Stefan's Law and Wien's Displacement Law - UNSOLVED PRACTICE SET

Q7. State Stefan's law and Wien's displacement law. Write their mathematical expressions.

Q8. The Sun's surface temperature is about 5800 K. Calculate the wavelength at which the Sun emits maximum radiation.

Q9. A black body at 1000 K radiates energy at rate E. At what temperature will it radiate at rate 16E?

Q10. In your school, a student notices that the filament of an electric bulb glows white when hot but red when cooler. Explain using Wien's law.

Q11. Why do we feel the heat from a distant fire even though convection cannot carry heat that far?

Q12. Explain why a red star is cooler than a blue star, even though both are extremely hot.

Q13. Explain black body radiation and the qualitative ideas of:

(i) Stefan's law: derive or state the expression, discuss its significance, calculate the total power radiated

(ii) Wien's displacement law: derive or state the expression, discuss its significance, explain stellar colours

(iii) Kirchhoff's law of radiation (qualitative)

(iv) Why classical physics failed to explain black body radiation (brief mention of quantum hypothesis)

Discuss applications in astronomy, infrared imaging, and climate science.

Q14. The Sun has a radius of 7 × 10⁸ m and surface temperature of 5800 K. Treat it as a perfect black body.

(a) Calculate the total power radiated by the Sun. (σ = 5.67 × 10⁻⁸ W/m²·K⁴)

(b) Calculate the wavelength of maximum emission.

(c) The Earth is 1.5 × 10¹¹ m from the Sun. Calculate the solar constant (energy received per unit area at Earth).

(d) If the Sun's temperature increased by 10%, calculate the percentage increase in radiated power.

(e) Discuss why the actual solar constant varies slightly throughout the year.

Q15. Analyse the following astronomical observations:

(i) Betelgeuse appears red while Sirius appears blue-white

(ii) The cosmic microwave background has λ_max ≈ 1.06 mm

(iii) Infrared cameras detect warm bodies in complete darkness

For each case, explain:

(a) The physics using Stefan's law and/or Wien's law

(b) The temperature estimate (where applicable)

(c) The practical application or significance

Q16. A black body at 3000 K has a surface area of 0.01 m².

(a) Calculate the power radiated.

(b) Calculate the wavelength of maximum intensity.

(c) If the temperature is raised to 6000 K, calculate the new radiated power and new λ_max.

(d) By what factor does the radiated power increase?

(e) In which region of the electromagnetic spectrum does each body radiate most intensely?

Q17. The filament of a 100 W incandescent bulb has a surface area of 5 × 10⁻⁵ m² and operates at 2500 K.

(a) Calculate the power radiated if the filament were a perfect black body.

(b) Calculate the efficiency of the bulb as a light source (visible radiation only, λ ≈ 400–700 nm).

(c) Using Wien's law, show that most of the radiation is in the infrared region.

(d) If the filament temperature is increased to 3000 K, calculate the new power and discuss the trade-off.

(e) Explain why LED bulbs are more efficient than incandescent bulbs.

Q18. In a school experiment, students investigate the cooling of a heated metal sphere:

Diameter = 4 cm, initial temperature = 100°C, room temperature = 25°C

The sphere cools to 75°C in 10 minutes

Emissivity = 0.8, density = 8000 kg/m³, specific heat = 500 J/kg·K

(a) Calculate the mass of the sphere.

(b) Calculate the heat lost in the first 10 minutes.

(c) Using Stefan's law, estimate the average rate of heat loss by radiation.

(d) Compare this with the rate predicted by Newton's law of cooling.

(e) Discuss why Newton's law is a good approximation for this temperature range.