Final answer:
The height of the atmosphere can be estimated using the formula h = P/(ρg), where P is pressure, ρ is density, and g is gravity. Given a pressure of 1.01 × 10⁵ Pa and a density of 1.3 kg/m³, the theoretical height is approximately 7,948 meters, assuming constant density.
Step-by-step explanation:
To calculate the height (or depth) of the atmosphere using the given atmospheric pressure and air density, we can use the formula for pressure due to a fluid column, which is P = hρg, where P is pressure, h is height, ρ is density, and g is the acceleration due to gravity (approximately 9.8 m/s² at Earth's surface).
Given that atmospheric pressure at the Earth's surface is 1.01 × 10⁵ Pa (Pascal), and the density of air (ρ) is 1.3 kg/m³, we can rearrange the formula to solve for height: h = P/(ρg).
Plugging the values into the equation, we get:
h = (1.01 × 10⁵ Pa) / (1.3 kg/m³ × 9.8 m/s²) ≈ 7,948 meters
This calculation, however, assumes a uniform density of the atmosphere, which is not accurate in reality as the density decreases with altitude. Nevertheless, it provides a theoretical model for the depth of an atmosphere with constant density.