Newton's Law of Cooling

Physics

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Plot of temperature vs time for Newton's Law of cooling

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Plot of log of temperature difference vs time for Newton's Law of cooling

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Experimental verification of Newton's Law of cooling

Newton's Law of cooling can be verified with the experimental set-up shown in the figure. The set-up consists of a double walled vessel (V) containing water in between the walls. A copper calorimeter (C) containing hot water is placed inside the double walled vessel. Two thermometers through the corks are used to measure the temperatures of water in calorimeter and of hot water in between the double walls respectively. Temperature of hot water in the calorimeter is noted after fixed intervals of time. A graph is plotted between  and time(t). The nature of graph is observed to be a straight line having a negative slope which is in accordance of the equation of Newton's Law of cooling.

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Describe the limitations of Newton's Law of Cooling

The limitations of Newton's Law of cooling are as follows:
1. It can be used only at lower temperatures.
2. It can only be use when difference between initial and final temperatures is less than 50-80 degree Celsius.
3. It 
holds true only if the temperature of the surroundings remains constant throughout the cooling of the body.

definition

Newton's Law of Cooling

Here, is time, is temperature of the object, and is the surrounding temperature. 
Newton's Law of Cooling :
Newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surrounding.

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Assumptions of Newton's Law of Cooling

Assumptions of Newton's Law of Cooling are as follow :
1. Temperature difference between the object and surrounding should be small.
2. The nature of radiating surface should remain same.

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Newton's Law of Cooling - L1

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Important Questions

A body cools from C to C in minutes. Calculate the time it takes to cool from C to C. The temperature of the surroundings is C.

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Certain quantity of water cools from to in the first minutes and to in the next minutes. The temperature of the surroundings is ;

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A body cools down from to in Minutes when the temperature of surrounding is . The temperature of the body after next minutes will be:

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A sphere , a cube and a thin circular plate,all of same materials and same mass, are initially heated to same high temperature. 

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A body cools in minutes from to . If the temperature of surrounding is , the temperature after next minutes will be :

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A pendulum clock is sec fast at temperature of and sec slow at a temperature of . At temperature does it give the correct time-

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A body cools from 50C to 45C in 5 min and to 40C in another 8 min. The temperature of the surrounding is

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Hot water cools from to in the first minutes and to in the next minutes. The temperature of the surroundings is :

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Spheres and are uniformly constructed from the same material which is a good conductor of heat and the radius of is thrice the radius of . The rate of fall of temperature of is times that of . When both are at the same surface temperature, the value of is :

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Two identical masses of each fall on a wheel from a height of . The wheel disturbs a mass of water, the rise in temperature of water will be:

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