Newtons law of Cooling - Definitions, Formula and Graph

Newton law of cooling

Hello student and my dear friends today here you learn about newtons laws of cooling. After reading this thing you will get knowledge about newtons laws of cooling. Here you will get Derivation, formula and definition as well as graph this all thing clear your topic.

What is Newton laws of Cooling ?

1. Definition

Newton's Law of Cooling states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its surroundings. In other words, the law describes how the temperature of an object changes as it loses heat to its surrounding environment.

Mathematically, the law can be expressed as:

dT/dt = -k(T - Tₒ)

where:

• dT/dt is the rate of change of temperature of the object with respect to time
• k is a constant that depends on the properties of the object and its surroundings
• T is the temperature of the object at any given time
• Tₒ is the temperature of the surrounding environment.

This equation states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the temperature of the surrounding environment. The constant k is determined by factors such as the material and shape of the object, the medium through which heat is transferred, and the temperature difference between the object and its surroundings.

2. Newton law of Cooling Graph

The graph of Newton's Law of Cooling shows the relationship between the temperature of an object and time as it loses heat to its surrounding environment. The graph is typically exponential in shape and can be used to determine the rate of cooling and the time required for an object to reach a specific temperature. The general shape of the graph is as follows: At the beginning, the temperature difference between the object and its surroundings is greatest, so the rate of cooling is highest. The temperature of the object decreases rapidly at first. As time goes on, the temperature difference between the object and its surroundings decreases, and so does the rate of cooling. The temperature of the object decreases more slowly. Eventually, the temperature of the object approaches the temperature of the surrounding environment, and the rate of cooling becomes negligible. The temperature of the object becomes constant. The exact shape of the graph depends on various factors, such as the initial temperature difference, the constant k, and the surrounding environment. However, it generally follows an exponential decay curve.

3. Limitation of Newton law of Cooling

Newton’s law of cooling explains how fast a hot object can cool down. While Newton's Law of Cooling is a useful tool for describing the behaviour of an object as it loses heat to its surrounding environment, it has certain limitations

Solved Example of newtons law of Cooling

Q. A body at temperature 40ºC is kept in a surrounding of constant temperature 20ºC. It is observed that its temperature falls to 35ºC in 10 minutes. Find how much more time will it take for the body to attain a temperature of 30ºC.

A. 112 min

B.  56 min

C. 28 min 

D 14 min 

This an one example of newton law of cooling. please students solve this example and let comment to for right answer. If You not getting answer then do comment and I will reply your answer and also I you have any doubt regarding Question let me know and put your comment