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Heat Transfer
Tags: Engineering Entrance  |  IIT JEE  |  Thermal Physics
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Stefan's Law of Radiation:
Stefan's Law of Radiation:
The total radient energy emitted E per unit time by a black body of surface A is propertional to the fourth power of its absolute temperature.

    E T4

or E = AT4      = Stefan's const

For abody which is not black body

E = AT4       = emmisitivity of te Black Body.

Note: Emmisitivity and absorptive power have the same value.

Net loss of thermal Energy[secondary information]:
If abody of surface area A is kept at absolute temp T in asurrounding of temperature T0(T0 > T) Then the energy emitted by the body per unit time.

E = AT4

And the energy absorbed per unit time by the body

E0 = AT04

Net loss of thermal energy per unit time.

E = E - E0 = A[T4 - T04]

Newton's Law of Cooling:
For a small temperature difference between a body and its surroundings, the rate of cooling of the body is dirctly propertional to the temperature difference. If abody of temperature T and surface area A is kept in a surrounding temperature T0(T0 < T). Then net loss of thermal energy per unit time.

= A(T0 - T00)

If the temperature difference is small

     T = T0 + T

=> A[(T0 + T)4] = A[T04 (1 + )4 - T04]
=> AT04[1 + 4 + higher powers of - 1]

= 4AT03T

Now, Rate of loss of heat at temperature T



mc = - 4AT03[T - T0]

= - K[T - T0]

K =

(T - T0)

WIENS LAW:
At a const temperature T, when wavelength is increased , the energy emitted E, first increases, reaches a maximumand then decreases i.e at a particulartemperatuure the spectral radiancy is a maximum at a particular wavelength m.

 

As the temperature increases , the maximum radiancy of energy occurs at shorter wavelength i.e

mt = b
b is a constant.
This is called wiens Displacement Law.
Dumb Question
:

Q: At a particular wavelength the bodies A, B, C, have their emmisive Power in Ratio 1:2:3. what is the ratio of the absorptive power ?
A: 1:2:3 became

= constant
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