# Stefan-Boltzmann Law

on . Posted in Electromagnetism

Stefan-Boltzmann law describes the power radiated from a black body, an ideal black surface that absorbs all radiant energy falling on it, in terms of temperature.  The Stefan-Boltzmann law relates the total radiant energy emitted by a black body to its temperature.  It provides a fundamental understanding of the relationship between temperature and the intensity of thermal radiation.

The Stefan-Boltzmann law states that the total power radiated per unit area (also known as the radiative flux) by a black body is proportional to the fourth power of its absolute temperature.  The Stefan-Boltzmann law reveals that as the temperature of a black body increases, the amount of energy radiated per unit area increases significantly.  It implies that hotter objects emit more thermal radiation than cooler ones.

It's important to note that the Stefan-Boltzmann law is applicable to ideal black bodies, which are theoretical objects that absorb all incident radiation and emit thermal radiation perfectly.  In reality, most objects are not ideal black bodies and have a property called emissivity that represents their efficiency in emitting thermal radiation compared to a black body.  The Stefan-Boltzmann law has significant applications in various fields, including astrophysics, climate science, thermodynamics, and engineering.  It helps determine the total power radiated by objects such as stars, calculate the energy balance of Earth's atmosphere, analyze the performance of thermal systems, and design heat transfer equipment.

## Stefan-Boltzmann Law formula

$$\large{ P = \epsilon \; \sigma \; A \; T^4 }$$     (Stefan-Boltzmann Law)

$$\large{ \epsilon = \frac{ P }{ \sigma \; A \; T^4 } }$$

$$\large{ \sigma = \frac{ P }{ \epsilon \; A \; T^4 } }$$

$$\large{ A = \frac{ P }{ \epsilon \; \sigma \; T^4 } }$$

$$\large{ T = \sqrt{ \frac{ P }{ \epsilon \; \sigma \; A } } }$$

Symbol English Metric
$$\large{ P }$$ = radiated energy $$\large{lbf-ft}$$ $$\large{J}$$
$$\large{ \epsilon }$$  (Greek symbol epsilon) = emissivity of the material $$\large{R}$$ $$\large{K}$$
$$\large{ \sigma }$$  (Greek symbol sigma) = Stefan-Boltzmann constant $$\large{\frac{Btu}{hr-ft^2-R^4}}$$ $$\large{\frac{W}{m^2-K^4}}$$
$$\large{ A }$$ = radiating area  $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ T }$$ = absolute temperature of the object emitting $$\large{R}$$ $$\large{K}$$ Tags: Temperature Energy