Question

At higher altitudes as altitude increases, pressure.

A. decreases at constant rate.
B. decreases exponentially.
C. increases exponentially.

Answer 1

At higher altitudes, as altitude increases, pressure decreases exponentially (Option B).

Step-by-step explanation:

The relationship between altitude and atmospheric pressure can be described by the barometric formula. According to this formula, atmospheric pressure decreases exponentially with an increase in altitude. The expression for the pressure (P) as a function of altitude (h) is given by
`\(P = P_0 * \left(1 - (Lh)/(T_0)\right)^(gM)/(RL)\)`, where
`\(P_0\)` is the pressure at sea level, (L) is the temperature lapse rate,
`\(T_0\)` is the standard temperature at sea level, (g) is the acceleration due to gravity, (M) is the molar mass of Earth's air, and (R) is the ideal gas constant.

As altitude increases, the term
`\(\left(1 - (Lh)/(T_0)\right)\)` in the formula approaches zero, causing the entire expression to decrease exponentially. This signifies that pressure decreases at a rate determined by the exponential decay function. It's important to note that this decrease is not linear but follows an exponential decay pattern, leading to a rapid reduction in pressure with increasing altitude.

In summary, the correct choice is B, as atmospheric pressure decreases exponentially with higher altitudes. Understanding this relationship is crucial in various fields, including aviation, meteorology, and the study of atmospheric conditions at different elevations.