Make solid ice from supercooled water?

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Supercooled water must be below zero degrees Celsius to freeze completely solid, as the phase change from liquid to solid releases heat. The discussion revolves around the energy balance required for this transition, specifically comparing the energy needed to warm supercooled water versus the energy released when water freezes. The specific heat of ice is lower than that of water, which complicates the calculations. Participants are considering different scenarios to understand the energy dynamics involved in freezing supercooled water. Ultimately, the conversation highlights the complexities of thermodynamics in phase changes.
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Im having a discusion reguarding what temperature (celsius) supercooled water needs to be if it was to freeze completely solid. Going from liquid to solid "produces" heat. Therefor it is obvious that the temperature needs to be somewhat below zero.

What temperature (celsius) is needed if all the supercooled water should turn into ice and stay at zero degrees afterwards?

Thanks!
 
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The energy to warm M grams of supercooled water from minus X degrees C to 0 degrees C equals the energy given off when M grams of water at 0 degrees C turns into ice at 0 degrees C?
 
Maybe it is more helpful to start with M grams of ice at 0 degrees C and then add energy E to turn the ice into M grams of water at 0 degrees C and then remove the same energy E from the water to bring it down to minus X degrees C?
 
Spinnor said:
The energy to warm M grams of supercooled water from minus X degrees C to 0 degrees C equals the energy given off when M grams of water at 0 degrees C turns into ice at 0 degrees C?

Mmmmm... I'd have thought that it would be the energy required to warm M gram of ice from minus X degrees C to 0 degrees C that has to balance the energy given off by the water turning to ice. The specific heat of ice is appreciably less than that of water.
 
Nugatory said:
Mmmmm... I'd have thought that it would be the energy required to warm M gram of ice from minus X degrees C to 0 degrees C that has to balance the energy given off by the water turning to ice. The specific heat of ice is appreciably less than that of water.

I think I had that backwards, yes?
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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