### 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 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 kelvin^{4} and multiply the area of radiation A_{(s/m)} in square per meter and multiply the radiator temperature T_{r(k)} in Kelvin and multiply the surrounding temperature T_{c(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)}(T_{r(k)}-T_{c(k)})^{4}**

Where,

P→ net power of radiation in electro volts

A→ area of radiation in square meter^{2}

Tr→ radiator temperature in kelvin

T_{c}→ 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 *T^{4}

where σ → Stefan’s constant =5.67*10^{-8} W/m^{2} K^{4}

u=e * σ*AT^{4}

Δu=u-u_{0}= e * σ*A[T^{4}-T_{0}^{4}]

dp/d λ =1/A=2 π hc^{2}/ λ^{5}(e^{hc/} ^{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 400cm^{2} and temperature 323^{0} c are kept in a room at temperature 47^{0}c and Stefan’s Boltzmann law.

### Answer:

P=e* σ*A (T^{4}-T_{0}^{4})

=(0.75)(5.67*10^{-8} W/m^{2}-K^{4})(400*10^{-4} m^{2})*[(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 A^{0}.When the temperature of this body is further increased and its most intense radiation corresponds to 30,000 A^{0},

### Answer:

Wein’s displacement law is λ_{m} *T=b

T∝[1/ λ_{m}]

Here λ_{m} becomes half, the Temperature doubles

Now from Stefan Boltzmann Law e=ST^{4}

e_{1}/e_{2}=(T_{1}/T_{2})^{4}

= e_{2} =(T_{1}/T_{2})^{4}

e_{1}=(4)^{2}.15

=16.15 J m^{-2} S^{-1}