Stefan-boltzmann Law Of Radiation

According to NCERT Class 11, Chapter 11 (Thermal Properties of Matter), the Stefan-Boltzmann law states that the energy radiated per unit area per unit time by a perfect black body is proportional to the fourth power of its absolute temperature, $E=\sigma T^4$, where $\sigma$ is the Stefan constant. This strong dependence arises because hotter bodies emit far more thermal radiation across all wavelengths. Doubling the absolute temperature multiplies the radiated power per unit area by $2^4=16$. The option 'four times' wrongly uses a square-law dependence. The option 'eight times' applies a cubic power. The option 'two times' assumes a simple linear relation, ignoring the fourth-power law. It is essential to use absolute (kelvin) temperature in this law, not Celsius, since the fourth power is meaningful only on the absolute scale where zero corresponds to no thermal radiation. As a plausibility check, this steep rise explains why a modest increase in a filament's temperature causes a dramatic jump in radiated energy and brightness, and why hot blue stars of higher surface temperature are vastly more luminous than cooler red stars of the same size. The sixteen-fold increase from merely doubling the temperature is exactly the dramatic sensitivity that the fourth-power law predicts, confirming the answer.