Stefan Boltzmann Law Formula and Problems

Stefan Boltzmann Law Calculator :

This Stefan Boltzmann law calculator describes the Area in meter square(m²), Temperature in °C, Radiated power in watts(W), and you get the calculator check it.

Stefan Boltzmann Law Calculator

Stefan Boltzmann Law Formula :

Stefan  Boltzmann law formula is the net power of radiation P(ev) in electro volts is equal to the emissivity e(w/m) in watt per meter and multiply the Stefan’s constant σ(wm-2 k4) in watts per meter kelvin4 and multiply the area of radiation A(s/m) in square per meter and multiply the radiator temperature Tr(k) in Kelvin and multiply the surrounding temperature Tc(k) in Kelvin. Hence the Stefan  Boltzmann law  formula can be written as

P(ev)=e(w/m)* σ(wm-2 k4) *A(s/m)(Tr(k)-Tc(k))4

Where,

P→ net power of radiation in electro volts

A→ area of radiation in square meter2

Tr→ radiator temperature in kelvin

Tc→ surrounding temperature in kelvin

e→ emissivity in w/m

σ→ Stefan’s constant(σ=5.67*10-8 Wm-2 K-4)

u/A= σ *T4

where σ → Stefan’s constant =5.67*10-8 W/m2 K4

u=e * σ*AT4

Δu=u-u0= e * σ*A[T4-T04]

dp/d λ =1/A=2 π hc2/ λ5(ehc/ λkT-1)

Problem :1

Calculate the initial value of net power emitted by the body? In a body of emissivity (e=0.75), the surface area of 400cm2 and temperature 3230 c are kept in a room at temperature 470c and Stefan’s Boltzmann law.

Answer:

P=e* σ*A (T4-T04)

=(0.75)(5.67*10-8 W/m2-K4)(400*10-4 m2)*[(500K)4-(300K)4]

=-29.9watts

Example:2

Calculate the value of energy radiated in Jm-2 S-1? In ahot black body emits the energy at the rate of 15 j m-2 s-1 and its most intense radiation corresponds to 40,000 A0.When the temperature of this body is further increased and its most intense radiation corresponds to 30,000 A0,

Answer:

Wein’s displacement law is λm *T=b

T∝[1/ λm]

Here λm becomes half, the Temperature doubles

Now from Stefan Boltzmann Law e=ST4

e1/e2=(T1/T2)4

= e2 =(T1/T2)4

e1=(4)2.15

=16.15 J m-2 S-1

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