# Limit of Newton's Law of Cooling....2

• MHB
In summary, the conversation discusses finding the limit of u(t) as t approaches 0 from the right side, which is determined to be u_0. The conversation also mentions the Law of Cooling and whether it can be graphed. In addition, the conversation briefly mentions problem 1.5.75.b and suggests posting a screenshot of the entire problem for better understanding. Finally, there is a request to not make helpers guess the condition for k and to instead provide a clear question.
Given u(t) = (u_0 - T)e^(kt) + T, find the limit of u(t) as t tends to 0 from the right side.

The answer is u_0. How is the answer found? Seeking a hint or two.
Can this Law of Cooling be graphed? If so, what does the graph look like?

Beer soaked ramblings follow.
Given u(t) = (u_0 - T)e^(kt) + T, find the limit of u(t) as t tends to 0 from the right side.

The answer is u_0. How is the answer found? Seeking a hint or two.
Can this Law of Cooling be graphed? If so, what does the graph look like?
Problem 1.5.75.b.
Some details left out.
Suggest you post a screenshot of the entire problem instead of making helpers guess the condition for k.

Look at 75 parts (a) and (b). You are not helping by telling me to go back to the question. I want to learn how this is done.

Beer soaked suggestion follows.
Look at 75 parts (a) and (b). You are not helping by telling me to go back to the question. I want to learn how this is done.

View attachment 11043
Do us all a favor and post a screenshot of your problem so we don't have to task our imagination with sloppy typing.

## 1. What is the Newton's Law of Cooling?

The Newton's Law of Cooling is a mathematical equation that describes the rate at which an object cools down or heats up when it is in contact with a medium that has a different temperature. It states that the rate of change of temperature of an object is proportional to the temperature difference between the object and its surroundings.

## 2. What is the limit of Newton's Law of Cooling?

The limit of Newton's Law of Cooling is the point at which the temperature difference between the object and its surroundings becomes zero. In other words, when the object reaches thermal equilibrium with its surroundings, the rate of change of its temperature will be zero and it will no longer cool down or heat up.

## 3. How is the limit of Newton's Law of Cooling calculated?

The limit of Newton's Law of Cooling can be calculated by setting the rate of change of temperature to zero and solving for the temperature difference between the object and its surroundings. This can be done by rearranging the equation and using algebraic methods.

## 4. What factors can affect the limit of Newton's Law of Cooling?

The limit of Newton's Law of Cooling can be affected by various factors such as the initial temperature difference between the object and its surroundings, the thermal conductivity of the medium, the surface area and shape of the object, and the presence of any insulating materials.

## 5. How is the limit of Newton's Law of Cooling used in real-life applications?

The limit of Newton's Law of Cooling is used in various real-life applications, such as in refrigeration and air conditioning systems, food preservation, and in predicting the rate of cooling of hot liquids in cooking. It is also used in industries that involve heat transfer, such as in manufacturing and chemical processes.

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