Created By : awnish

Reviewed By : Phani Ponnapalli

Last Updated : Apr 10, 2023

Stefan Boltzmann Law Calculator is a handy, flexible and free tool that helps to determine the power radiated from a body at a high temperature. You just need to provide inputs such as the surface area, temperature, material type and emissivity to get the radiated power easily.

Material:
Choose a Calculation
Area
Temperature
Emissivity

### How to Find Power Radiation?

Get the step by step process to calculate the power radiation.

• Get the surface area, temperature and material.
• Multiply the emissivity by the Stefan Boltzmann constant, and surface.
• Find the fourth power of the temperature.
• Multiply the product from step 2 by the result from above steps to check the power.

### Stefan Boltzmann Law

Stefan Boltzmann Law states that the power radiated from a black body is directly proportional to its temperature raised to the fourth power.

P = σ ε A TΓü┤

Where,

P is the power of the body's temperature

σ is the Stefan Boltzmann constant and its value is 5.670367 x 10-8

ε is the emissivity

A is the surface area of the body

T is the body temperature

Example

Question: A black body emitts of 0.1 and its area is 200 m² at 500 K. Find at what rate does it radiate the energy?

Solution:

Given that

Temperature T = 500 K

Surface area A = 200 m²

Emittivity ε = 0.1

Radiated energy P = σ ε A TΓü┤

P = 5.670367 x 10-8 x 0.1 x 200 x (500)

= 113.40734 x 625

= 7.08 x 104 W

Therefore, the radiated energy is 7.08 x 104 W.

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### Frequently Asked Questions on Stefan Boltzmann Law Calculator

1. Define Stefan Boltzmann Law?

Stefan Boltzmann law states that the amount of radiation energy emitted per unit time from an area of a black body at absolute temperature is directly proportional to the fourth power of the temperature.

2. What is the value of Stefan Boltzmann constant?

Stefan Boltzmann constant value is approximately 5.67 x 10-8 W/m²K4

3. A body emissivity (e = 0.75), the surface area of 300 cm2 and temperature is 227°C are kept in a room at temperature 27°C. Calculate the initial value of net power emitted by the body using the Stephens Boltzmann law.

Emmissivity e = 075

surface area A = 300 cm² = 3 x 10-2 m²

Power P = σ ε A TΓü┤

= 0.75 x 5.67 x 10-8 x 3 x 10-2 x [(500)4 - (300)4]

= 69.4 Watts

4. What is the relationship between the Stefan-Boltzmann law and Wien's law?

Wine's law tells the relationship between the wavelength of maximum intensity a blackbody emits and its temperature. While the Stefan Boltzmann law tells that the energy radiated from a blackbody is proportional to the fourth power of its temperature.