Stefan Boltzmann Law Calculator

Stefan Boltzmann Law Calculator helps to determine the unknown quantity among radiation emitted by the body, temperature and the surface area.

It states that:
A body emits radiation that will be proportional to fourth power of absolute temperature and for any body.

Stefan-Boltzmann Law can be given by        
P = $\varepsilon$ $\sigma$ A  T4
Where
$\sigma$ = Stefan-Boltzmann Constant = 5.67 × 10−8 W/m2 K4
$\varepsilon$ = Emissivity
A = Surface Area
T = Temperature
P is the Radiation Energy.
 

Steps for Stefan Boltzmann Law Calculator


Step 1 :  

Analyze the problems, list the given parameters.



Step 2 :  

Using the formula


P = $\varepsilon$ $\sigma$ A  T4



Where
$\sigma$ = Stefan-Boltzmann Constant = 5.67 × 10−8 W/m2 K4
$\varepsilon$ = Emissivity
A = Surface Area
T = Temperature
P = Radiation Energy.


Substitute the given parameter in this problem and get the unknown parameter.



Problems on Stefan Boltzmann Law Calculator


  1. A 100 Watt bulb is having length 40 cm, radius 0.05 m. if emissivity is 0.85. Calculate the temperature?


    Step 1 :  

    Given that: length l = 0.4 m,


    radius r = 0.05 m,


    emissivity $\varepsilon$ = 0.85,


    T =?


    Area A = $\pi$ r2


              = 3.142 $\times$ (0.05)2


              = 0.007855 m2



    Step 2 :  

    Using the formula


    P = $\varepsilon$ $\sigma$ A  T4


    T4 = $\frac{100}{0.85 \times 5.67 × 10^{−8} \times 0.007855}$



    Answer  :  

    T = 716.9 K.



  2. A Metal ball 3 cm in radius is heated in a furnace to 5000C. If its emissivity is 0.5, at what rate does it radiate energy?


    Step 1 :  

    Radius r = 3 cm


    The Surface area of the ball is
    A = 4 $\pi$ r2 = (4 $\times$ 3.142)(0.03 m)2


       = 0.0113112 m2


    and absolute temperature is T = 500 0 C + 273 = 773 K.


    emissivity $\varepsilon$ = 0.5



    Step 2 :  

    The Stefans Boltzmann law is given by
    P = e $\sigma$ A T4
       = 0.5 $\times$ 5.67 $\times$ 10-8 $\times$ 0.0113112 $\times$ (773)4



    Answer  :  

    Radiation energy P = 114.37 W.