- #1

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Say I don't like to drink hot tea, in fact I don't like to drink anything hot. It is beyond my comprehension why anyone would want to drink something above 40C ;)

I have cup of hot tea 100C and i want to know how long will it take to cool down to 40C.

[tex] \frac{\Delta Q}{\Delta t}[/tex] = -k A [tex]\frac{\Delta T}{\Delta x} [/tex]

(for some reason I can't get the equation to display correctly)

so i have k of course, "delta x" would be the thickness of the mug wall, A is also given . The "delta T" part is the difference between tea and air temperature, i guess?

Now my approach would be to write an iterative algorithm, that will calculate the "instantaneous" heat flux, then lower the temperature a bit and advance time, then calculate heat flux again. Unless there is some other equation which will let me calculate it in a non-iterative way?

It seems silly that I have to iterate just to get an answer to such simple question...

This is of course if I neglect the evaporation effect, say the mug is closed, it is a fancy mug.