Milk+and+Coffee+Problem+(group+2)

Imagine that you have just poured yourself a mug of coffee (250mL) and since you prefer your coffee to be white, are about to add the milk (30mL), when the phone rings and you have to leave for 5 minutes. The question you ask yourself is if you want to drink the coffee as hot as possible, is it better to add the milk before you leave or after you return? What do you think? Does it make a difference?
 * __The Milk and Coffee Problem__**

Here is some information that will help you explore this further... The coffee when poured is 70 degrees Celsius. The milk is 5 degrees Celsius. The room stays at a constant temperature of 20 degrees Celsius. If the milk and coffee are left to stand seperately, during the 5 minutes the coffee would have fallen to 60 degrees Celsius, the milk would have risen to 8 degrees Celsius.
 * The Calculated Version:**


 * The Actual Experiment:**


 * Cooling time of coffee only**
 * Minutes Passed || Degrees In Celsius ||
 * 0 || 70.3 ||
 * 0.5 || 68.7 ||
 * 1 || 67.5 ||
 * 1.5 || 66.3 ||
 * 2 || 65.1 ||
 * 2.5 || 64.0 ||
 * 3 || 63.3 ||
 * 3.5 || 62.5 ||
 * 4 || 61.9 ||
 * 4.5 || 61.2 ||
 * 5 || 60.6 ||

Expreg: 69.50894938 * 0.971139196 ^ x

Expreg: 5.084423464 * 1.095570341 ^ x
 * Heating time of milk only**
 * Minutes Passed || Degrees In Celsius ||
 * 0 || 5.1 ||
 * 0.5 || 5.3 ||
 * 1 || 5.6 ||
 * 1.5 || 5.8 ||
 * 2 || 6.1 ||
 * 2.5 || 6.4 ||
 * 3 || 6.7 ||
 * 3.5 || 7.0 ||
 * 4 || 7.3 ||
 * 4.5 || 7.6 ||
 * 5 || 8.1 ||

Calculating the temperature for adding milk after leaving coffee for 5 minutes:

Using the results obtained from our experiment, we concluded that if you left the coffee out for 5 minutes before adding the milk in, the temperature would be 54.98 degrees, which is 0.56 degrees off from the calculated version.


 * Coffee and milk added before leaving**


 * Minutes Passed || Degrees in Celsius ||
 * 0 || 63.1 ||
 * 0.5 || 62.1 ||
 * 1 || 61.2 ||
 * 1.5 || 60.2 ||
 * 2 || 59.4 ||
 * 2.5 || 58.4 ||
 * 3 || 57.5 ||
 * 3.5 || 56.7 ||
 * 4 || 55.9 ||
 * 4.5 || 55.0 ||
 * 5 || 54.1 ||

Expreg: 63.07607199 * 0.9699315431

Using the results obtained from our experiment, we concluded that if you left the coffee and milk out for 5 minutes, the temperature would be 54.10 degrees, which is 0.329 degrees off from the calculated version.

Conclusion: From our experiment, there was approximately a 1 degree difference in the two scenarios, which we believe would really not make a difference if you were to drink it, as you wouldn't be able to tell anyway.

There were many sources of error in our experiment. We didn't start at 70 degrees C, and the constant temperature was 17 degrees C instead of 20. We encountered a lot of problems during the experiment such as not having enough calculators to graph the data and using a thermometer to measure the temperature. Our data did not fit our 'perfect' model because the environment was different.