Question

select the true statements. air pressure at the top of a mountain is higher than air pressure at the base. when air rises from the base to the top of the mountain, it loses energy. air particles at the base of a mountain are more dense than air particles at the top of the mountain. the air temperature at the base of a mountain is warmer than at the top of a mountain.

Explanation:

• Air pressure decreases with altitude. So, air pressure at the top of a mountain is lower than at the base. The first statement is false.
• When air rises, it expands (due to lower pressure at higher altitudes) and does work against the surrounding air. According to the first law of thermodynamics ($\Delta U = Q - W$), if it does work ($W>0$) and assuming no heat transfer ($Q = 0$ in an adiabatic process which is a good approximation for rising air parcels in the atmosphere), its internal energy decreases. So, when air rises from the base to the top of the mountain, it loses energy. The second statement is true.
• Density of air is related to pressure (using the ideal gas law $PV=nRT\Rightarrow

ho=\frac{P}{RT}$ where $
ho$ is density, $P$ is pressure, $R$ is the specific gas constant, and $T$ is temperature). Since pressure is higher at the base (and assuming temperature differences are not extremely large to override the pressure - density relationship), air particles at the base of a mountain are more dense than at the top. The third statement is true.

• As air rises, it expands and cools (adiabatic cooling). So, the air temperature at the base of a mountain is warmer than at the top. The fourth statement is true.

Answer:

• "When air rises from the base to the top of the mountain, it loses energy."
• "Air particles at the base of a mountain are more dense than air particles at the top of the mountain."
• "The air temperature at the base of a mountain is warmer than at the top of a mountain."