# 5.38 Stefan-Boltzmann Law

## Stefan-Boltzmann Law

• An objects luminosity depends on two factors:
• Its surface temperature
• Its surface area

• The relationship between these is known as the Stefan-Boltzmann Law, which states:

The total energy emitted by a black body per unit area per second is proportional to the fourth power of the absolute temperature of the body

• So, L AT4

• The Stefan-Boltzmann Law equation is:

L = σAT4

• Where:
• L = luminosity of the star (W)
• A = surface area of the star
• σ = the Stefan-Boltzmann constant
• T = surface temperature of the star (K)

• The surface area of a star (or other spherical object) can be calculated using:

A = 4πr2

• Where:
• r = radius of the star

#### Worked example

A camel has a body temperature of 40 ⁰C and a surface area of 16 m2. The peak wavelength of the emitted spectrum from the camel is λmax = 8.6 × 10–6 m. Calculate the total power radiated by the camel.

Step 1: Write down the equation

L = σAT4

Step 2: Convert temperature from ⁰C to K

• 40 + 273 = 313 K

Step 3: Substitute in the values

• L = (5.67 × 10–8) × 16 × 3134 = 29387 W = 8 707

Step 4: Write answer to correct significant figures and include units

Luminosity (power emitted) of the camel = 8 700 W (2 sig figs)

#### Exam Tip

Remember to convert temperatures into Kelvin.

If you are given the radius of a spherical object then its surface area A can be calculated using A = 4πrfor the radius of the object r ### Get unlimited access

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