the pressure by removing the air, obviously rather rapidly. "I once observed a viper furiously tortured in our exhausted receiver… that had manifestly a conspicuous bubble moving to and fro in the waterish humour of one of its eyes."(3) Upon increasing the pressure, the bubble disappeared, and the snake seemed happy as it could be in a small jar. He put forward no theory as he had no idea what had happened, and it would be a good two centuries until there were any further discoveries on decompression sickness. Still, it was from this experiment that the idea began to arise.
Boyle's law is perhaps the most valuable and important gas law in diving, so much so that it is the first question in the first knowledge review in your open water course (although you were probably not aware of that at the time).
This law affects you on every dive. It affects your BCD, mask, sinuses, ears, and lungs (think of these as little gas-filled containers). It affects your wetsuit, with its millions of tiny bubbles in its neoprene, and your dry suit, with its one big one. It can help you calculate how fast you will consume air in varying depths (and hence how much time you have) or how much usable gas volume you have in a cylinder at a given pressure. It explains why you should not hold your breath while scuba diving, why you need to add air to your BCD upon descent and release air from it upon ascent, and why you need to equalize your ears.
Understanding this law will also help you understand and avoid diving injuries such as ear squeezes, lung overexpansion injuries, and decompression sickness.
If a diver takes a lungful of air underwater, that air will expand in the lungs upon ascent. From 10msw to the surface, the pressure halves. If a dive is holding their breath, the air in their lungs will double in volume, causing a ruptured lung. This is Boyles Law in action and the reason why the golden rule of diving is: Never, never hold your breath!
Understanding Boyles`s Law
The law states the PRESSURE AND VOLUME OF A GAS ARE INVERSELY PROPORTIONAL TO EACH OTHER, and PRESSURE AND DENSITY ARE DIRECTLY PROPORTIONAL. We assume there is no temperature change as temperature changes the pressure/volume relationship, which we discuss in Charles`s law.
Put simply, the greater the pressure, the less the volume and the greater the density. As you increase the pressure, the volume will decrease proportionately to the amount of pressure, and the same number of molecules must occupy less space, making it denser. The density is, therefore, in direct proportion to the pressure.
This explains why we breathe more air at depth. The air volume and density inside a scuba tank will not change when we descend as the tank is inflexible, but the moment it leaves that tank, the air compresses and becomes denser, entering our flexible lungs. Physiologically, we need to breathe at the same pressure as that which surrounds us.
At 2 bar, we will breathe twice the number of molecules, and our air supply will only last half as long. At 3 bar, three times the molecules, one-third the time, and so on.
If we pump air down from the surface, the same rules will apply to fill a tank at depth in that the molecules of air compress in direct relation to the pressure.
Capillary gauges are tubes with a very small diameter, smaller than the surface tension of a drop of water which means you cannot pour water in or out of the tube without force. They are inexpensive, being a simple, clear piece of tubing that is sealed at one end and open at the other. This tube acts the same way an inverted container filled with air would. Ambient pressure pushes water into the tube, and at 10mt (2 bar), it is half the length of the tube (10 mt being double the pressure of the surface and half the volume), 20mt a third, and so on, in accordance with Boyles Law. They are hard to read deeper than 10 mt. Some divers prefer capillary gauges for altitude diving because it takes into account variations in atmospheric pressure.
Remember this for your exams.
B -Boyle`s Law
Boyle's law is very important to tech and cave divers who dive long and/or deep dives. They must use twin tanks, high capacity, and/or station extra tanks along their dive. Imagine; a tank that lasts 2 hours at the surface will only last around 10 minutes at 100 meters, so gas supply is vital. Even then, calculating air supply is only an estimate as it can be significantly influenced by factors such as cold, stress, exertion, and depth changes. Closed circuit scuba recirculates gas exhaled, and that is why there is a growing interest in this type of diving.
DO NOT CONFUSE BOYLE`S LAW WITH ARCHIMEDES` PRINCIPLE, which is about buoyancy, not pressure.
So, let's start with pressure. Before going any further, ensure you understand how to calculate pressure and the difference between salt water (10m/atm) and freshwater (10.3m/atm). We always use absolute pressure to calculate changes in volume and density, so don`t forget to add that 1atm at the surface. "If we desire to isolate a specific amount of pressure inside a process, regardless of what happens in the atmosphere, then we should use a system of absolute pressure." (5)
If unsure, refresh your knowledge with our blog on Understanding Pressure and test your knowledge with the inbuilt exam.
Scientists largely use the metric system (International Systems of Units or SI) as it uses only one unit for each type of measurement (meters, for example, covering kilo-meters, centimetres, etc). The metric system is used by 96% of the world’s population and by all countries for scientific use. As it is a simpler system, I will mostly use it here.
To the surface and back - single depth changes
How to examine the questions for Boyles Law
Find the unit of measurement.
Look at the answers. The unit of measurement will be stated there (always multiple choice in IE final exams)
What is the question asking for?
PSI or Bar
Find the number inside the question in that unit and write it down.
Think about the question.
More = ×
Less = ÷
The shallower you are, the slower you consume air (you have more time) ×
The deeper you go, the faster you consume air. (you have less time). ÷
More minutes ×, less minutes ÷
If you take a balloon up from depth, its size increases (more volume) ×
If you take a balloon down to depth, its size decreases (less volume) ÷
Bigger volume ×, less volume ÷
Air (PSI or Bar)
The shallower you are, the fewer molecules of air (less dense) you breathe with each breath, and the amount of air consumed in PSI/Bar will decrease ÷
The deeper you go, the more molecules of air (more dense) you breathe with each breath; the amount of air consumed in PSI/Bar will increase ×.
More PSI/Bar ×, Less PSI/Bar ÷
This is THE most critical step and where the most errors occur. Think it through first.
STOP, BREATHE, THINK, ACT
Find the surrounding pressure.
READ THE QUESTION and find the depth in meters (or feet)
Determine the pressure at that depth
think Saltwater (10mt/33ft) vs Freshwater (10.3mt/34ft).
Always +1 (you are determining absolute pressure)
Write that pressure down
Find the answer
Use the unit of measurement (step 1) and multiply or divide (step 2) the surrounding pressure (step 3) = The answer.
Air consumption in minutes
Q It takes 60 minutes to breathe through a tank of air at the surface. If all factors remain unchanged, how long will it take to breathe through the same tank at 20 mt?
A 180 minutes
B 60 minutes
C 30 minutes
D 20 minutes
STEP 1 Answer is asking for minutes. So, we look for minutes in the question and write it down 60 minutes.
STEP 2 Think! Do you use air faster at 20 meters than at the surface? We know that we use air much faster at depth; therefore, the answer will be LESS TIME than 60 minutes (÷)
STEP 3 The depth is 20 meters. 20÷10+1=3ATA
STEP 4 60 minutes ÷ 3 ata = 20 minutes (therefore, the answer is D)
Volume (flexible container)
Q If we have a balloon with a volume of 8 litres at the surface, what would its volume be at 30mt?
A 32 litres
B 24 litres
C 2 litres
D 2.6 litres
STEP 1 Answer is asking for litres. So, we look for litres in the question. 8 litres
STEP 2 Think! Does the volume increase or decrease as we descend? The air becomes denser, so the volume becomes smaller; therefore, the answer will be LESS VOLUME than 8 litres (÷)
STEP 3 The depth is 30 meters. 30÷10+1=4ATA
STEP 4 8 litres ÷ 4 ata = 2litres (therefore the answer is C)
Air consumption in PSI/Bar
Q A diver breathes through 60 Bar of air in 60 minutes at the surface. If all factors remain unchanged, how many BAR will the diver breathe in 40 minutes at 30 meters?
A 160 Bar
B 120 Bar
C 10 Bar
D 45 Bar
STEP 1 Answer is looking for BAR. So, we look for BAR in the question and write it down
60 bar in 60 minutes (here is the trick. We need to know how many bar per minute)
60÷60=1BAR per min
STEP 2 Think! Do we consume more air at depth or less? The air is denser, so we use more air with each breath. Therefore, the answer will be MORE BAR than 1 bar per min (X)
STEP 3 The depth is 30 meters. 30÷10+1= 4ATA
STEP 4 The answer is to multiply bar per min by ATA and then again for 40 min!!!
1 bar per min X 4 ata = 4 bar per min
4 bar per min X 40 min= 160Bar (therefore, the answer is A)
Test your knowledge; CLICK HERE.
Multiple depth changes
The easiest way to deal with problems of changing levels, regardless of volume (or time) or density, is to go from the first level to the surface, find its surface value, and then go down to the second level.
Use a transposed formula.
V1P1=V2P2 OR D1/P1=D2/P2
Volume becomes smaller as you descend and gets larger as you ascend. Think of how you need to equalize your ears as you go down. This is why. As you increase the pressure, the volume will decrease proportionally (inverse relationship).
ANSWER IS LITRES
FILL IN ALL KNOWN VALUES (IN BOLD)
First, take the volume to surface
- multiply volume by surrounding pressure (multiply to go up)
Then take the volume back down to the new depth
- divide the surface volume by the atmospheres of the depth you are going down to (divide to go down, the volume gets less at depth)
Example 1: A flexible container with a volume of 35 litres is at 28m of fresh water, is taken up to 24m of Sea Water; what would the new volume be?
First, work the ata at each depth (make sure you note if it is salt water or fresh water and do not forget to add the 1 surface atmosphere).
To take it to the surface, we take the volume and multiply it by the surrounding pressure (greater volume at the surface) 35 litres × 3.7 ata = 129.5 litres at surface
We then divide it by the ata of the depth we go down to (less volume at depth) 129.5 litres ÷ 3.4 ata = 38 litres
Answer is 38 litres
V=Volume (or time) and P=Pressure
V2 =? litres
P2 = 3.4 ata (24÷10+1=3.4ata)
V2 = 35×3.7÷3.4 = 38 litres
DENSITY (= atmospheres)
Air becomes denser (more pressure) as you descend underwater. A diver will use more air due to the increased (more) pressure (He’s going deeper…more pressure). A diver will use less air due to the decreased (less) pressure as he ascends. (He’s going up… less pressure)
(density is directly proportional to pressure- more pressure, more dense)
ANSWER IS BAR
FILL IN ALL KNOWN VALUES FIRST (IN BOLD)
First, take air consumption (bar/psi) to surface
- divide bar/psi by surrounding atmospheres to get Surface Air Consumption (SAC) (Divide to go up)
Then take it down to the new depth to find air consumption at that depth
- Multiply SAC by the atmospheres of the depth you are going down to (Multiply to go down, remember you use more air at depth)
Example: A diver consumes 4 bar per minute at 10mt in seawater with a given cylinder. Using the same cylinder, what is the diver’s consumption rate at 33mt?
First, work the ata at each depth (make sure you note if it is salt water or fresh water and do not forget to add the 1 surface atmosphere).
To take it to the surface, we take the air consumption (bar/psi) and divide it by the surrounding pressure (consume less bar/psi at the surface) 4 bar ÷ 2 ata = 2 bar at surface (SAC)
We then multiply it by the depth we go down to (consume more bar/psi at depth) 2 bar × 4.3 ata = 8.6 bar.
The answer is 8.6 Bar.
Although I cannot find an official equation for density, logically, the equation would be like this:
D=Density (Air -Bar/PSI) and P=Pressure
D1 = 4 bar
P1 = 2 ata (10÷10+1=2ata)
D2 =? bar
P2 = 4.3 ata (33÷10+1=4.3ata)
D2 = 4÷2×4.3 = 8.6 bar
* Note: - If the question states Bar consumption in "X" minutes. Divide until you determine Air Consumption per Minute and then begin the equation, i.e., 120 bar per hour is 120/60= 2 bar per min
Test your knowledge; CLICK HERE for part 2
Test 1 is single-level depth changes (to the surface and back)
Test 2 is multiple-level changes
Here are links to all the physics blogs
And to all the exams
Water, Heat, Light, Sound, and Gases Exam
Archimedes' Exam part 1
Archimedes' Exam Part 2
Under Pressure Exam
Boyle's Law Exam Part 1
Single-Level Depth Changes
Boyle's Law Exam Part 2
Multi-Level Depth Changes
Charles' Law Exam
Henry's Law Exam
Dalton's Law Exam
(1) Wikipedia contributors. (2021, February 28). Robert Boyle. Wikipedia. https://en.wikipedia.org/wiki/Robert_Boyle
(2) West, J. B. (2005, January 1). Robert Boyle’s landmark book of 1660 with the first experiments on rarified air. Journal of Applied Physiology. https://journals.physiology.org/doi/full/10.1152/japplphysiol.00759.2004
(3) Robert Boyle, Hyperbaric Chambers - A history of hyperbaric chambers and dive medicine, Midlands Recompression & Hyperbaric facilities - The Midlands Diving Chamber.
(2019). Midlands Diving Chamber. http://midlandsdivingchamber.co.uk/index.php?id=history&page=3#:%7E:text=Boyle%20also%20first%20described%20the,fro%20in%20the%20waterish%20humour
(4) Hempleman, H. V. (1984). Decompression Theory. SpringerLink. https://link.springer.com/chapter/10.
(5) Absolute vs gauge: choosing the right pressure control. (2021, January 27). Alicat Scientific. https://www.alicat.com/knowledge-base/absolute-vs-gauge-choosing-the-right-pressure-control/
(6) The Encyclopedia of Recreational Diving (3rd ed.). (2008). PADI.
(7) Divemaster Course Instructor Guide (1999 edition). (2005). PADI.
(8) Why teach the metric system (SI)? (2000, March 1). US Metric System. https://usma.org/why-teach-the-metric-system-si
(9) Benefits. (2017, July 8). Think Metric! https://thinkmetric.uk/benefits/