# Pressure and Temperature proportionality.

## Homework Statement

So, this isn't a homework problem as such just something that I'm after confusing myself about. Pressure is proportional to Temperature. So, a rise in pressure leads to an increase in temperature and vice versa, right? However, an increase in pressure leads to an increase in density (contraction), which should also increase the temperature. But, an increase in temperature would usually lead to expansion, no? What am I not getting?

## The Attempt at a Solution

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arildno
Homework Helper
Gold Member
Dearly Missed
I assume you are starting out with the ideal gas law.
It can be written as.
P=K*D*T,
where P is pressure, K is some constant, D is density, and T is Temperature.

gneill
Mentor
If you have a fixed-sized container then the density will not change unless you change the amount of stuff inside.

You can increase pressure in that container by either adding more stuff, or by heating the stuff that's inside.

If the container volume can be varied then you can increase the pressure and density by shrinking the volume (and as a side effect, the work done squeezing the stuff increases its temperature).

The full relationship is described by the equation P*V = n*R*T. P is the pressure, V is the volume, n represents the amount of stuff inside (typically given in moles), and R is the constant of proportionality that turns a proportionality into an equation.

So there are three variable quantities that are interrelated:P, V, and T.

phinds
Gold Member
2021 Award
... an increase in pressure leads to a decrease in density

How do you figure that?

If you have a fixed volume and add heat, you get an increase in pressure but no change in density

If you have a reduced volume due to pressure, then you have an increase in density.

Under what conditions could an increase in pressure possibly lead to a DECREASE in density ???

EDIT: I see gneil beat me to it How do you figure that?

If you have a fixed volume and add heat, you get an increase in pressure but no change in density

If you have a reduced volume due to pressure, then you have an increase in density.

Under what conditions could an increase in pressure possibly lead to a DECREASE in density ???

EDIT: I see gneil beat me to it Apologies! That was a typo!

I'm fine with the ideal gas law...I think. I honestly think I may have thought about this so much in the past 20 minutes that I've confused myself. Are pressure and temperature only proportional for ideal gasses?

So, pressure can stay constant as temperature increases if the volume increases? This is fairly basic stuff. I'm not sure why I'm struggling with it all of a sudden.