# A general curve for the coffee cup problem.

• mooobag
In summary, the conversation discusses the concept of graphing the temperature of a hot coffee cup as it cools on a table. The individual is seeking resources, such as formulas and graphs, to accurately complete their calculus homework. They also question the shape of the temperature function and how to calculate the amount of heat the coffee cup transfers to the room. A link is provided for further information on the topic.
mooobag
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?

## What is the coffee cup problem?

The coffee cup problem is a mathematical puzzle in which a loop of string is placed around the handle of a coffee cup and then the string is pulled tight. The question is whether the string can be moved around the cup in such a way that it can be removed without cutting or breaking the string.

## What is a general curve for the coffee cup problem?

A general curve for the coffee cup problem is a mathematical formula that represents the shape of the loop of string as it is pulled tight around the cup. This curve can be used to analyze and solve the problem for different sizes and shapes of cups.

## Why is the coffee cup problem important?

The coffee cup problem is a fun and challenging puzzle that can help develop problem-solving skills and critical thinking. It also has real-world applications in fields such as mathematics, physics, and engineering.

## What are some possible solutions to the coffee cup problem?

There are several possible solutions to the coffee cup problem, including using multiple loops of string, creating a knot in the string, or using different methods of pulling the string tight around the cup. The specific solution may vary depending on the size and shape of the cup.

## How can a general curve be used to solve the coffee cup problem?

A general curve can be used to analyze the properties of the loop of string as it is pulled tight around the cup. By studying the curve, we can determine if the string can be removed without cutting or breaking it and find the most efficient way to do so.

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