Latte's temperature

I first have to admit that I'm not very good at physics, this is a really simple post (I know that I always say the same but it's true). Last Friday I was preparing myself a latte, what can I say, It was four o'clock in the afternoon  and I was hungry!. At work we have cups made of Styrofoam, so I picked one and mixed coffee with milk (I prefer more coffee than milk). One of my colleges that  was at the kitchen with me said: "Be careful!, coffee is really, really hot!". I thanked him, but I thought: "but, I'm not drinking coffee, I'm drinking latte!, what about the temperature of the latte?", so I did a bit of research to answer my question, I must admit I studied this at the university but I completely removed it from my brain.


Basically, every fluid (every material indeed) has something called calorific capacity, which is the capacity of transferring heat to another fluid, this capacity is calculated per mole of material, so every time we want to use it in a real problem we need to know the mass or the moles of the fluid. For my particular problem I'm going to omit that the cup is open, I mean, the fluid doesn't have any contact with the air (it is just a simplification,  sorry for this, but I'm calculating the temperature of my latte, not calibrating the CERN's LHR!).


As we don't have a heat transference to the air, we might establish that (adiabatic system):

(the heat absorbed by the milk is equals to the heat delivered by the coffee), each heat can be calculated by the following integrals:

I searched for the calorific capacity of the milk and coffee and they are independent of the temperature of the fluid, so:

So the final temperature is:

what I only need to do is calculate the mass of the coffee and milk and their initial temperatures!.

Well, this is a stupid post but quite interesting for this daily problem :-).

Cheers