Unit 28: Atmospheric Pressure & the Barometric Equation
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q28.1) Calculate the atmospheric pressure at the top of Mount Everest 8.85km above sea level. Assume an air temperature of 0°C and the molar mass of air to be 29g/mol.
**Q28.2) At what height above sea level will the Earth’s atmospheric pressure be 20% that at sea level? Assume an air temperature of 0°C and the molar mass of air to be 29g/mol.
***Q28.3) You find yourself on an unknown planet with nothing but a barometer and an altimeter. You don’t know the acceleration due to gravity on the surface of this planet, nor do you know the composition or density of its atmosphere. While standing at the base of a mountain, you measure an atmospheric pressure of 60 kPa (of absolute pressure). You hike up the mountain until your altitude is 400m above where you began and measure the atmospheric pressure to be 50 kPa (also absolute pressure). What should the atmospheric pressure be at the top of the mountain, 2000m above the base of the mountain where you began?
***Q28.4) Mars has 10.7% the mass of Earth, 53.1% the radius of Earth, a surface atmospheric pressure of 635 Pa, an atmospheric molar mass of 43.34 g/mol, and an average surface temperature of -65°C.
a) Calculate the acceleration due to gravity on the surface of Mars in units of g.
b) At what height above sea level on Earth would the atmospheric pressure be the same as on the surface of Mars? Assume an air temperature of 0°C and the molar mass of air on Earth to be 29g/mol.
c) The tallest mountain in the solar system, Olympus Mons, resides on Mars and has an astonishing height of 25km (triple the height of Mount Everest). Calculate the pressure of the Martian atmosphere at the top of Olympus Mons.
d) Do you think it would be more difficult or less difficult to sustain flight on Mars compared to on Earth? Justify your response.