Question

Use the kinetic theory of gases to explain why hot air rises.

Short answer

Hot air rises because it becomes less dense and buoyancy forces it upwards.

Step-by-step solution

Understanding Kinetic Theory of Gases

The kinetic theory of gases states that gas molecules are in constant, random motion. This theory also relates temperature to the kinetic energy of these molecules. As the temperature increases, the average kinetic energy of the gas molecules increases, causing them to move more rapidly and spread apart.

Consider the Effect of Increasing Temperature

When air is heated, its temperature increases, thereby increasing the kinetic energy of the molecules. As a result, the molecules move faster and tend to occupy more space, which means the air expands. This expansion causes the density of the air to decrease because the same number of molecules now occupies a larger volume.

Apply Archimedes' Principle

According to Archimedes' principle, an object submerged in a fluid (in this case, air) will experience a buoyant force equal to the weight of the fluid it displaces. Because heated air becomes less dense, it displaces less dense air upwards, causing it to rise due to the buoyancy force that acts upward.

Relating Density and Buoyancy

Since the expanded warmer air is less dense than the cooler air surrounding it, the warmer air is buoyed up by the slightly denser, colder air, causing the heated air to rise relative to the surrounding air. This movement is directional: upwards, as buoyancy works against gravity.

Key concepts

Temperature and Kinetic Energy

The kinetic theory of gases provides a clear connection between temperature and kinetic energy. In this theory, molecules of a gas are depicted as being in constant, random motion.
As temperature increases, this motion becomes more rapid. But why does this happen? The answer lies in kinetic energy, which is the energy possessed by an object due to its motion. When the temperature of a gas increases, the kinetic energy of its molecules also increases, leading to more vigorous movements.
This relationship can be mathematically expressed as:

• The average kinetic energy of gas molecules is proportional to the absolute temperature of the gas.

So, a rise in temperature leads to a rise in the average speed and energy of the molecules, causing them to collide more frequently and with more force. This increase in collision activity results in a wider spread, as molecules strive to occupy a larger volume.

Gas Molecule Motion

Gas molecules are perpetually on the go, and this motion is random yet constant. Imagine tiny billiard balls that are always bouncing off of each other and the walls of their container.

This ceaseless motion contributes to the properties of gases such as pressure and volume. It also has a direct impact when temperature changes occur.
When the molecules' kinetic energy rises due to an increase in temperature, there is a tendency for the gas to expand.

• As molecules move faster, they need more space, which means that the gas expands.
• This expansion results in lower density.

This transformation is vital in understanding how and why heated air behaves differently than cooler air, especially in terms of rising when heated.

Density and Buoyancy

Density, a measure of mass per unit volume, plays a crucial role in the concept of buoyancy. As a gas heats up and its molecules spread out, the gas occupies more volume while having the same mass, effectively reducing its density.

Buoyancy, on the other hand, is the tendency of an object to float in a fluid. This is directly linked to the difference in density between the object and the surrounding fluid. The principle that governs buoyancy is that less dense substances will tend to rise through more dense substances.
So when air is heated:

• Its density decreases.
• It becomes less dense than the cooler air around it.
• This density difference causes buoyancy.

Thus, in an atmosphere of cooler air, warmer air will rise naturally due to reduced density and buoyancy.

Archimedes' Principle

Archimedes' principle is a fundamental concept that explains the buoyant force acting on an object submerged in a fluid. This principle states that an object will experience a buoyant force equal to the weight of the fluid it displaces.

In the context of hot air, Archimedes' principle can be applied to understand why hot air rises. When air is heated, it expands and becomes less dense than the surrounding cooler air.

• According to Archimedes' principle, this less dense, warmer air experiences an upward buoyant force.
• The weight of the displaced cooler, heavier air underneath effectively pushes the hotter air upwards.

Therefore, the combination of lower density and buoyant force results in the rising of hot air, demonstrating the practical application of Archimedes' principle in daily life.