Pressure increases as density increases.

[Physics197]

Homework Statement

Water contracts when cooled (at least above 4 °C). A beaker of water is cooled from 50 °C to 20 °C. The pressure at the bottom of the beaker increases.

Does the pressure increase or decrease as temperature decreases

The absolute pressure at the bottom of a cylinder filled with liquid is Pa=2.0 atm. The liquid is poured into another cylinder having half the radius. The absolute pressure at the bottom of that cylinder is Pa=5.0 atm.

I believe this is false.

Two cylinders are filled with water to the same height, but have different radii. The pressures on the bottoms of the cylinders are the same.

True - radii has no effect, just height?

Homework Equations

The Attempt at a Solution

 

[Delphi51]

I think your answers are correct. For the first one, you really need a formula to indicate the answer. Do you have a formula for pressure that involves density? Or maybe one without density in it would be even better!

 

[Physics197]

I do have Pressure = F/Area (surface)
also, Pressure = pgh

 

[Delphi51]

Pressure = ρgh is pretty good.
The cooler water will have a larger ρ, but the water has less volume, so smaller h.
Not very conclusive!

If you multiply by the area of the bottom of the container, and divide by it, you have
Pressure = ρgh = ρAhg/A
Since A*h is the volume, this is P = ρVg/A
Looks just as hopeless, but note that ρV is the mass of the liquid.
Can you finish it off and say what happens to P as the density increases?