HEAT TRANSFER - 3

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