Can Ice Remain After Water Cools to 0°C?

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SUMMARY

The discussion centers on the thermodynamic principles governing the coexistence of ice and water at 0°C. It establishes that if the heat required to raise ice to 0°C and convert it to water (qi1 + qi2) is less than or equal to the heat released by water as it cools to 0°C (qw), then all ice will melt. The conclusion is definitive: under the specified conditions, no ice remains in the system once the water reaches 0°C, as the heat lost by the water is sufficient to melt all the ice present.

PREREQUISITES
  • Understanding of thermodynamics, specifically heat transfer concepts.
  • Knowledge of phase changes, particularly the melting of ice.
  • Familiarity with specific heat capacities of water and ice.
  • Basic algebra for manipulating heat equations.
NEXT STEPS
  • Study the principles of thermodynamics, focusing on the first and second laws.
  • Learn about specific heat capacities of different substances, particularly water and ice.
  • Explore phase change equations and their applications in real-world scenarios.
  • Investigate the effects of pressure on melting points and phase transitions.
USEFUL FOR

This discussion is beneficial for students of physics, thermodynamics enthusiasts, and anyone interested in understanding the behavior of water and ice at freezing temperatures.

kieselxeren
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Consider that we have ice and water together ( no heat exchange with surrounding ) and
qi1 = heat required by ice to reach 0 C from ti ( < 0 )
qi2 = heat required by ice at 0 C to convert into water at 0 C
qw = heat that can be released by water after reaching 0 C from tw ( > 0 )

if ( qi1 + qi2 ) <= qw

can there be a case when some ice is left in the system ?
 
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No, your equation says that there is enough heat in the water to after it has reached 0 degrees to melt any ice in the water. In fact, all heat the water loses while dropping to 0 degrees would also contribute to melting the ice.

If you had set qw as the "heat contained by the water at tw" degrees and qi1+ qi2= qw then you would be "right on the verge" where whether there was a tiny amount of ice or not would depend on local effects. But is qi1+ qi2< qw or with your definition of qw as "heat still in the water after reaching 0 C", all ice will be melted.
 

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