Calculate melting point of ice under pressure

In summary, at 1atm (101,325KPa) and 0oC, the densities of ice and liquid water are 917Kg/m3 and 999,8Kg/m3, respectively. The heat of fusion of water is 334720J/Kg. At 0,5atm (50,662KPa) and 101atm (10,2338MPa), the densities of ice and liquid water are 917Kg/m3 and 999,8Kg/m3, respectively. The melting points of ice and liquid water are -0.4438K and 1000K, respectively.
  • #1
Pete_01
51
0

Homework Statement


The density of solid water is approximately 920 kg m^-3 and that of liquid water is 1000 kg m^-3. Calculate the melting point of ice under a pressure of 6000 kPa.


Homework Equations



This is my problem. How do I approach this? I don't see any relevant equations in my textbook.


The Attempt at a Solution


See 2.
 
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  • #2
Clausius–Clapeyron relation perhaps?
 
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  • #3
Borek said:
Clausius–Clapeyron relation perhaps?

Not really. That has to do with pressure, but how does the density fit in?
 
  • #4
Use it to calculate volume change.
 
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  • #5
Borek said:
Use it to calculate volume change.

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I'm not following. Use the density to calculate volume change? Or use the Calpeyron equation to calcululate it? The equation I have found so far is:

delta(ln p) = delta_vapH/RT^2 * delta T

Is this correct? Thanks
 
  • #6
No, this is version for evaporation, you need version for melting. Use given densities to calculate volume change.

See wikipedia article on Clausius–Clapeyron relation.
 
  • #7
Borek said:
No, this is version for evaporation, you need version for melting. Use given densities to calculate volume change.

See wikipedia article on Clausius–Clapeyron relation.

So, like their example at the bottom of the page...

7ccf0e9ffa7dc258672182cdaa1060e4.png


and then rearrange and solve for deltaT and I get -0.4438K which doesn't mke much sense?
 
  • #8
What is delta T?
 
  • #9
Borek said:
What is delta T?

Change in temperature (melting temp).
 
  • #10
And what was delta T you calculated?
 
  • #11
Borek said:
And what was delta T you calculated?

Ok, so it would be: melting point water - (-0.4438K) for a final melting point?
 
  • #12
That would sound logical.
 
  • #13
Borek said:
That would sound logical.

Awesome! Thanks, I appreciate the help!
 
  • #14
i have something like it:

The densities of ice and liquid water at 1atm (101,325KPa) and 0oC are
917Kg/m3 and 999,8Kg/m3, respectively. The heat of fusion of water is 334720J/Kg.
Calculate the melting point of ice at 0,5atm (50,662KPa) and 101atm (10,2338MPa).

i don't know how i find "delta"H
 
  • #15
What IS delta H?
 

1. What factors affect the melting point of ice under pressure?

The melting point of ice under pressure is affected by the amount of pressure applied, the purity of the ice, and the presence of impurities such as salt or other substances. The type of pressure, whether it is hydrostatic or confining, can also impact the melting point.

2. How is the melting point of ice under pressure calculated?

The melting point of ice under pressure is typically calculated using thermodynamic equations, which take into account the pressure and temperature conditions. Other factors such as the heat capacity and density of ice may also be considered in the calculation.

3. Can the melting point of ice under pressure be accurately predicted?

While there are equations and models that can be used to predict the melting point of ice under pressure, there may be variations due to factors such as impurities or changes in the ice structure. Thus, the predicted melting point may not always be completely accurate.

4. What is the significance of understanding the melting point of ice under pressure?

Understanding the melting point of ice under pressure is important for various fields of study, such as climate science, geology, and materials science. It can also have practical applications in industries such as food preservation and engineering.

5. Is the melting point of ice under pressure the same as the melting point of regular ice?

No, the melting point of ice under pressure is different from the melting point of regular ice. As pressure is applied to ice, its melting point decreases, meaning it will melt at a lower temperature than regular ice. This is due to the changes in the ice's structure and properties under pressure.

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