Mountain Top On A Faraway Planet

Classical Mechanics Level 5

Consider a planet with an atmosphere of ideal gas at constant temperature. The following is known:

  • Pressure at the surface: \(P_0 = 100\ \text{kPa};\)
  • Pressure gradient at the surface: \(-dP/dy|_0 = 12\ \text{Pa/m};\)
  • Height of highest mountain: \(y^\star = 9000\ \text{m}.\)

Determine the atmospheric pressure near the top of the highest mountain. Give your answer in kilopascals, rounded to the nearest integer.


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