According to the kinetic molecular theory, if you double the typical speed of the molecules in a gas, what happens to the average kinetic energy of the gas molecules?

• A. It doubles.
• B. It remains the same.
• C. It decreases by half.
• D. It increases by a factor of 4.

Answer: (D)

Verified step by step guidance

1. Recall the formula for the average kinetic energy of a gas molecule according to the kinetic molecular theory: \(\text{KE}_{avg} = \frac{1}{2} m v^2\), where \(m\) is the mass of a molecule and \(v\) is its speed.
2. Understand that kinetic energy depends on the square of the speed, meaning if the speed changes, the kinetic energy changes by the square of that factor.
3. If the speed of the molecules is doubled, express the new speed as \(v_{new} = 2v\).
4. Substitute the new speed into the kinetic energy formula: \(\text{KE}_{new} = \frac{1}{2} m (2v)^2 = \frac{1}{2} m \times 4v^2\).
5. Compare the new kinetic energy to the original: \(\text{KE}_{new} = 4 \times \text{KE}_{avg}\), showing that the average kinetic energy increases by a factor of 4 when the speed is doubled.