Practice portal › Thermal Properties of Matter › Radiation, Stefan's Law and Cooling

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q? (σ stands for Stefan's constant)

Asked in CBSE AIPMT 2012 · Stefan-Boltzmann law

• (1) Q/(4π R²σ)
• (2) (Q/(4π R²σ))^-1/2
• (3) ((4π R²Q)/σ)^-1/4
• (4) (Q/(4π R²σ))^1/4

Step-by-step solution

Why the other options are wrong

• (1) comes from stopping at T⁴=Q/(4π R²σ) and never taking the fourth root, so the expression has the dimensions of T⁴ rather than of a temperature
• (2) comes from the fourth root replaced by an inverse square root; Q∝ T⁴ forces the exponent to be +1/4
• (3) comes from inverts the bracket as well, putting R² in the numerator and using -1/4, so the star would cool down as it produced more energy

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.