Question

density decreases with increased altitude because?

temperature drops more quickly than pressure

they both drop at the same rate

pressure drops more quickly that temperature

Explanation:

To determine why density decreases with altitude, we analyze the relationship between density, pressure, and temperature in the atmosphere. Density ($
ho$) is related to pressure ($P$) and temperature ($T$) by the ideal gas law $
ho=\frac{PM}{RT}$ (where $M$ is molar mass, $R$ is gas constant). As altitude increases, pressure drops more rapidly than temperature in the troposphere (the lower atmospheric layer). A faster drop in pressure (compared to temperature's change rate) leads to a decrease in density because pressure is more directly proportional to density when temperature effects are considered.

• Option 1 (temperature drops more quickly than pressure): Incorrect. In the troposphere, pressure drops faster than temperature.
• Option 2 (they both drop at the same rate): Incorrect. Pressure and temperature do not drop at the same rate with altitude.
• Option 3 (pressure drops more quickly than temperature): Correct. Since pressure has a stronger direct relationship with density (from the ideal gas law) and it drops faster than temperature with increasing altitude, density decreases.

Answer:

The option "pressure drops more quickly that temperature" (assuming a typo and it should be "than") is the correct one. If we consider the options as presented (with the third option being "pressure drops more quickly that temperature"), that is the correct choice.