Calculating the fraction of water that freezes.

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SUMMARY

The discussion focuses on calculating the fraction of water that freezes when 1 kg of subcooled liquid water at -6ºC is brought to 0ºC and subsequently freezes. The latent heat of fusion for water is specified as 333.4 J/g, and the specific heat of subcooled liquid water is 4.226 J/g/ºC. The process is analyzed in two stages: heating the water to 0ºC and then determining the fraction that freezes at that temperature. The total change in entropy (dS) for the process is derived from the sum of the entropy changes during both stages.

PREREQUISITES
  • Understanding of thermodynamics, specifically phase changes.
  • Knowledge of entropy calculations and the second law of thermodynamics.
  • Familiarity with latent heat concepts and specific heat capacities.
  • Ability to perform calculations involving temperature changes and energy transfer.
NEXT STEPS
  • Calculate the change in entropy for phase transitions using the formula dS = mC dT/T.
  • Explore the concept of adiabatic processes in thermodynamics.
  • Investigate the implications of irreversible processes in thermodynamic systems.
  • Learn about the relationship between temperature, pressure, and phase changes in water.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those focusing on phase transitions, as well as educators and professionals in physics and engineering fields who require a deeper understanding of entropy and heat transfer processes.

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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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