The amount of time it will take to melt ice

[ChessEnthusiast]

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.

 

[mjc123]

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 T_w. Stirring will disperse this layer and assist heat transfer and melting.) This looks like a candidate for some suck-it-and-see practical experimentation.

 

[ZapperZ]

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.

 

[sophiecentaur]

Making cocktails involves cracked ice and a lot of agitation - just saying'.

 

[Nik_2213]

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.