Hot Coffee with cream

[TakenItSeriously]

You've just poured yourself a hot cup of coffee.

 

Before you can do anything, something comes up which will take you about 15 minutes.

 

You take your coffee with cream which is at room temperature. In order for your coffee to be as hot as possible when you get back when should you mix in the cream?

 

A) now

B) when you get back in 15 minutes

C) it doesnt matter

 

Logic based riddle

Edited July 9, 2016 by TakenItSeriously

[Phi for All]

Since you said cream, and not milk, I'm going to guess:

 

 

A) now, because in 15 minutes the cream will have formed a skin of proteins and fat that acts as a heat barrier, trapping steam inside the cup and keeping the liquid hotter.

 

[imatfaal]

....Logic based riddle

 

This is not a logic based riddle

[John Cuthber]

This is not a self referential statement.

[TakenItSeriously]

This is not a logic based riddle

It depends, you could use logic, you could use thermal dynamics. You could use a lot of methods. Its easier, for me at least, to use logic.

 

Edit to add: after reconsidering the problem, I can now see that imatfaal has a valid point.

 

While I could use logic, it is still dependant on using the laws of thermal dynamics as its starting premis.

 

As the problem is defined, its a rather obvious premise but not necessarily a valid premis without understanding it's origin is from one of the laws thermal dynamics.

 

So to be fair, it does require some knowledge of thermal dynamics in order to solve the problem.

 

I appologize for my premature jumping to conclusions.

 

Since you said cream, and not milk, I'm going to guess:

 

 

 

A) now, because in 15 minutes the cream will have formed a skin of proteins and fat that acts as a heat barrier, trapping steam inside the cup and keeping the liquid hotter.

 

Not the answer I was looking for. Since I have no trivial way to verify your solution one way or the other. I changed the wording to say mix in the cream, which I'm pretty sure would create a solution that would prevent a skin from forming, though I could be wrong. I don't take cream with my coffee

 

BTW, the cream reference just dates when I heard the riddle. I suppose you could use milk but refrigerated milk changes the riddle.

Edited July 9, 2016 by TakenItSeriously

[Phi for All]

Not the answer I was looking for. Since I have no trivial way to verify your solution one way or the other. I changed the wording to say mix in the cream, which I'm pretty sure would create a solution that would prevent a skin from forming, though I could be wrong. I don't take cream with my coffee

 

Coincidentally enough, as I read your thread this morning, I was on my third cup of French-pressed Carte Noire with milk (arrived yesterday). Even with just mixing in milk, a bit of a skin forms by heating the fats and proteins and then letting it sit untouched. I'll admit I haven't checked this formally yet, but a layer of solid fat at the top should act as an insulator, trapping heat inside the cup, keeping the drink warmer.

[TakenItSeriously]

Coincidentally enough, as I read your thread this morning, I was on my third cup of French-pressed Carte Noire with milk (arrived yesterday). Even with just mixing in milk, a bit of a skin forms by heating the fats and proteins and then letting it sit untouched. I'll admit I haven't checked this formally yet, but a layer of solid fat at the top should act as an insulator, trapping heat inside the cup, keeping the drink warmer.

 

Lol, I should have understood the consequences of choosing a riddle formum thats part of a science themed forum. I'll need to choose my riddles with a little more foresite than Im used to.

[imatfaal]

This is not a self referential statement.

 

ceci n'est pas une pipe

[TakenItSeriously]

Solution:

 

 

According to one of the laws of thermodynamics, I forgot which lol, the rate at which the coffee cools is proportional to the difference in temperature between the hot liquid and the room temperature. So I admit its a thermodynamics problem and not just a logic based riddle.

 

Since the cream is always at room temperature the temperature drop is just a matter of taking the weighted average temp.

 

adding the cream earlier lowers the difference in temperature and therefore slows down the cooling rate of the combined coffee with cream.

 

While waiting twenty minutes and then adding the cream, means that the coffee will cool at a faster rate before adding the cream leaving the coffee with cream cooler than when adding the cream earlier.

 

 

Edited July 16, 2016 by TakenItSeriously

[imatfaal]

Although most people stir their coffee with a metal spoon when the add the cream. This heats the spoon up which is then removed, it also agitates the coffee causing potential greater cooling, and incorporates air; these effects are weakened if the spoon stirring is done at an already lowered temperature

[John Cuthber]

Although most people stir their coffee with a metal spoon when the add the cream. This heats the spoon up which is then removed, it also agitates the coffee causing potential greater cooling, and incorporates air; these effects are weakened if the spoon stirring is done at an already lowered temperature

The heat capacity of the metals typically used in spoons is a lot lower than that of the water that makes up most of the coffee.

Convection currents will agitate the coffee until it is cold. But viscosity will stop the coffee rotating fairly shortly after you stop stirring- so that effect is also small.

I don't stir my coffee so vigorously that I get bubbles in it. It's unclear whether (if I did) the incorporated air would speed up the cooling process through enhanced evaporation, or slow it down due to insulation.

In principle, if you stir the cold coffee long enough and hard enough, you will heat it back up again.

[Phi for All]

Although most people stir their coffee with a metal spoon when the add the cream.

 

Maybe people who don't take advantage of physics, and feel like cleaning extra silverware. I add the milk/cream first, then let the thermal and kinetic energies of pouring do the mixing for me.

[TakenItSeriously]

Although most people stir their coffee with a metal spoon when the add the cream. This heats the spoon up which is then removed, it also agitates the coffee causing potential greater cooling, and incorporates air; these effects are weakened if the spoon stirring is done at an already lowered temperature

Since mixing was added to the riddle after the fact we will use a wooden stir stick with negligible conduction properties.

 

Also assume the agitation created by stirring has negligible effect on cooling through convection and adds negligible energy to brownian motion.

 

Right track though

 

Edited July 17, 2016 by TakenItSeriously