# I The amount of time it will take to melt ice

Tags:
1. Aug 9, 2018 at 11:24 AM

### 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.

2. Aug 9, 2018 at 12:00 PM

### 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 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.

3. Aug 9, 2018 at 12:15 PM

### ZapperZ

Staff Emeritus
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.

4. Aug 9, 2018 at 2:57 PM

### sophiecentaur

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

5. Aug 11, 2018 at 9:10 PM

### 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.