Physics
Physics
Problem
A planet orbiting a distant star has a thin atmosphere that is transparent to the radiation emitted by its surface. During the night the planetary surface behaves like a near-perfect blackbody at 250 K, while at local noon strong solar heating raises the surface temperature until the total radiant power per unit area doubles. Answer the following with clear derivations. a. (i) Determine the surface temperature at local noon. b. (ii) Compute the ratio of the peak daytime wavelength λ_day to the peak nighttime wavelength λ_night. c. (iii) If λ_night lies in the far infra-red region at 11.6 µm, find λ_day numerically and state whether this wavelength is still in the infra-red region or moves toward the visible range. d. (iv) Explain why the proportional reasoning used in parts (i) and (ii) is justified for an ideal blackbody but may require corrections for real planetary surfaces.Intuitive explanation
The core concept here is Stefan-Boltzmann radiation and how surface temperature responds to energy balance. The key insight is that radiant power scales as , so when power doubles, temperature doesn't double—it increases by a much smaller factor. You're using the relationship to connect the nighttime and noon temperatures, then working backward from the power ratio to find the actual temperature change.
Intuitive explanation
The core concept here is Stefan-Boltzmann radiation and how surface temperature responds to energy balance. The key insight is that radiant power scales as , so when power doubles, temperature doesn't double—it increases by a much smaller factor. You're using the relationship to connect the nighttime and noon temperatures, then working backward from the power ratio to find the actual temperature change.