Edexcel A Level (IAL) Physics-5.38 Stefan–Boltzmann Law- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.38 Stefan–Boltzmann Law- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.38 Stefan–Boltzmann Law- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
Stefan–Boltzmann Law for Black Body Radiators
The Stefan–Boltzmann law describes how the total power radiated by a black body depends on its temperature.
Stefan–Boltzmann Law
The total power (luminosity) radiated by a black body is given by:
\( L = \sigma A T^4 \)
- \( L \) = total power radiated (W)
- \( \sigma \) = Stefan–Boltzmann constant \( = 5.67\times10^{-8}\,\mathrm{W\,m^{-2}\,K^{-4}} \)
- \( A \) = surface area of the radiator (m²)
- \( T \) = absolute temperature (K)
Meaning of the Equation
- Total power depends very strongly on temperature.
- A small increase in temperature produces a large increase in radiated power.
- Temperature must be in kelvin.
Key idea:
- Doubling the temperature increases power by a factor of 16.
Application to Spherical Objects (Stars and Planets)
For a spherical black body of radius \( r \):
Surface area: \( A = 4\pi r^2 \)
Substitute into Stefan–Boltzmann law:
\( L = 4\pi r^2 \sigma T^4 \)
This equation is widely used for stars.
Assumptions of the Law
- The object behaves as a perfect black body.
- All emitted radiation escapes.
- Emission depends only on temperature.
Note:
- Always convert temperature to kelvin.
- Square brackets matter: use \( T^4 \).
- Use correct area formula.
- State assumptions clearly.
Example (Easy)
A black body has surface area \( 2.0\,\mathrm{m^2} \) and temperature \( 300\,\mathrm{K} \). Calculate the total power radiated.
▶️ Answer / Explanation
\( L = \sigma A T^4 \)
\( L = (5.67\times10^{-8})(2.0)(300)^4 \)
\( L \approx 920\,\mathrm{W} \)
Example (Medium)
A star can be treated as a black body of radius \( 7.0\times10^8\,\mathrm{m} \) and surface temperature \( 5800\,\mathrm{K} \). Calculate its luminosity.
▶️ Answer / Explanation
\( L = 4\pi r^2 \sigma T^4 \)
\( L = 4\pi(7.0\times10^8)^2(5.67\times10^{-8})(5800)^4 \)
\( L \approx 3.9\times10^{26}\,\mathrm{W} \)
Example (Hard)
The temperature of a black body increases from \( 300\,\mathrm{K} \) to \( 600\,\mathrm{K} \). By what factor does the power radiated increase?
▶️ Answer / Explanation
The Stefan–Boltzmann law gives:
\( \dfrac{L_2}{L_1} = \left(\dfrac{T_2}{T_1}\right)^4 \)
\( \dfrac{L_2}{L_1} = \left(\dfrac{600}{300}\right)^4 = 2^4 = 16 \)
The power increases by a factor of 16.