Question about Newton's Law of Cooling

In summary, the conversation discusses Newton's law of cooking, which states that the rate of change of an object's temperature is proportional to the difference between its temperature and the ambient temperature. The constant k represents this proportionality and is dependent on the physical properties of the system. Larger or smaller values of k indicate a higher or lower rate of temperature change, respectively. There is also a suggested link for a clearer formula of the law.
  • #1
gokuls
35
0
Newton's law of cooking
T(t)= Ta+(To-Ta ) e^(-kt)
or search it up online for a cleaner formula.

Anyways, what does the cooling constant k represent. What do larger or smaller values of k mean?

Thanks
 
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  • #2
What do you mean by a "cleaner" formula? Are you working on a specific problem? Perhaps it doesn't need Newtons law of cooking to solve it?

Anyway scroll down..

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

k is a constant. Newton says the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. "Proportional to" implies a constant...

dT/dt = -k(T-Ta)k depends on the physical properties of the system... How well insulated it is, the heat capacity of the object etc
 

Related to Question about Newton's Law of Cooling

1. What is Newton's Law of Cooling?

Newton's Law of Cooling is a mathematical law that describes the rate at which a hot object cools in a cooler environment. It states that the rate of change of the temperature of an object is directly proportional to the difference between its temperature and the temperature of its surroundings.

2. Who is Sir Isaac Newton and how is he related to this law?

Sir Isaac Newton was a famous English physicist and mathematician who is credited with discovering the Law of Cooling. He developed this law while studying the cooling of hot objects in his experiments.

3. What are the applications of Newton's Law of Cooling?

Newton's Law of Cooling has a wide range of applications in various fields such as physics, engineering, and meteorology. It is used to predict the rate of cooling of hot objects and to design efficient cooling systems.

4. How is Newton's Law of Cooling different from Newton's Law of Universal Gravitation?

Newton's Law of Cooling and Newton's Law of Universal Gravitation are two different laws developed by Sir Isaac Newton. While the Law of Cooling deals with the cooling of objects, the Law of Universal Gravitation explains the force of attraction between two objects with mass. They are both important laws in physics.

5. Can Newton's Law of Cooling be applied to all types of cooling situations?

Newton's Law of Cooling is most accurate for situations where heat is transferred through convection, such as the cooling of a hot cup of coffee. It can also be applied to other situations, but the results may not be as accurate due to other factors such as radiation and conduction.

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