If the temperature of the Sun were to increase from T to 3T and its radius from R to 3R, then the ratio of radiant energy received on Earth to what it was previously will be ______.
Physics · Mixed Chapter
JEE Main Practice

Question

If the temperature of the Sun were to increase from T to 3T and its radius from R to 3R, then the ratio of radiant energy received on Earth to what it was previously will be ______.

G1 Physics · Accepted Answer

Step 1: Total luminosity of a blackbody Sun is L = 4πR²σT⁴. Step 2: With unchanged Earth–Sun distance, energy received per unit area at Earth is proportional to L. Step 3: Radius factor: (3R/R)² = 3² = 9. Step 4: Temperature factor: (3T/T)⁴ = 3⁴ = 81. Step 5: New-to-old received radiation ratio = 9 × 81 = 729. Final answer: 729.