Question

a class conducts an experiment with a hot air balloon, observing how heating the air inside the balloon affects its motion.
as the air is heated, what change occurs in the kinetic energy of the air molecules, and how does this influence the balloons ability to rise?
a. the kinetic energy of the air molecules decreases, causing the balloon to sink due to increased density.
b. the kinetic energy of the air molecules increases, leading to more collisions and decreased density, allowing the balloon to rise.
c. heating the air maintains constant kinetic energy, resulting in no change in the balloons motion.
d. the kinetic energy increases but is offset by the weight of the balloon, keeping it stationary.

Explanation:

When air is heated, the temperature of the air increases. According to the kinetic - molecular theory, the average kinetic energy of gas molecules is directly proportional to the temperature ($KE_{avg}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the absolute temperature). So, as the temperature ($T$) increases, the kinetic energy of the air molecules increases.

As the kinetic energy of the air molecules increases, the air inside the balloon expands (Charles's law: $V\propto T$ for a fixed amount of gas at constant pressure). When the air inside the balloon expands, its density ($
ho=\frac{m}{V}$) decreases. A less - dense object (the hot - air balloon) can rise in a more - dense medium (the surrounding cooler air) due to buoyancy (Archimedes' principle: $F_b=
ho_{fluid}gV_{displaced}$).

Now let's analyze each option:

• Option A: The kinetic energy of gas molecules should increase with temperature, not decrease. So, this option is incorrect.
• Option B: The kinetic energy of the air molecules increases (correct from the kinetic - molecular theory). More kinetic energy leads to more molecular motion and expansion of the gas (increase in volume). Since density $

ho=\frac{m}{V}$ (mass of air in the balloon is approximately constant as it's a closed system for the purpose of this basic analysis), an increase in volume causes a decrease in density. A lower - density balloon can rise in the surrounding higher - density air. This option is correct.

• Option C: Heating the air changes the temperature, and since $KE_{avg}\propto T$, the kinetic energy does not remain constant. So, this option is incorrect.
• Option D: There is no indication in the basic principles (kinetic - molecular theory, Charles's law, Archimedes' principle) that the increase in kinetic energy is offset by the weight of the balloon in the way described. The main factor for rising is the density difference due to temperature - induced volume change. So, this option is incorrect.

Answer:

B. The kinetic energy of the air molecules increases, leading to more collisions and decreased density, allowing the balloon to rise.