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# Can anyone explain briefly explain about the NEWTONS METHOD OF COOLING and WEINS DISPLACEMENT...??

11 years ago

Newton's method of cooling explains the rate of cooling of a substance when it is placed in the surroundings having a temperature lower than its own temperature. It can be derived from stefan boltzmann law of radiation of energy. i.e. it radiates more energy than it receives.. hence, its temperature drops.

Newton's law of cooling, states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. The law is $\frac{d Q}{d t} = h \cdot A( T_{\text{env}}- T(t)) = - h \cdot A \Delta T(t)\quad$
Q = Thermal energy in joules
h = heat transfer coefficient
A = Surface area of the heat being transferred
T = Temperature of the object's surface and interior (since these are the same in this approximation)
Tenv = Temperature of the environment
ΔT(t) = T(t) − Tenv is the time-dependent thermal gradient between environment and object

Now, for wein's displacement law, it says that, radiation is emitted by any black body in the form of combination of many electromagnetic waves, i.e. the radiation consists of many wavelengths out of which one wavelength has a maximum intensity. This maximum wavelength is inversely proportional to Temperature, i.e. higher temperature => higher energy => lower wavelength. $\lambda_{\mathrm{max}} = \frac{b}{T}$

Where $\lambda_{\mathrm{max}}\!$ is the wavelength of peak intensity in meters; $T\!$ is the temperature of the blackbody in kelvin; $b\!$ is a constant of proportionality called Wien's displacement constant and is equal to 2.8977685(51)×10−3 m·K

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Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We

Regards,

Rohith Gandhi P

11 years ago

To explain the Newtons law in a precise u can conduct  a simple experiment. Take hot coffee in a cup and measure its temperature. Now after some time again take the measurement and continue the coffee  to cool again. After making such measurements untillthe cofee reaches the room temperature, we notice that the cooling was fast when the temperature difference between the coffee and the surroundings is high and as the temperature difference decreases then the time of cooling increases.

Rate of cooling is nothing but rate of heat transfer is directly realated to the temperature difference between the substance to be cooled and the surroundings.

Also instead of conducting the experiment in a cup if do it in a plate which has larger surface area then this rate even increases more. Thus, we can  write a relation between these factors with a constant called heat transfer coefficient we get a relation as shown in the figure

Veins Displacement law:

To know about this law we have to study about black body radiations emitted. The black bodies are the objects that can absorb all kinds of radiations incident on it and can emit all kinds of radiations. At a given temperature it cannot emit a paticular wavelenth it would emit a broad band of wavelengths that show a peak in the intensity distribution at certaian wavelength λmax.

λmax= b/T

Where λmax=  the wavelength of peak intensity

b = constant of proportionality,

T = Temperature of the black body

This value decreses as the temperature of the black body decreses signifying that at higher temperatures the peak emission wavelength decreases i.e., peak shits towards left signifying the emission of more energetic radiations.  This is also shown in the figure below the first figure.

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We

All the best  !!!

Regards,  