First-year calculus

Two people drinking coffee. One immediately adds a teaspoon of cream to his. The other waits 5 minutes then adds the cream (which is at a constant temperature). Then they both drink their cofee.

Who has the hotter coffee? Assume that the cream is cooler than the air and use Newton's law of cooling.

Now, I know Newton's law of cooling, but I can't figure out how to solve this one using it (and not just logicing my way through). I mean, how do I start it? Should I assign arbitrary temperatures (ie cream - 60, room-70, coffee - 100) and try to do the math? If so, I'd need to decide on how much coffee is in each cup and then use some physics to calculate how much the coffee is affected by a teaspoon of cream... Which seems ridiculous considering I don't think my professor would want us to do that for our calc class.

I know that I shouldn't be asking for homework help on the internet, but this isn't really a homework problem and it's been bugging me. I just can't think of the proper way to approach it...

I think the patient man has the cooler coffee, but I'm really not sure how I can show this using Newton's Law of Cooling...

I think it depends whether the cream is cooler than room temperature

>>3
Assume the cream is cooler than the air ...

No need to get physical and use actual numbers. Just call the room temperature T, the coffee temperature at time t C(t) and the cream temperature D or something, and then use the fact that C(0) > T > D plus Newtons equation. The effect of the cream can be considered a constant drop in temperature, probably.

Get a better creamer.

I think you assume that the cream drops the coffee's temperature instantaneously.  >>2 is right; Newton's law of cooling comes in from the fact that temperatures approach equilibrium by an exponential curve (derivative -> 0 as t->infinity).

No need to do any calculation.

The energy in the cup at the end is equal to the energy in the cream and tea at the start, minus energy lost to surroundings.

Which scenario loses more heat to the surroundings? Clearly the one that started out hotter. (calculate it if you have to, trivial)

So adding the cream first cools it faster.

Which scenario loses more heat to the surroundings? Clearly the one that started out hotter.

So if you lose more heat over the time period if you start out hotter, shouldn't you not add the cream first, because then you will start out with a cooler cup of liquid?

Yeah, sorry, adding the cream at the end cools it faster. Whoops.

OP, several problems.
1) What IS Newton's Cooling Law? Post the relevant equation please.
2) F is for Fahrenheit... But also fail.
3) Going from what >>7 said, obviously both will have the same average temperature.
4) Going from 3, the question is bullshit. Say you swallow a niggercock which is 80C on one end and -20C on the other. Have you swallowed a hot niggercock, or a cold one?

Because temperature is defined in relation to the average kinetic velocity, by definition and 3 both *liquids* have the same temperature. They may have different entropies when drank. This might mean the average kinetic energy of cream molecules is lower than that of coffee molecules, but that is stupid.

Anyway, if Newton's law says what 4tran says it says, then what the question means, I think, is:

You have 2 slabs at T(1) and 2 slabs at T(2). All are cubes of equal volume. You put one hot slab on a cold slab, wait 5 minutes, then put the second hot slab on the second cold slab. Which is closer to equilibrium? Obviously, the one you put in contact first.