Thermodynamics Pressure Problem Help

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Homework Help Overview

The problem involves calculating the pressure at the bottom of a thick ice cap at the North Pole, given its density and thickness. It also requires determining the corresponding melting temperature based on the pressure calculated.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of pressure using the formula ΔP = ρgH and express uncertainty about the initial pressure needed for the calculation. There are hints about considering atmospheric pressure and the conditions at the surface of the ice cap.

Discussion Status

The discussion is progressing with participants offering insights into the initial pressure and how to approach finding the melting temperature. There is a recognition of the need for accuracy in temperature estimation, and some participants are exploring the implications of pressure on temperature using phase diagrams.

Contextual Notes

Participants note the importance of understanding the initial conditions and the assumptions regarding atmospheric pressure at the surface of the ice cap. There is an acknowledgment of potential variations in temperature estimates based on pressure changes.

MechE2015
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Homework Statement



The ice cap on the North Pole could be 1000 m thick with a density of 920 kg/m3. Find the pressure at the bottom and the corresponding melting temperature.

Homework Equations



Steam tables
ΔP = ρgH

The Attempt at a Solution



ΔP = (920 kg/m3)*(9.28 m/s2)*(1000) = 9022 kPa
P = Pinitial + 9022 kPa

I have no idea how to find initial pressure, which I think is my main information missing, then from there I would need to find the corresponding temperature.
 
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MechE2015 said:

Homework Statement



The ice cap on the North Pole could be 1000 m thick with a density of 920 kg/m3. Find the pressure at the bottom and the corresponding melting temperature.

Homework Equations



Steam tables
ΔP = ρgH

The Attempt at a Solution



ΔP = (920 kg/m3)*(9.28 m/s2)*(1000) = 9022 kPa
P = Pinitial + 9022 kPa

I have no idea how to find initial pressure, which I think is my main information missing, then from there I would need to find the corresponding temperature.
Welcome to Physics Forums.

The initial pressure is the pressure at the top of the ice cap ... which is the pressure pretty much anywhere on the surface of Earth. :wink:

EDIT added:
You're a tad slow today, SteamKing! :smile:
 
What's on top of the polar ice cap? That's how you find the initial pressure.

Hint: it blows past you in the breeze.
 
Alright, so the pressure at the surface is 1 atm = 101.325 kPa, which gives me:

P = Po + ΔP = 101.325 + 9022 = 9123 kPa

From here, finding temperature would be found by maybe a P-T chart, where the substance goes from solid -> liquid? Around 275 K is what I get.
 
MechE2015 said:
Alright, so the pressure at the surface is 1 atm = 101.325 kPa, which gives me:

P = Po + ΔP = 101.325 + 9022 = 9123 kPa
Looks good.
From here, finding temperature would be found by maybe a P-T chart, where the substance goes from solid -> liquid?
Yes, that should work.
Around 275 K is what I get.
That's not a terrible approximation, though it is possible they are looking for a more accurate value. I'm not saying they are, just saying it's a possibility.

For a more accurate value, think about how does the 9000 kPa temperature on the chart compare to the temperature at 101 kPa?

p.s to SteamKing: I think this is getting more into your territory than mine. :smile:
 

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