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# Properties of Matter Study Guide (page 2)

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#### Example

At sea level, the average atmospheric pressure is 760 mmHg. Find the SI value of this pressure and in inch Hg.

#### Solution

This problem requires us to convert pressure to SI units.

## Density

As pressure takes the place of the simple forces acting on an area, what is similar to mass in the case of fluids? Mass is a quantity associated with matter, but at the same amount of mass, some objects occupy a lot of space. In fact, they will take all that you give them in the case of gases; some other objects will take very little space. The quantity that measures the amount of mass relative to the space occupied is called density.

As with pressure, density can be measured in many different units. The SI unit is kg/m3. Other units for density are Vcm3, g/m3, lb/ft3, oz/in3, and Ib/gal. The device used to measure density is a specific gravity bottle, called a pyknometer. The most commonly known density is for water at standard atmospheric pressure and temperature of 4° C: 1,000 kg/m3, or 1 kilogram of water occupying a volume of 1 liter.

Atomically, the explanation of different densities associated with different materials and phases is the arrangement of atoms in the structure of the material. Solids are more compact, presenting a clear structure, and their atoms and ions are closer to each other amounting to a larger mass in a given volume. This structure is mostly missing in liquids and is not existent in gases, where particles are freely moving, hence, they can occupy large volumes.

### Density

Density measures the mass per unit volume.

#### Example

The Malibu Maxx's cargo space, according to GM data from 2003, is about 50% larger than other midsize sedans, and it is calculated to be 22.8 cubic feet. If the air density is 1.2 kg/m3, what is the quantity of air occupying that space?

#### Solution

The first step is to convert all data into SI.

V = 22.8 ft3 = 22.8 ft3 · 0.0283168 m3/1 ft3 = 0.65 m3

p = 1.2 kg/m3

m = ?

p = m/V

1.2 kg/m3 = m/0.65 m3

m = 1.2 kg/m3 · 0.65 m3 = 0.78 kg

m = 0.78 kg

## Pressure and Depth

Let's begin with the definition of pressure and then isolate a cylindrical volume inside a container filled with a liquid as shown in Figure 10.2. The liquid is at rest and is occupying a space between levels h1 and h2 inside the water. The volume considered has a certain mass, and the pressure at the bottom of the column is due to the weight of the liquid. Hence, we can calculate the pressure of this volume of liquid.

If we consider a pressure exerted upon a fluid (air pressure at the surface of a lake for instance), then the variation of the pressure with depth is:

Where pois the pressure of the air and the second term, p · (h2 - h1) · g, is the contribution of the liquid.

In addition to this depth dependence, we have to add that at the same level in a fluid, the pressure is the same in all directions as shown in Figure 10.3. For example, an object floating in a liquid will be exerted with a pressure p in all directions.

### Pressure

The pressure exerted by a fluid at rest is proportional to the height or depth of the fluid column and the density of the liquid.

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