## Density

I am addressing density separately because the best approach to density questions is subtly different to the questions we have looked at so far.

There is still a three step process. It is similar to the one you should by now be familiar with, but a little different.

The density of a gas is directly proportional to the pressure the gas is under. So these questions are about calculating the proportional change in pressure between one depth and another depth. You then describe that change in terms of density.

The way density questions can be worded combined with the way the answers are worded can make them a little confusing. But if you just apply the following method, you should quickly and easily find the answer, regardless of how awkwardly the question is worded.

**Step 1** Look at the question and identify what depth the diver is NOW at. Write down the pressure at that depth.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. Write down the pressure at that depth. If it is the surface, write down the number 1.

A few example questions should make this clearer:

1. What is the difference in the density of the air a diver breathes at 50m compared to the surface?

a. 4 times as dense

b. 5 times as dense

c. The same

d. 6 times as dense

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at 50m. The pressure at 50m is 6ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is to the surface. The pressure at the surface is 1.

1/6=6 Answer D

2. At a depth of 10m approximately how much denser is the air a diver breathes compared to the surface?

a. The same

b. ½ as dense

c. Twice as dense

d. Three times as dense

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at 10m. The pressure at 10m is 2ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is to the surface. The pressure at the surface is 1ata.

2/1=2 Answer C

3. What is the difference in the density of the air a diver breathes at the surface compared to a depth of 30m?

a. 4 times as dense

b. 1/4 of the density

c. 3 times as dense

d. 1/3 of the density

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at the surface. The pressure at the surface is 1ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is 30m. The pressure at 30m is 4ata

1/4 = 0.25 In this case we didn’t need to use a calculator to find 0.25 as they gave the answer to us as a fraction. What we wrote down from the depths given in the question IS the answer!

4. How much denser is the air a diver breathes at 40m compared to the surface? (approximately)

a. 4 times as dense

b. ¼ of the density

c. 5 times as dense

d. 1/5of the density

**Step 1** Look at the question and identify what depth the diver is NOW at. They are AT 40m. The pressure at 40m is 5ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is to the surface. The pressure at the surface is 1ata.

5/1=5 Answer C

5. How does the density of the air a diver breathes at a depth of 20m compare to the density of the air they breathe at a depth of 5m?

a. 3/5 as dense

b. Twice as dense

c. 6 Times as dense

d. 1.5 Times as dense

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at 20m. The pressure at 20m is 3ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is 5m. The pressure at 5m is 1.5ata

3/1.5 = 2 Answer B

6. The density of the air a diver breathes changes with pressure. A diver ascends from a depth of 20m to the surface. How does the pressure at the surface compare to a depth of 20m?

a. 2 times less pressure

b. 2 times more pressure

c. 3 times less pressure

d. 3 times more pressure

If I have got a little tricky with you here. I have dressed up a question to look like a density question. But if you focus n the last sentence it asks what the change in PRESSURE is, not the change in density. However it is basically the same thing, since density is directly proportional to pressure.

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at the surface. The pressure at the surface is 1ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is 20m. The pressure at 20m is 3ata

1/3=3 - The answer three comes up twice, (Answer c and d). We need to stop and think. Is the pressure going to increase or decrease as we go from 20m to the surface? It’s going to decrease. So answer C, three times less pressure, would be correct.

7. The density of the air a diver breathes changes with pressure. A diver ascends from a depth of 30m to a depth of 10m. How does the pressure at 10m compare to a depth of 30m?

a. 1/2 the pressure

b. 2 times more pressure

c. 3 times less pressure

d. 3 times more pressure

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at 10m. The pressure at 10m is 2ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is 30m. The pressure at 30m is 4ata

2/4=0.5 – Which is the same as ½ Answer A

8. A Diver descends from a depth of 15m to a depth of 40m. How does the pressure at 40m compare to a depth of 15m?

a. 1/2 the pressure

b. 2 times more pressure

c. 1.5 times more pressure

d. 1.5 times less pressure

**Step 1** Look at the question and identify what depth the diver is NOW at. We see they are at 40m. The pressure at 0m is 5ata.

**Step 2** Divide – It’s a simple as that, ALWAYS divide.

**Step 3** Find the depth that you should be comparing to. The comparison is 15m. The pressure at 15m is 2.5ata

5/2.5=2 – Answer B