A mountain climber has reached an altitude of 3000 m. What is the approximate air pressure at this altitude?

A.90,000 g/cm^2
B.60,000 g/cm^2
C.45,000 g/cm^2
D.70,000 g/cm^2

1 answer

To determine the air pressure at an altitude of 3000 m, we can use the standard atmospheric pressure at sea level (approximately 101,325 Pa or 1013.25 hPa) and the approximate decrease in pressure with altitude.

The air pressure decreases roughly by 12 hPa for every 100 m increase in altitude. Therefore, for an altitude of 3000 m, the pressure decrease would be approximately:

\[ \text{Pressure decrease} = 12 \text{ hPa/100 m} \times 30 \text{ (100 m)} = 360 \text{ hPa} \]

Now, we subtract this from the standard sea level pressure:

\[ \text{Pressure at 3000 m} = 1013.25 \text{ hPa} - 36 \text{ hPa} = 973.25 \text{ hPa} \]

To convert this to g/cm² (since 1 hPa = 0.001 g/cm²):

\[ 973.25 \text{ hPa} = 973.25 \times 0.001 \text{ g/cm}^2 = 0.97325 \text{ g/cm}^2 \]

However, the options you provided (90,000 g/cm², 60,000 g/cm², 45,000 g/cm², 70,000 g/cm²) appear to be in a larger, incorrect unit, suggesting there may have been an error in the units.

It's clear that none of the options match conventional pressures in either format. Typical air pressure at 3000 m is about 70,000 Pa, which is equivalent to 0.7 g/cm², or under the assumption the values could be misinterpreted. The pressure commonly measured at such altitudes is closer to 70,000 Pa.

Thus, the most reasonable answer choice based on common atmospheric data would be D. 70,000 g/cm², but with the realization that this value might not express the intended physical measurement clearly.