# Stefan Boltzmann Law Calculator

For determining the power emitted by a body at a high temperature, the Stefan Boltzmann Law Calculator is a useful, adaptable, and free tool. Simply enter parameters such as surface area, temperature, material type, and emissivity to compute the radiated power.

### What Does the Stefan Boltzmann Law Mean?

The total amount of radiation energy radiated from a surface is directly proportional to the fourth power of its absolute temperature, according to Stefan Boltzmann's law. Only black things and theoretical surfaces that absorb all incident heat radiation are subject to this law. The Stefan Boltzmann constant has a value of roughly 5.67 x 10^-8 W m^-2 K^-4.

The thermal radiation formula is **P = σ ε A T⁴**

- Where, P = power of the body's temperature
- σ = Stefan Boltzmann constant and its value is 5.670367 x 10^-8
- ε = emissivity
- A = surface area of the body
- T = body temperature

### How to Calculate Power Radiation?

Learn how to calculate the power radiation step by step.

- Step 1: Get the area, temperature, and material of the surface.
- Step 2: Surface by multiplying the emissivity by the Stefan Boltzmann constant.
- Step 3: Calculate the temperature's fourth power.
- Step 4: To check the power, multiply the product from step 2 by the result from the previous steps.

### How Do I Use the Stefan Boltzmann Law Calculator?

The following is the procedure on how to utilise the Stefan Boltzmann Law Calculator

- Step 1: In the appropriate input fields, enter the temperature, surface area, and x for the unknown.
- Step 2: To receive the result, click the "Calculate x" button.
- Step 3: Finally, using Stefan Boltzmann's law, the radiation energy will be displayed in the output field.

### Stefan Boltzmann Law Problems

**Question 1:** A black body emits 0.5 and its area is 400 m^2 at 600 K. Determine the rate at which it emits energy?

**Solution:**

Given

Given:

Temperature T = 600 K

Surface area A = 400 m²

Emittivity ε = 0.5

Radiated energy P = σ ε A T⁴

P = 5.670367 x 10^-8 x 0.5 x 400 x (600)^4

= 1.134 x 10^-5 x 1.296 x 10^11

= 1469664 W

Hence, the radiated energy is 1469664 W.

**Question 2:** In a 27°C chamber, a body with an emissivity of 0.55, a surface area of 400 cm^2, and a temperature of 227°C is kept. Using the Stephens Boltzmann law, determine the starting value of net power emitted by the body.

**Solution:**

Given: Emmissivity e = 0.55

surface area A = 400 cm^2 = 4 x 10^-2 m^2

Power P = σ ε A T⁴

= 0.55 x 5.67 x 10^-8 x 4 x 10^-2 x [(500)^4 - (300)^4]

= 67.85 Watts

Hence, the starting value of net power emitted by the body is 67.85 Watts.

### FAQs on Stefan Boltzmann Law

**1. What is the formula for Stefan Boltzmann's Law?**

According to the Stefan-Boltzmann formula W = ε σT4, all bodies radiate energy W dependent on temperature T, where emissivity is equal to 1 for black bodies and less than 1 for grey ones, with the Stefan constant. Planck's law determines the energy density for a given wavelength.

**2. What is the Boltzmann Equation and how is it calculated?**

The entropy of a macroscopic state is related to the number of configurations of microscopic states in a system where all microstates are equiprobable, according to the Boltzmann formula S = kB ln Ω.

**3. What is the best way to apply the Stefan-Boltzmann constant?**

The Stefan-Boltzmann constant can be used to calculate the amount of heat emitted by a blackbody. A blackbody, according to physicists, is an object that absorbs 100% of the radiant energy striking it and if in harmony with its surroundings, radiates 100% of the radiant energy.

**4. What is the emissivity formula?**

The rate of heat transmission is proportional to the surface area and the absolute temperature to the fourth power: Qt = σeAT4, where = 5.67 x 10^8 J/s m^2 is the Stefan-Boltzmann constant, K4 is the Stefan-Boltzmann constant, and e is the body's emissivity.