The amount of time it will take to melt ice

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Discussion Overview

The discussion revolves around estimating the time required to melt an ice cube of a specific temperature and mass in a given mass of water at a different temperature. Participants explore the theoretical and practical aspects of heat transfer, the effects of ice geometry, and the influence of water movement on melting rates.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the feasibility of calculating the melting time, emphasizing the need for specific formulas and information.
  • Another participant highlights the complexity of the problem, mentioning the importance of the heat transfer rate at the water-ice interface and the variable parameters such as the surface area to mass ratio of the ice cube.
  • A third participant reiterates the significance of the surface area-to-volume ratio, noting that different shapes of ice (e.g., thin sheet vs. spherical block) will affect melting rates.
  • One participant suggests that practical experimentation may be necessary to gain insights into the melting process.
  • Another participant discusses the role of convective circulation and agitation in enhancing melting rates, indicating that these factors can influence the stagnant layer of water around the ice.

Areas of Agreement / Disagreement

Participants express a general agreement on the complexity of the melting process and the factors that influence it, but there are multiple competing views regarding the specific parameters and conditions that need to be considered. The discussion remains unresolved with no consensus on a definitive approach or formula.

Contextual Notes

Participants note limitations such as the dependence on the surface area-to-volume ratio, the effects of stirring, and the variability of heat transfer rates, which complicate the theoretical analysis of the melting process.

ChessEnthusiast
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What information / formulas do I need to calculate / estimate the amount of time required to melt an ice cube of temperature $T_i$ and mass $m$ in $M$ kg of $T_w$ temperature water?

Assume that the system is insulated.
Is it even possible?

I'm fine with Calculus.
 
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This is very difficult to answer theoretically. You would need to know the rate of heat transfer at the water-ice interface, and the kinetics of melting of ice, but also about very variable parameters such as the surface area to mass ratio of the ice cube (which will change as it melts) and the stirring of the water. (As the ice melts, it will be surrounded by a layer of water at 0°C that will insulate it from the surrounding water at Tw. Stirring will disperse this layer and assist heat transfer and melting.) This looks like a candidate for some suck-it-and-see practical experimentation.
 
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ChessEnthusiast said:
What information / formulas do I need to calculate / estimate the amount of time required to melt an ice cube of temperature $T_i$ and mass $m$ in $M$ kg of $T_w$ temperature water?

Assume that the system is insulated.
Is it even possible?

I'm fine with Calculus.

A thin sheet of ice will melt faster than a spherical block of ice, both of the same mass.

As mjc123 has stated, one also needs to know the surface area-to-volume ratio, because just using the parameters that you gave are not sufficient to answer your question.

Zz.
 
Making cocktails involves cracked ice and a lot of agitation - just saying'.
 
As I see it, thaw rate comes down to heat transfer across the ice surface 'stagnant' zone. Yes, this chilled layer will 'drip' due higher density. The bigger the ice surface to volume ratio, the greater the 'natural' rate. If a significant convective circulation develops, this may diminish the stagnant zone. A stirrer or sonic bath would strip it.
 

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