HELP Derive Newton's Law of cooling

• Doctor_Doom
In summary, Newton's Law of Cooling is a mathematical equation that describes the rate of heat loss of an object as it cools in a surrounding environment. It can be derived by conducting experiments and has many practical applications in various fields. The law is based on the Second Law of Thermodynamics and has some limitations, such as assuming a constant environment and no external factors.
Doctor_Doom
Hey guys was hoping someone could give me a hint for the derivation of Newton's Law of cooling stated in the following equation form:http://img263.imageshack.us/img263/3143/a6e5a27835e9e5738016606.png

http://img716.imageshack.us/img716/8728/75784887.jpg

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Bump!

Found plenty of derivations in the form of temperature or temperature change but nothing in the form of heat (energy) rate transfers.

1. What is Newton's Law of Cooling?

Newton's Law of Cooling is a mathematical equation that describes the rate of heat loss of an object as it cools in a surrounding environment. It states that the rate of change of temperature of an object is directly proportional to the difference between the object's temperature and the temperature of its surroundings.

2. How can Newton's Law of Cooling be derived?

Newton's Law of Cooling can be derived by conducting experiments and collecting data on the temperature of an object as it cools in a controlled environment. The data can then be plotted on a graph and analyzed to determine the rate of heat loss and the proportionality constant. This process can be repeated with different objects and environments to validate the law.

3. What is the significance of Newton's Law of Cooling?

Newton's Law of Cooling has many practical applications in various fields such as engineering, physics, and meteorology. It is used to predict the cooling rates of objects in different environments and to design efficient cooling systems. It also helps in understanding the thermal behavior of different materials.

4. How does Newton's Law of Cooling relate to the Second Law of Thermodynamics?

Newton's Law of Cooling is based on the Second Law of Thermodynamics, which states that heat always flows from a hotter object to a colder object. This law provides a mathematical framework to quantify the rate of heat transfer and the direction of heat flow in a cooling process.

5. Are there any limitations to Newton's Law of Cooling?

Yes, there are some limitations to Newton's Law of Cooling. It assumes that the surrounding environment is at a constant temperature and that there are no external factors affecting the cooling process. In real-life situations, this may not always be the case, and the law may not accurately predict the cooling rate.

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