Final answer:
Warm air is less dense and exerts less pressure than cold air at the same altitude. However, the pressure of a hot-air balloon's gas might be greater than atmospheric pressure at the same altitude to allow it to rise. Air pressure also decreases with increasing altitude due to less dense air.
Step-by-step explanation:
In relation to air pressure, whether warm air or cold air has more pressure depends on several factors, but generally speaking, warm air is less dense and exerts less pressure compared to cold air when measured at the same altitude. This is because the molecules in warm air are moving more rapidly, causing the air to expand and therefore occupy a greater volume. However, when considering a hot-air balloon, the pressure of the gas inside the balloon must be sufficient to lift it, which means it could be greater than the atmospheric pressure at the same altitude. The pressure also depends on the altitude because air pressure decreases with increasing altitude due to the decrease in air density. For instance, air at sea level is denser and has higher pressure than air at the top of a mountain like Mount Everest. Moreover, buoyant force plays a role for hot air to rise, as warm air expands, displaces cold air, and experiences a greater buoyant force due to the difference in density.