# Minimizing melted ice in my home-made iced coffee

brightsideben
Hello - first post to PF. I was making my iced coffee this morning as usual by pouring hot, freshly brewed coffee atop a large cup of ice. I then began to wonder about the thermodynamics of this situation. Will the dV/dt (V=volume, t=time) affect how quickly the ice melts? As I pour in the hot coffee the ice melts, and my question is whether the newly-formed, colder liquid will help cool down the hot coffee being poured in. I am not clear on how the law of conservation of energy would apply here.

In short, my question is this: to minimize melted ice, should I pour in my hot coffee a little at a time, all at once, or does it even matter?

Staff Emeritus
2021 Award
It takes a certain amount of energy to melt a certain amount of ice. So long as all the energy comes from the coffee (i.e. you don't use an eyedropper and put one drop in every hour) it doesn't matter. Of course, any ice you put in beyond this will remain ice.

brightsideben
That's interesting - almost counter-intuitive. I would conjecture that the colder liquid would help cool down the new hot coffee so that it doesn't melt as much ice.

You conjecture wrongly. For the most part, the amount of ice that melts is proportional to the amount you need to cool your coffee to reach the freezing point.

brightsideben
Still an interesting phenomenon! That the cold liquid does not reduce the amount of ice needed to cool the coffee back down.

2021 Award
The thermal capacity of the hot coffee, (= water), must supply the energy to melt the ice.
Too little ice and the temperature will no reach freezing point.
Too much ice will result in ice remaining.
If the ratio of ice mass to coffee mass is correct then the ice will melt and the temperature will settle at freezing point.
You can work out the critical mass ratio from the thermal energy of the coffee and the energy needed to melt ice.

Gold Member
The thermal capacity of the hot coffee, (= water), must supply the energy to melt the ice.
Too little ice and the temperature will no reach freezing point.
Too much ice will result in ice remaining.
If the ratio of ice mass to coffee mass is correct then the ice will melt and the temperature will settle at freezing point.
You can work out the critical mass ratio from the thermal energy of the coffee and the energy needed to melt ice.

Your morning routine must be down right Byzantine.

2021 Award
Recipe for Byzantine Iced Coffee.

Water to ice, latent heat of fusion is 334. J /g
Specific heat of water is 4.186 J /g /K

If you add sugar to your coffee, do it before the ice for the most rapid dissolution. Note that, like ice, adding sugar will also cool the coffee as the sugar melts. (Sugar, latent heat of fusion).

If you now have say 100 g of coffee, at 80°C and it is to be cooled to 0°C by the addition of ice, then you will need to remove 80° * 4.186 * 100g = 33488. J of energy.
That will require 33488. / 334. = 100.26 g of ice. The result will be 200.26 g of iced coffee.

The fastest way to cool the coffee with ice is to first crush the ice to increase the surface area which will increase the rate of heat exchange.

Enjoy.

Staff Emeritus