Greetings Patrik
i follow the development of your model..so far.
I get stuck on the next step.
where an amount of cold milk/cream is added to the coffee(assuming black) after a specified time usually t=0 and t=300seconds
volume ~10ml
Cp will be different to water . skim milk 3.97; 'regular' milk 3.77 compared to water 4.18 kJ/?C/kg
the total volume changes from 200ml to 210ml
assuming complete mixing the 'new' temperature will decrease , however the mixed Cp is unknown so the standard calculation of ratios is difficult to use.
the contrasting treatments are to add milk at the beginning, or to wait 5 minutes (300 seconds) and add milk after allowing the coffee to cool and the milk to warm(!) ambient is 20?C
once a working model has been achieved, can the details be calibrated using 'real' data?
similar to the WSM example of the cooling kettle?
http://www.wolfram.com/system-modeler/examples/consumer-products/electric-kettle-fluid-heat-transfer.html
Looking good, so far!
My approach for High school would be to research the history of Newton and differential equations.
Identifying the scope and constraints on the 'ideal' solution.
Then introduce the concept of modelling and calibration.
the main idea to highlight the benefits of theory and experience, where there is 'never the ideal', however there can be very close approximations.
in physics anything better than 5% is considered a 'good fit', 2% a 'close' fit and <1% always the goal.
Gary
