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°C 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: List the known quantities
-
- Surface area, A = 16 m2
- Temperature (in K), T = 40 + 273 = 313 K
- Stefan-Boltzmann constant, σ = 5.67 × 10–8 W m−2 K−4
Step 2: Write down the Stefan-Boltzmann equation
L = σAT4
Step 3: Substitute in the values
L = (5.67 × 10–8) × 16 × 3134 = 8707 W
Step 4: Write the answer to correct significant figures and include units
Luminosity (power emitted) of the camel = 8700 W (2 s.f.)
Examiner 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 = 4πr2 for the radius of the object r.
