Calculating the fraction of water that freezes.

In summary, the conversation discusses the process of subcooling pure liquid water at atmospheric pressure and the addition of a small ice crystal to initiate freezing. The question at hand is the fraction of water that will freeze and the final temperature after the change occurs adiabatically. The change in entropy and the process's irreversible feature are also mentioned. The conversation also brings up the equations involved in calculating the change in entropy and the difficulty in determining the fraction of water that freezes.
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Homework Statement



Very pure liquid water can be subcooled at atmospheric pressure to temperatures well below 0ºC. Assume that 1kg has been cooled as a liquid to -6ºC. A small ice crystal (negligible mass) is added to "seed" the subcooled liquid. If the subsequent change occurs adiabatically at atmospheric pressure, what fraction of the system freezes and what is the final temperature? What is the DELTA(ENTROPY) total for the process and what is its irreversible feature? The latent heat of fusion of water at 0ºC is 333.4 J/g and the specific heat of subcooled liquid is 4.226 J/g/ºC.

Homework Equations



I am pretty sure I can calculate the change in entropy of the system, I am just having a hard time finding the fraction of water that freezes.

I think the process is taken in two stages,
1 - System is taken from -6ºC to 0ºC
2 - Fraction of water freezes at 0ºC

dS[step1] = mC dT/T
dS[step2] = -xQ(fusion)/T

The Attempt at a Solution



I think the dS(total) would be the addition of the above two dS terms, however, I am having difficulty calculating the fraction of water that freezes when the system is brought to 0ºC.

Thank you for your help!
 
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  • #2
have you considered energy?
 

1. What is the formula for calculating the fraction of water that freezes?

The formula for calculating the fraction of water that freezes is the amount of frozen water divided by the total amount of water.

2. How do you measure the amount of frozen water?

The amount of frozen water can be measured by weighing the ice or using a thermometer to measure the temperature of the water and determining when it reaches the freezing point.

3. What factors can affect the fraction of water that freezes?

The temperature, pressure, and impurities in the water can all affect the fraction of water that freezes. Higher temperatures, lower pressures, and more impurities can all decrease the fraction of water that freezes.

4. Can the fraction of water that freezes be greater than 1?

No, the fraction of water that freezes cannot be greater than 1. This would mean that more water has frozen than is actually present, which is not possible.

5. How does the fraction of water that freezes relate to the concept of freezing point depression?

The fraction of water that freezes is directly related to freezing point depression. As the fraction of water that freezes decreases, the freezing point of the water also decreases due to the presence of impurities.

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