# Pressure and density of compressible fluids.

1. May 19, 2014

### Nathanael

If a fluid is compressible, will the density be directly proportional to the pressure?

(I'm sure there's a limit where an increase in pressure stops producing a change in density, but I'm talking about for more "normal" (smaller) amounts of pressure.)

2. May 19, 2014

### paisiello2

Are you assuming constant temperature as well?

3. May 19, 2014

### Nathanael

Temperature would effect the energy, right?

And pressure is essentially the density of energy, (Newton-Meters per Cubic Meter)

So wouldn't a change in temperature only effect the pressure? And so it doesn't really need to be considered when considering the relationship between pressure and density, right?

Or no?

4. May 19, 2014

### Staff: Mentor

The word "proportional" has a certain exactness to it, and nothing is exact. The most one can say is that the density increases with increasing pressure. Over limited regions of pressure, the density change is approximately proportional to the pressure change.

Chet

5. May 19, 2014

### paisiello2

Well, if temperature affects pressure and pressure in turn affects density then the conclusion is that temperature would also affect density.

Or no?

6. May 19, 2014

### Staff: Mentor

I think Nathanael, in his original post, was referring to the effect of pressure on density at constant temperature. At least that was my interpretation.

Nathanael, is that what you meant?

Chet

7. May 20, 2014

### Nathanael

Sorry, I wasn't thinking about my last post. I was under the unexamined impression that a change in pressure caused by temperature would affect the density (simply because it affects pressure) but now that I'm thinking about it, I realize that a change in pressure caused by temperature will have no effect on density (right?).

In a sense I was talking about constant temperature, (in the sense that temperature was not a part of my picture) but honestly I didn't think about temperature.

(I never learned or thought of temperature affecting pressure, even though it's a common-sense kind of idea.)

My original question was just asking is if the increase in density was (approximately) linear, or if it curved upward, or curved downward, (or what I really mean is does it "bend" downward) or what?

8. May 20, 2014

Temperature absolutely and directly affects the pressure and density. For example, many gases behave as ideal gases at most ordinary conditions and so very closely follow the ideal gas law, which can be expressed as

$$p = \rho R T$$

where $p$ is pressure, $\rho$ is density, $R$ is the specific gas constant, and $T$ is temperature.

9. May 22, 2014