According to the kinetic theory of gases, the pressure exerted by a gas on the walls equals.

Analysis

The question asks for the definition of pressure in the context of the kinetic theory of gases. To answer this, we must relate the microscopic behavior of gas molecules (collisions) to the macroscopic property of pressure.

Concept Explanation

In the kinetic theory of gases, pressure is defined as the force exerted by gas molecules per unit area of the container walls.

1. Newton’s Second Law: Force is defined as the rate of change of momentum ($F = \frac{\Delta p}{\Delta t}$).
2. Pressure Definition: Pressure ($P$) is Force divided by Area ($A$), so $P = \frac{F}{A}$.
3. Combining these: If we substitute the definition of force into the pressure formula, we get: $$P = \frac{\text{Rate of change of momentum}}{\text{Area}}$$ This means pressure is the rate of change of momentum (force) exerted on the walls per unit area.

Step-by-Step Solution

• Step 1: Identify that gas molecules are in constant, random motion and collide with the walls of the container.
• Step 2: Each collision results in a change in momentum of the gas molecule. By Newton’s Third Law, the wall experiences an equal and opposite change in momentum.
• Step 3: The total force exerted on the wall is the sum of all these changes in momentum per unit time (the rate of change of momentum).
• Step 4: Dividing this total force by the surface area of the wall gives the pressure.
• Step 5: Therefore, pressure is the rate of change of momentum (force) imparted to the walls per unit area.

Looking at the options:

• Option A is incomplete because it misses the "rate" (time) component.
• Option B is incorrect because pressure is related to area, not volume.
• Option C is incomplete because it misses the "per second" (rate) component.
• Option D correctly identifies that pressure is the rate of change of momentum (force) per unit area.

Conclusion

This aligns with the physical definition derived from the kinetic theory of gases, where pressure is the force (rate of change of momentum) per unit area.

Exam Tip

Whenever you see "Pressure" in a mechanics or kinetic theory context, remember the formula $P = F/A$. Since $F$ is the rate of change of momentum ($\Delta p / \Delta t$), always look for the option that includes both "rate" (time) and "area."