[VISUAL] The volume of a sample of air in a cylinder with a movable piston is 2.0 L at a pressure P1 — States of Matter Chemistry Question

STEPS:

1. Identify the thermodynamic variable being analyzed: The question asks for the effect of the expansion on the average kinetic energy of the gas molecules.
2. Apply the Kinetic Molecular Theory (KMT) relationship: According to the Kinetic Molecular Theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature ($T$) of the system.
$$KE_{\text{avg}} \propto T$$
Because of this direct relationship, temperature is the *only* thermodynamic variable that determines the average kinetic energy of a gas sample.
3. Evaluate the conditions of the process: The prompt explicitly states that the volume is increased from $2.0\text{ L}$ to $5.0\text{ L}$ "as the temperature is held constant".
4. Determine the final effect: Since the temperature does not change, the average kinetic energy of the gas molecules must remain completely unchanged. The corresponding changes in volume and pressure have zero impact on the average kinetic energy of the molecules, confirming Option C as the correct answer.

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WHY_OTHERS_WRONG:

• A is incorrect: The average kinetic energy would only increase if the temperature of the gas increased. While a rapid adiabatic expansion can sometimes cause temperature changes in real systems, the problem explicitly constrains this process to be isothermal (constant temperature).
• B is incorrect: A student might intuitively but incorrectly assume that because the gas has expanded into a larger volume at a lower pressure, the molecules must be moving slower or have "lost" energy. However, gas expansion at a constant temperature does not reduce the average speed or kinetic energy of the molecules.
• D is incorrect: It is entirely possible to determine the effect on the average kinetic energy without knowing the specific pressure values of $P_1$ and $P_2$. The single piece of information that the temperature remains constant is fully sufficient to know that the average kinetic energy must also remain constant.