Which of the following best describes the relationship between the temperature of an ideal gas and the average kinetic energy of its molecules?

• A. The average kinetic energy decreases as temperature increases.
• B. The average kinetic energy increases exponentially with temperature.
• C. The average kinetic energy increases linearly with temperature.
• D. The average kinetic energy is independent of temperature.

Answer: (C)

Verified step by step guidance

1. Recall the kinetic molecular theory of gases, which relates the average kinetic energy of gas molecules to the temperature of the gas.
2. Understand that the average kinetic energy (KE) of an ideal gas molecule is given by the formula: \(\text{KE}_{avg} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvins.
3. Note that this formula shows a direct proportionality between average kinetic energy and temperature, meaning as temperature increases, average kinetic energy increases as well.
4. Recognize that the relationship is linear because the average kinetic energy depends on temperature to the first power (no exponents or other nonlinear terms involved).
5. Conclude that the best description is: 'The average kinetic energy increases linearly with temperature.'