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

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