USAAAO 2022, I кръг — Задача 10
USAAAO 2022 - First Round · 5 февруари 2022 г.
Условие
Jupiter’s deep atmosphere is very warm due to convection leading to an adiabatic temperature profile that increases with increasing pressure. Assuming (for simplicity) that this outer layer of Jupiter has a temperature of 500 K, perform a back-of-the-envelope estimate of the characteristic thickness (or e-folding scale) of the envelope of Jupiter (you may find that this is independent of pressure level). You may further use that the specific gas constant in Jupiter’s atmosphere is 3600 J kg K.
(a) 20 km
(b) 73 km
(c) 568 km
(d) 3,120 km
(e) 10,233 km
Отговори
- B
Решение
From hydrostatic equilibrium, .
From the ideal gas law,
Solving for H, we find:
A more accurate answer would integrate hydrostatic equilibrium to determine the e-folding length scale (H), which is equivalent to the derived in the isothermal limit.
Plug in for R, T, and to find:
Answer: B
Оригинал в Архива: usaaao_first_exam_2022_problems.pdf · официални решения: usaaao_first_exam_2022_solutions-1.pdf