How Does a Graph Demonstrate Newton's Law of Cooling?

In summary, the conversation discusses the task of using a graph of T-TR vs. Time to demonstrate Newton's Law of Cooling. The speaker is unsure of the exact requirements and asks for clarification on how to "show" this relationship. They also request suggestions on how to approach the task.
  • #1
Procrastinate
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Hi, I have a graph of T-TR vs. Time. These values were given to us for an assignment. However, the question then says using these values, "show" that it obeys Newton's Law of Cooling.

I can't ask my teacher because it's meant to be done on your own but show means many things to me.

Does show mean manipulate the equation from the graph to that of Newton's Law of Cooling? Does it mean that I have to substitute values into see if Newton's Law of Cooling works?

Could someone provide me with a few ideas? Thanks.
 
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  • #2
Draw a suitable graph of the data.
From the graph, show that the rate of cooling is proportional to the temperature difference. (Which is what Newton's Law would predict in this case.)
 

Related to How Does a Graph Demonstrate Newton's Law of Cooling?

What is Newton's Law of Cooling?

Newton's Law of Cooling is a physical law that describes the rate at which an object cools down when placed in a surrounding environment with a different temperature. It states that the rate of change of temperature of an object is proportional to the difference between its temperature and the temperature of the surrounding environment.

What is the equation for Newton's Law of Cooling?

The equation for Newton's Law of Cooling is T(t) = Te + (T0 - Te)e-kt, where T(t) is the temperature of the object at a given time, Te is the temperature of the surrounding environment, T0 is the initial temperature of the object, and k is a constant known as the cooling constant.

What are the assumptions of Newton's Law of Cooling?

The assumptions of Newton's Law of Cooling are that the object is in a well-mixed environment, the temperature difference between the object and the surrounding environment is small, and the object has a constant surface area and thermal conductivity.

How is Newton's Law of Cooling used in real life?

Newton's Law of Cooling is used in various applications, such as predicting the cooling rates of hot drinks, food items, and electronic devices. It is also used in weather forecasting to estimate the rate at which the temperature of the atmosphere changes.

What are some limitations of Newton's Law of Cooling?

Some limitations of Newton's Law of Cooling are that it assumes a constant surrounding temperature, which may not always be the case in real life. It also assumes that the object has a uniform temperature throughout, which may not be true for large or irregularly shaped objects. Finally, it does not take into account other factors that may affect the cooling rate, such as humidity and air flow.

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