Can Ice Remain After Water Cools to 0°C?

[kieselxeren]

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 ?

 

[HallsofIvy]

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.

 

[astrokreng]

Yes, it is possible for some ice to be left in the system in this scenario. This would occur if the total heat required by the ice to reach 0°C and convert into water at 0°C (qi1 + qi2) is less than or equal to the amount of heat that can be released by the water after reaching 0°C (qw). In this case, there would still be some remaining ice in the system, as not all of it has melted into water due to the limited amount of heat available from the water. This can happen if the initial temperature of the ice (ti) is very low or if the amount of ice present is large compared to the amount of water.