What is the atmospheric pressure at the top of Mount Everest, which stands approximately 9000 meters above sea level? (Assume an average air density = 0.8 kg/m^{3} and g = 10 m/s^{2})

- 7200 Pa
- 29000 Pa
- 72,000 Pa
- 101,000 Pa

**Explanation**

This question asks the examinee to determine the pressure due to the atmosphere at the top of Mount Everest. To answer this question, you must determine the difference in air pressure between sea level (101,000 Pa) and the top of Everest. The best method to calculate the pressure differential is to apply the gauge pressure formula, P_{gauge} = ρgh, where P_{gauge }is the pressure due to the atmospheric column of height h, ρ is the density of the fluid, and g is the gravitational acceleration constant. The difference between the atmospheric pressure at sea level and the gauge pressure applying the equation above yields the atmospheric pressure at the top of Mt. Everest, as follows:

P_{Everest }= P_{Sea Level }– P_{gauge}

P_{Everest }= 101,000 Pa– ρgh

P_{Everest }= 101,000 Pa– (0.8 kg/m^{3})(10 m/s^{2})(9000 m)

P_{Everest }=29,000 Pa

Thus, the correct answer is 29,000 Pa, which is answer choice B.

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I don’y understand this. Am I applying the formula where P total= P atm +P gauge? if so does that mean that P everest=P atm?

Hi Mulki! Yes, exactly. The question asks for the “atmospheric pressure at the top of Mount Everest.” So the pressure on Mount Everest is our Patm. Now, using the equation you gave, we have:

Ptotal = PEverest + Pgauge

We know the pressure at sea level – it’s our typical approximation of 101,000 Pa. Now, be careful here – this should be our Ptotal! Think of it this way – we often use Ptotal = Patm + Pgauge when finding the pressure at a certain point in a fluid. In such problems, our Ptotal refers to the pressure at that point. In other words, Ptotal is the pressure at the deeper point, as that pressure should be higher there. So we now have Psea level = PEverest + Pgauge, and we can solve this using the method shown in the explanation. Let us know if we can help with anything else!