My coffee is cooling down so fast ... Simulation with the Vensim ...

My coffee is cooling down so fast ...
Kick-off
Your mobile rings at a very unsuitable moment:
Your coffee is ready, the cream not yet put in.
You don’t like cold coffee ...
Do you finish the preparation of your coffee or put in the cream after answering the
phone?
What does the cooling down of a liquid depend on?
Write down the parameters.
How could you decelerate the cooling down of your coffee?
What measurements could you perform?
Another approach might be to deal with the warming process of a fresh bottle of coca
cola on the beach ...
Proceeding with the Vernier equipment
Connect the temperature probe to LabQuest or Go!Link, and LabQuest or Go!Link to
your computer.
Stop and think!
Discuss the setup of the experiment with an other group and make sure to choose
different setups.
Design the graphs as you would expect them for the different setups!
Start the Logger Pro program and follow your teacher’s explanations.
Fix the temperature probe at a tripod and prepare your liquid for the experiment.
Start the data collection by clicking the green button.
Observe the curve on the screen and stop the data collection at an adequate
moment.
Presentation of the results
a) Copy your graph into a word document.
b) Give an explanation of the graph.
c) How could you express the curve shape in one constant?
d) Where did you meet similar forms of graphs?
e) As an exercise in Excel you can transfer the table with all the measured values
from LabPro to Excel and establish an XY-graph of the absorbance as a function
of time.
f) Determine the mathematical function of the trend line and the value of the
constant with help of the trend line (menu diagram / trend line) as follows:
Click once at any part of the curve in the diagram / choose the menu diagram /
Choose add trend line ... / choose the type of trendline / in the options mark place the formula
in the diagram
Simulation with the Vensim software
Free download Vensim PLE: http://www.vensim.com/download.html
Design a model and simulate the shape of the curve measured.
Write down dependencies as ...
The higher the ..., the faster ...
You can find out how the model will look like on the next page.
But first try to design your own model.
Cooling down of liquids Christian Eggenberger 2011 page 1 of 2

Diagram of the simulation model
temperature of
ambiance
heat in the
liquid
half life
k
cool down
temperature difference
Documentation: equations and parameters
(01) cool down=k*temperature difference / Units: °C/Second [0,?]
(02) FINAL TIME = 6000 / Units: Second / The final time for the simulation.
The higher the temperature
difference between the liquid and the
ambiance, the faster the liquid will
cool down, the greater the value of
the cooling down constant k.
In an extrem case with an ambiance
of the same temperature as the
liquid, the liquid would not cool down.
(03) half life=950 / Units: Second
(read out of the cooling down curve of the same liquid in the same experimental setup over night from
64°C to 22°C)
(04) heat in the liquid= INTEG (-cool down,65) / Units: °C [0,90]
(heat quantity as temperature per cup)
(05) INITIAL TIME = 0 / Units: Second / The initial time for the simulation.
(06) k=LN(2)/half life / Units: 1/Second
(07) SAVEPER = TIME STEP / Units: Second [0,?]
The frequency with which output is stored.
(08) temperature difference=heat in the liquid-temperature of ambiance / Units: °C [0,?]
(09) temperature of ambiance=22 / Units: °C [5,40,1]
(10) TIME STEP = 10 / Units: Second [0,?] / The time step for the simulation.
Special thanks go to Barbara Melo for her collaboration with the English revision.
Cooling down of liquids Christian Eggenberger 2011 page 2 of 2