Calculating Atmospheric Pressure Change

The change in atmospheric pressure ($\Delta P$) due to a change in height ($\Delta h$) can be approximated using the formula:

$\Delta P = -\rho \cdot g \cdot \Delta h$

Where:

• $\rho$ is the density of the air.
• $g$ is the acceleration due to gravity.
• $\Delta h$ is the change in height.

The negative sign indicates that pressure decreases as height increases.

Applying Given Values

We are given:

• $\Delta h = 200 \text{ m}$
• $\rho = 1.0 \text{ kg/m}^3$
• $g = 9.8 \text{ m/s}^2$

Substitute these values into the formula:

$\Delta P = -(1.0 \text{ kg/m}^3) \times (9.8 \text{ m/s}^2) \times (200 \text{ m})$

Pressure Calculation Result

Performing the calculation:

$\Delta P = -1960 \text{ kg} \cdot \text{m/s}^2 / \text{m}^2$

$\Delta P = -1960 \text{ Pa}$

To convert Pascals (Pa) to Kilopascals (KPa), divide by 1000:

$\Delta P = \frac{-1960 \text{ Pa}}{1000 \text{ Pa/KPa}} = -1.96 \text{ KPa}$

The closest approximate answer among the options is -1.9 KPa.