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Newton's Law of Cooling

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Newton's Law of Cooling - Lesson Summary

It is a common phenomenon that a hot body exchanges heat with its surroundings and cools.
The heat lost by the body to its surroundings per unit time is called the rate of cooling of the body and depends on several factors.When a graph is plotted by taking delta T along the y-axis and time t along the x-axis we get a curve.
 
 
 
The graph indicates that the cooling of water depends on the temperature difference between the water and its surroundings.
The greater the temperature difference, the greater the fall in the temperature of the hot water.
With the passage of time, the temperature difference between the hot water and its surroundings decreases, and hence the change in the temperature of the water also decreases.
Newton made a systematic study of the cooling of different bodies and proposed a law known as Newton’s Law of Cooling that holds good for small differences in temperature between a hot body and its surroundings.
 
Newton’s Law of Cooling states that the rate of heat lost by a body is directly proportional to the difference in temperature between the body and its surroundings.


The law is applicable to small temperature differences. Even when the transfer of heat is due to a combined effect of conduction, convection and radiation, the rate of cooling is proportional to the difference in temperature.
 
Newton’s Law of Cooling can be verified by conducting the following experiment.
A double-walled vessel is filled with water between the walls and the mouth of the vessel is closed with a cork through which a thermometer is inserted.

Let the temperature reading be T 1 degrees Celsius.
A copper calorimeter with hot water is placed inside the vessel.
Close the mouth of the calorimeter with a two-holed cork with a stirrer passing through one hole and a thermometer through the other.
 
Let the reading in this thermometer be T 2 degrees Celsius.
The temperature of the hot water in the calorimeter is noted after equal intervals of time.
When a graph is plotted with log to the base e into T 2 - T 1 along the y-axis and time t along the x-axis based on the experimental results, we get a straight line with a negative slope.

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