Maximizing Heat Retention: The Effect of Adding Cream to Hot Coffee

[Backtoschool]

I am learning the concepts of thermodynamics and this one is confusing me! The question is - If I pour myself a cup of hot coffee and then the phone rings, is it better to pour the cream (room temperature) before walking away, or when I return in order to have the hottest coffee when I return?

I believe that convection applies to liquids and movement, but I'm just not getting it. My instinct tells me that the increased density would slow the energy of the particles, therefore decreasing the heat loss. But I keep getting stuck on whether the cream would act as a coolant - or whether it's relevant at all! Can anyone help? Thanks so much! I have a feeling you'll be seeing a lot of me on this site...

 

[robb_]

Well, the cream is at room temp. and the coffee is "hot." What will happen when you take two liquids at dif. temps and combine them?

 

[Backtoschool]

My first thought was that the cream would cool the initial temperature of the coffee as there would be an equalizing effect of the two different temperatures, but I'm still trying to understand whether it makes any difference as to WHEN the fluids are combined. If the coffee is allowed to sit for a few minutes before the cream is added, it will lose heat into the cooler surrounding air and then be additionally cooled when the cream is added. If the cream is added initially, it would lose heat due to the difference in temperatures, but wouldn't the increased density of the combined liquids then lose heat more slowly due to a decrease in the convection energy?

 

[robb_]

Okay, I think I missed the subtlety of the question.
We might assume that after the cream has been added, the time it takes for the two liquids to reach an equilibrium temperature, with each other, is very small. Does that seem reasonable to you. (Small compared to the time it takes both liquids to reach eq. with the environment)

 

[Backtoschool]

Oh, absolutely. But what I'm not getting is whether there is a benefit (the drink will be hotter) to adding the room temperature cream BEFORE answering the phone or will the final result be the same if I were to add the cream to the hot coffee following the phone call. Maybe I can illustrate better:

The coffee starts at the same temperature. 5 minutes will pass. If I were to add the cream and then wait, vs waiting and then adding the cream, would there be a difference as to how hot the coffee will be after the five minutes?

I really appreciate your help - I don't know why I'm having so much difficulty with this one!

 

[robb_]

Yes I understand the question. Let me think about this while I have my dinner.

 

[robb_]

Can we assume that the cream increases the viscosity of the liquid?

 

[robb_]

I think your original intuition is correct, in that the thicker cream doesn't migrate around as quickly in the cup. What does this imply?

 

[Backtoschool]

That the increased viscosity would slow the dissipation of the heat due to the reduced kinetic energy of the molecules within the mixture?

 

[robb_]

Not quite. If it is more viscous, how does that effect convection?

 

[Backtoschool]

The viscosity would slow the process of convection. (?)

 

[denverdoc]

are you guys sure this isn't more a matter of Newtons cooling law?

In other words adding the cream initially, will reduce the gradient between the surroundings and let's assume the rate constant is the same.

Contrast that with larger grdient for 5 minutes while you talk on phone, then adding cream?

 

[Backtoschool]

If the more viscous cream sinks to the bottom, and the convection is slowed due to this viscosity - the coffee will cool more slowly? AARRRRGGGHHH.
I hate coffee now.

 

[robb_]

I understand your point. I am not sure of the level of the problem as given and what type of answer to give.
If the OP has studied said law, it seems the most reasonable.

 

[Backtoschool]

Could be, however we haven't discussed Newton's cooling law in class yet, so I don't think I'm supposed to use it to determine my answer.

 

[robb_]

Have you studied heat transfer equations?

 

[robb_]

are you guys sure this isn't more a matter of Newtons cooling law?

In other words adding the cream initially, will reduce the gradient between the surroundings and let's assume the rate constant is the same.

Contrast that with larger grdient for 5 minutes while you talk on phone, then adding cream?

I understand your point. I am not sure of the level of the problem as given and what type of answer to give.
If the OP has studied said law, it seems the most reasonable.

*edit again* Sorry for the double post here. I am having some troubles today it seems. Well it is a holiday of sorts. : )