A general curve for the coffee cup problem.

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mooobag
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This isn't really homework but my homework made me wonder about this. Any good links to formulas, graphs etc would help make my calc homework unnecessarily accurate.

I'm in a calc class we've been getting problems that require us to graph the temperature of a hot coffee cup as it sits on a table.

All the problems require is that we know that the coffee cup sinks to the temperature of the room over time and stays there but I wonder this:

What shape does the temperature function take?
is it a curve?
is it a line?
does the temperature plummet and take a sharp turn toward the infinite?

Also, how do I figure out how much the coffee cup heats the room? This is the second law of thermodynamics right?
 
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