Half-Life Phenomena: Comparing to Hot Coffee

[barcat]

The book we are using (Physics 101) has shown quit
well that there will be a greater quantity of heat
loss (and faster), of a substance to it’s environment,
if the difference of temperatures between the two is
greater. Also, there will be initially a faster rate
of heat loss / time due to this greater difference in
temperature.

Can one compare this effect to that of the half-life of
radioactive decay? I believe I understand correctly,
that a “Hot” radioactive substance will lose (decay)
more energy during the same time frame (half-life cycle)
than a same sample that is “Cold” as there is more
energy to be cut in half during the same amount of time.

If this is correct, then it shows that as a substance
looses heat, the slower it looses heat, as it gets
cooler.

The reason I say this is we had a discussion question that
asked when to add cream to hot coffee. If there was going
to be a wait prior to drinking it, do you add the the cream
as soon as possible, or just before you drink it? The idea
is the best way to have the hottest coffee that has sat for
length of time.

Does anyone have any thoughts about this?

 

[jamesrc]

I don't know if this answers your question, but there are 3 basic types of heat transfer:

1.) conduction: heat transfer is proportional to the change in temperature (something like qdot = k(Thot-Tcold), where qdot is heat flux rate and k is thermal conductivity))

2.) convection: heat transfer is proportional to the temperature change, but also has factors that are dependent upon geometry and temperature (fluid mechanics gets involved here).

3.) radiation: the rate of heat transfer here is proportional to T^4

So in any case, the closer a substance is to ambient temperature to begin with, the lower the heat transfer will be.

 

[barcat]

jamesrc;
I re-read my post and it even confused me. I guess the questions I am asking is: is it true the hotter a susbtace is the faster it will cool during a particular time period? Will cooling the coffee by adding the cream sooner (rather than waiting) provide the hottest result later.
I agree there are quit a few variable not taken into account. By adding the cream, doesn't it lighten the solution making it less of an absorber/emitter? Does the density of the cream also affect this rate of heat transfer of the final solution?
Thanks-barry.

 

[jamesrc]

Hmmm...

I don't drink coffee, so don't take this as definitive, but here's my initial reaction: the sooner you put the cream in, the hotter the coffee will be. (If you wait long enough, it won't make a difference, because it will end up at room temperature anyway.) If you simplify the situation and assume that heat is lost to the environment purely through conduction and the relationship between heat and temperature of the substance is from calorimetry, then you have an exponential decay in temperature (which you were driving at with your half-life analogy). The drop in temperature due to the addition of the cream will be on a much faster time scale than the overall cooling of the coffee. If you drop the cream in earlier, you will reduce the temperature difference between the mixture and the environment and, therefore, reduce the rate of heat transfer. This way, the earlier you drop in the cream, the hotter the coffee stays.

Oh, and by cream I'm assuming it's some slightly lower than room temperature half-and-half as opposed to some kind of solid cream (that would undergo a phase change).

 

[barcat]

jamesrc, you hit the nail right on the head. That is exactly what I was trying to say but could'nt get it out.

Originally posted by jamesrc

Oh, and by cream I'm assuming it's some slightly lower than room temperature half-and-half as opposed to some kind of solid cream (that would undergo a phase change).

This is another variable that I never thought to think of.

This Conceptual Physics course I'm taking seems to leave quit a bit of room for personal opinion to play a role.

On my last exam, there was a question with regard to Chemistry.

The question was- What lends more to the properties of a chemical; a. electrons, b. protons, c. it's size, or d. the distance the protons and electrons?

I chose (b) because the Chem-101 class I just finished indicated that it is the number of protons in the nuclus that dictate the chemical properties of an element. I ended up getting it wrong...no explanation!