Newton’s Law of Cooling Lab Experiment

This experiment was designed to model the process in which thermal energy moves from one body to another. Newton observed that the energy transfer between two bodies is proportional to the difference in temperature between the bodies. The cooling of hot water to room temperature will be observed for the model.

Data table:

Analysis:

Newton’s cooling law was given above as:
T = T0 e–kt + Troom

Match the variables x, y, A, B, and C in the fitted equation to terms T, T_{o ,} Troom, k, and t in the expression of Newton’s Cooling Law. What are the units of A, B and C?
x = time, t; y = temperature, T; A = T_o; B = T_room; C = k
A is in Celcius; B is in Celcius; C is a co-efficient

When t = 0, what is the value of e–kt?
1 = e–k(0)

When t is very large, what is the value of temperature difference? What is the temperature of the water at this time?
The value of the temperature difference is zero when t is large and therefore the water temperature is about room temperature.

What could you do to your experimental apparatus to decrease the value of k in another run? What quantity does k measure?
K is the coefficient of cooling and it will experimentally decrease if the calorimeter is better insulated.

QUESTIONS

1.   Is it better to immediately add the room temperature cream, stir the coffee, and let it sit for tem minutes, or is it better to let the coffee sit for tem minutes and then add and stir in the cream?  Which results in a higher temperature after ten minutes?  Explain your results in terms of the assumptions Newton made about cooling.

It is better to immediately add the room temperature cream because it will allow a smaller temperature difference between the contents of the cup and the surroundings for the 10 minutes. The rate of cooling is proportional to the difference in temperature of the cup and the surroundings, so the coffee will stay warm longer with the cream added initially.

2.  You want to design an experiment to determine whether a drink cool faster in a ceramic cup than in a Styrofoam cup?  What variables must you hold constant in order to guarantee that the difference in the data is due to the cup?  What part of the exponential equation is related to the cup?

Variables that must remain constant are room temperature and initial temperature. The rate of cooling, k, is related to the cup.

CONCLUSION
The equipment used in the experiment observed the room temperature in error, about 10 degrees Celcius higher than the actual value. However, the model was accurate in showing Newton’s law of cooling.