Calculating the fraction of water that freezes.

[Prospal]

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!

 

[lanedance]

have you considered energy?