I sometimes like to make hot chocolate, though when I do usually use powdered hot chocolate that you mix with hot water. However I think it taste better with some actual milk added in from the fridge. But since the milk is cold (4 ºC) I can't add too much or the Hot Chocolate won't be hot anymore. The water kettle that I use to warm up the water goes up to 90 ºC, and I don't think I can/should warm milk with it.
So my question is how much milk can I add to the drink while having the temperature stay hot (≥60 ºC). Let's assume the I have a container that can hold 0.5 L and doesn't dissipate heat to the outside environment. Also I don't know if this is necessary information but this is done at sea-level, so 1 atm. Not doing this in space or something crazy like that.
I also want to say I don't care about how long it takes the mixture to become a single even temperature. Nor how the heat distribute itself while the liquid is being mixed. I only care about the final temperature after a equilibrium has been reached and how the amount of milk affects that number.
I would guess energy is preserved in this system so an energy equation could be used. Though I don't know how the temperature of a liquid relates to it's energy, neither of water, milk or the resulting mix between the two. Hopefully someone here with more knowledge can help me out.