AIIMS 2019 Physics Radiation MCQ Question

To find the temperature of the Earth in thermal equilibrium, we apply the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its temperature (T⁴). Given the distance from the Sun (2×10⁸ km), the Sun's temperature (6000 K), and its radius (7×10⁵ km), we can calculate the effective temperature of the Earth using the formula $T_E = \left( \frac{(1 - A) \cdot L}{4 \pi \sigma d^2 \cdot \epsilon} \right)^{1/4}$, where $A$ is the albedo, $L$ is the luminosity of the Sun, $\sigma$ is the Stefan-Boltzmann constant, $d$ is the distance to the Sun, and $\epsilon$ is the emissivity of the Earth.

Option B (3.4 bar) is correct because it accurately reflects the calculated equilibrium temperature considering the given parameters. The other options are incorrect as they do not align with the derived temperature based on the laws of thermodynamics and radiation balance.