Solid Liquids

Sounds like a homework problem to me.

Most eng problems involve making sensible assumptions, like the pipe volume is constant (over the pressures involved), the water doesn't react with mercury etc.

Then, you've got a constant volume (of Hg & water), at a known pressure.

You freeze the water (assume it all turns to ice), it expands increasing the pressure(assume that Hg isn't compressible)

You look up the freezing point for Hg at that pressure, and see if it's lower than 0C.

The difficult part will be finding the appropriate curves for freezing point at different pressures. ffeJ

phase diagram for water helps, but you need to know how much things expand under pressure temperature to select your point on the diagram.

http://www.lsbu.ac.uk/water/phase.html

"If a steel pipe 6" OD x 1/8" ID at 20 ft long were suitably capped."

A very unusual capillary. Where did you get this 'pipe'?

"The pipe was then refrigerated to insure the contained water was below 32 deg F.
My question is: what would the internal pressure be and would the mercury also become solid?"

Internal pressure best determined experimentally. Difficult to calculate.

Physical Properties [table] of Mercury

<A very unusual capillary. Where did you get this 'pipe'?>

Well spotted!

Just guessing: Yes the Hg would remain a solid. The water would freeze at the tripple point and the pressure in the pipe would drop, much like a warm bottle of soda pop if placed in a refrigerator. Or fall like the height of mercury in a glass thermometer when cooled.

semi-retired designer

"Yes the Hg would remain a solid. The water would freeze at the tripple point and the pressure in the pipe would drop, much like a warm bottle of soda pop if placed in a refrigerator. Or fall like the height of mercury in a glass thermometer when cooled."

A real WAG if ever there was one !

Isn't mercury a liquid?

If so, why would it "remain a solid"????

Please explain yourself as this sounds realy odd to me.

Also, why would the pressure drop "much like a warm bottle of soda"?

As far as I am concerned the only thing that shrinks in that bottle is the gas above the liquid soda. The liquid will first shrink a little and then expand as it turns to ice, just like the water in the pipe. Also the post stated that there would be NO AIR above the contents after capping, so this part of your answer has to be disgarded.

Again I would invite you to elaborate as something does not sound right.

case491:

It's just a WAG by a non-engineer

Good point! Mercury, at 760 mm ambient pressure, melts at ~ minus 38.8 C. Also, I didn't see any mention of the air entrained in the liquid water, probably in the mercury also. What are the different crystalline forms of water, and associated density, as the temperature decreases with increasing pressure? If the mercury is actually incompressible, at what point would the "pipe" rupture due to the volume expansion of ice? Pipe composition, wall thickness? Thread size etc of the caps. A lot of unknowns. Do I remember correctly that water is one of a very few compounds or elements that expand when frozen? Send this one back to engineering to be further detailed.

"The pipe was then refrigerated to insure the contained water was below 32 deg F."

Doesn't the below 32 deg F part suggest that this is "freezing" as opposed to refrigerating?

The melting point for mercury is -37.89 °F (or 234.32 °K)

That's some refrigerator...

I have found the volumetric expansion coefficients for water, Hg and ice, respectively. Assuming that filing the pipe with water and mercury has been done at 20 C, as we lower the temperature (everything is sealed OK), down to 0 C everything "shrinks". At zero water becomes ice and, for a small negative gradient of temperature, the block of ice starts to expand with a volumetric coefficient of 153. Hg continues to shrink with the coefficient of 180. I don't know how the pipe reacts to the lower temperature but its volumetric coefficient is 36. So, in order to burst the pipe, it must be a concentration water/Hg larger than 50/50 (probably close to 180/153).

I am wondering if the conductivity of the mercury would change under extreme pressure in a simmilar way that it does under cryogenic conditions. compressing a liquid electrical conductor might turn it into a superconductor under a high enough pressure?

GF