A general curve for the coffee cup problem.

AI Thread Summary
The discussion focuses on understanding the temperature behavior of a hot coffee cup cooling on a table, specifically questioning the shape of the temperature function over time. It suggests that the temperature likely follows a curve rather than a straight line, as it approaches room temperature gradually. The cooling process is linked to Newton's law of cooling, indicating that the rate of temperature change is proportional to the difference between the coffee's temperature and the room temperature. Additionally, there's curiosity about how the coffee cup's heat affects the surrounding room, relating to the second law of thermodynamics. Resources and formulas for better accuracy in calculations are sought to enhance understanding of these concepts.
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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