Stefan-Boltzmann Law (Edexcel International A Level (IAL) Physics): Revision Note
Exam code: YPH11
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.
Answer:
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 Tips and Tricks
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.
Unlock more, it's free!
Join the 100,000+ Students that ❤️ Save My Exams
the (exam) results speak for themselves:
Was this revision note helpful?
Build on this topic
