At absolute zero temperature, the average velocity of the molecules

1. Analyze the question

The question asks for the behavior of the average velocity of gas molecules when the temperature of a system reaches absolute zero ($0\text{ K}$).

2. Explain the concept

In the Kinetic Theory of Gases, the temperature of a substance is a measure of the average kinetic energy of its molecules. The relationship is given by the formula:

Where:

• $K.E._{avg}$ is the average kinetic energy.
• $k$ is the Boltzmann constant.
• $T$ is the absolute temperature in Kelvin.

Since kinetic energy is defined as $K.E. = \frac{1}{2}mv^2$, it follows that:

From this equation, you can see that the velocity ($v$) is directly proportional to the square root of the absolute temperature ($\sqrt{T}$).

3. Show the solution

• Step 1: Identify the temperature at absolute zero. Absolute zero is $0\text{ K}$.
• Step 2: Substitute $T = 0$ into the velocity relationship: $$v \propto \sqrt{0}$$ $$v = 0$$
• Step 3: At $0\text{ K}$, the thermal motion of the particles ceases. Because there is no thermal energy to drive the movement of the molecules, their average velocity becomes zero.

4. Identify the answer

Based on the kinetic theory, at absolute zero, the molecules lose all their kinetic energy and come to a state of rest. Therefore, the average velocity is zero.

The correct option is C.

5. Exam Tip

Always remember that in physics, "Absolute Zero" ($0\text{ K}$ or $-273.15^\circ\text{C}$) is the theoretical limit where all molecular motion stops. If you ever see a question about "absolute zero," think "zero energy" and "zero motion." This will help you quickly eliminate options that suggest the molecules are still moving or increasing in speed.