Radiated power (Stefan–Boltzmann law): Class 11 practice
A black body radiates power P = σAT⁴ (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Powers
The idea behind radiated power (stefan–boltzmann law)
A black body radiates power P = σAT⁴ (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴). Doubling the absolute temperature multiplies the power by 16. Wien's law: λₘT = 2.9 × 10⁻³ m K.
Step-by-step method
- Use T in kelvin.
- P = σAT⁴, or compare (T₂/T₁)⁴.
- For peak wavelength use λₘ = b/T.
Worked example 1 (Basic)
By what factor does radiated power change if a body's absolute temperature becomes 3 times?
- P ∝ T⁴ → 3⁴
- Answer: 81 times
Worked example 2 (Standard)
A black body of area 0.1 m² is at 1545 K. Find the power radiated.
- P = 5.67 × 10⁻⁸ × 0.1 × 1545⁴
- Answer: 3.231e+4 W
Worked example 3 (Challenge)
Find the wavelength of peak emission of a body at 1825 K.
- λₘ = 2.9 × 10⁻³/1825
- Answer: 1589.0 nm
Common mistakes and misconceptions
- Using °C
- Raising to the square instead of the fourth power
Practice questions
- (Basic) By what factor does radiated power change if a body's absolute temperature becomes 2 times?
- (Basic) By what factor does radiated power change if a body's absolute temperature becomes 1.5 times?
- (Standard) A black body of area 0.03 m² is at 2830 K. Find the power radiated.
- (Standard) A black body of area 0.04 m² is at 1272 K. Find the power radiated.
- (Challenge) Find the wavelength of peak emission of a body at 2727 K.
- (Challenge) Find the wavelength of peak emission of a body at 1345 K.
Answer key with full working
- Q1: P ∝ T⁴ → 2⁴ → Answer: 16 times
- Q2: P ∝ T⁴ → 1.5⁴ → Answer: 5.06 times
- Q3: P = 5.67 × 10⁻⁸ × 0.03 × 2830⁴ → Answer: 1.091e+5 W
- Q4: P = 5.67 × 10⁻⁸ × 0.04 × 1272⁴ → Answer: 5937 W
- Q5: λₘ = 2.9 × 10⁻³/2727 → Answer: 1063.4 nm
- Q6: λₘ = 2.9 × 10⁻³/1345 → Answer: 2156.1 nm
Syllabus note
This skill is listed under "Thermal Properties of Matter" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is radiated power (stefan–boltzmann law) in?
"Thermal Properties of Matter", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.