Disclaimer: more dive master physics to follow. May not be suitable for the easily bored ;)
Today, we are going to take a brief look at what happens to a gas when you apply pressure to it.
The first thing to remember is that as the pressure on the gas increases, the volume of the gas will decrease in relation. In SCUBA diving we are very familiar with this from our very first open water classes. Most classes start off by talking about what happens when you take a flexible container of air down to 100 feet or so. Of course as every one probably knows, the air in the container will compress and the container will look like most of the air has been sucked out of it. Of course the air is still there, it is just that is has been compressed (squeezed by the pressure of the water).
Remember that the pressure multiplied by the volume is the same for a given container at any depth.
P1 x V1 = P2 x V2
The pressure multiplied by the volume at the surface will be the same answer as the pressure times volume at depth (for the obvious reason that as the pressure increases, the volume decreases).
Lets do a simple example to demonstrate the relationship and how it is used in dive master physics.
You take a container with the volume of 2 cubic feet (at the surface) to a depth of 66 feet. What will the new volume be.
Remember that 66 feet is equal to 3 atmospheres. So the 2 cubic feet at 66 feet will be compressed by the water pressure so that the gas inside the container will one third of that at the surface - 2 cubic feet divided by 3 (0.67 cu ft)
However, for the dive master exams the examiners try to be a little tricky so you have to read the questions very carefully. For example they might throw in the words "fresh water" into the question, which means you need to use 34 feet instead of 33 feet per atmosphere etc. Be sure to read the questions very carefully.
To make these pressure calculations more challenging, the examiners will ask you to determine what happens to a given volume of gas when you take it from one depth to another. It is not that the work is much harder, it is just that they seem to try to see if you are paying attention.
Lets do an example of a potentially trickier question. Note that we are now starting at depth and not the surface.
You need to take a volume of 20 cu ft from 99 feet to 66 feet in sea water.
First we need to calculate the original pressure at 99 feet - which calculate as 4 ata (p1).
Next we need to calculate the pressure at 66 feet - which is 3 ata (p2).
Remember the formula: p1 x v1 = p2 x v2
We have p1, v1, p2 but not v2. What we need to do is find out what v2 is. So to calculate the new pressure we use a ratio calculation
v2 = p1 / p2 x v1 (the slash is shorthand for divided by)
4 ata / 3 ata x 20 cu ft = 26.67 cu feet.
Of course in the dive master exams they will not give you easy numbers like these, but the principle is the same. Lets do a more realistic example.
15 cubic feet at 105 feet to 41 feet in fresh water.
v1= 15 cu ft
p1 = 105 ft / 34 (3.09 + 1 ata = 4.09 ata)
p2 = 41 ft / 34 (1.2 + 1 ata = 2.2 ata)
So lets plug the numbers into the ratio we used above
v2 = p1 / p2 x v1
v2 = 4.09 ata / 2.2 ata x 15 cu ft = 27.88 cu ft
The calculations are not difficult, but do remember the following key things
Make sure you know whether you are working with fresh water or salt water.
Make sure that you add in the surface atmosphere to get the ata pressure at depth.