Wonderment Question:If you buy a cup of coffee off campus, but want to wait until you get

to class to drink it, which is better - adding the cream right away when you buy it, or adding it later, right before you drink the coffee?

Research leads us to:Newton’s Law of Cooling

• Rate of cooling for a hot body is proportional to the difference in temperature between the body’s temperature and the temperature of its surroundings - ∆T/t = k∆T

• This results in an exponential decay curve of temperature change over time

How we propose to test this?

• Start out with a container of hot water.

• Take the temperature at regular intervals with a thermometer.

• At varying times add in a small amount of cool water.

• See how this affects the resulting temperature.

Prediction/Initial Theory:• Is it better to add cool water right away?• Is it better to add the cool water at the later time?• Or does it not make a difference either way?

Jim and I think that the later we add the cool water, the hotter the resulting temperature of the liquid will be. We based this on our understanding of Newton’s law of cooling. We base this prediction on our understanding of Newton’s Law of Cooling which states “that the rate of cooling is proportional to the difference in temperature”. So we think that if you add the cool water when the hot water is hotter it will drop the temperature more than if you add it after the hot water has cooled. (Plus, it just intuitively seems right to add the cream later.)

Getting to do actual Science

Very fun and exciting!!

Control run (w/o adding cool water)

Inconclusive ResultsFirst Run:

If we knew what we were doing, it would not be called research, would it?

-Albert Einstein

An Experiment Modified• Used a cooler temperature for liquid added, 13 ْ vs. 23˚

• More cool liquid was added: 40ml vs. 20ml

• One thermometer was used

• Improved techniques were learned from our first run

• Beer & Food = Happy Researchers

Second Run

In order to ensure a

warmer overall liquid temperature, you should add a cool liquid to a hot

liquid at the earliest possible time.

The Claim:

The Evidence

Four Varying Time Trials, or “Is it true for all times?”

Oh Those Assumptions

• We assumed that coffee reacts to Newton’s Law of Cooling the same as water. (the literature supported this)

• We assumed that a small amount of cool water would react similarly to cool cream when we added it to the coffee or hot water.

• We theorized and thus assumed, but did not have time to test that our claim holds true for any container, as we only tested in a glass beaker. (Again, this is supported in the literature and is taken into account somewhat by the constant k in Newton’s Law of cooling. But of course the cooling graph will be much flatter for a better insulated container.)

Dump in the Creamer ASAP!!!!!

• We have determined that the sooner you add a cool liquid to a hot liquid the higher the temperature of the resulting liquid mixture.

• In order to better understand this, we revisited Newton’s Law of Cooling and we believe that we initially misled ourselves. We now believe that it makes sense that it is better to have the greatest temperature change at a point on the decay curve where the rate of cooling is greatest

Another way of looking at why adding sooner is better:

• There are two things that happen when you dump the cool water into the hot water:

1. The temperature of the hot water immediately drops - and the hotter the water is, the greater the temperature drop will be.

2. The rate of cooling slows down - and the sooner you slow down the cooling rate the warmer the resulting water will be.

• The second behavior (item number 2) turns out to be more important and has a larger impact on the final resulting temperature.