A general curve for the coffee cup problem.

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    Coffee Curve General
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SUMMARY

The discussion centers on modeling the cooling of a hot coffee cup using Newton's Law of Cooling. The temperature of the coffee cup decreases over time, approaching room temperature asymptotically. The temperature function is a curve, reflecting an exponential decay rather than a linear decline. Additionally, the impact of the coffee cup on room temperature is linked to the second law of thermodynamics, emphasizing the heat transfer process involved.

PREREQUISITES
  • Understanding of Newton's Law of Cooling
  • Basic calculus concepts, particularly related to exponential functions
  • Familiarity with the second law of thermodynamics
  • Graphing skills for temperature vs. time analysis
NEXT STEPS
  • Research Newton's Law of Cooling and its mathematical formulation
  • Explore differential equations related to cooling processes
  • Learn about the second law of thermodynamics and its implications in heat transfer
  • Practice graphing exponential decay functions to visualize temperature changes over time
USEFUL FOR

Students in calculus or physics courses, educators teaching thermodynamics, and anyone interested in the mathematical modeling of heat transfer processes.

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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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