Examkin

Question

Difficulty: MediumPostulates of Kinetic Theory and States of Matter

According to the kinetic theory of matter, the average kinetic energy of the molecules of any gas is directly proportional to its absolute temperature, independent of the mass or identity of the gas.

Answer: Answer

Answer

The statement is True.
The postulates of kinetic theory define absolute temperature as a measure of the average kinetic energy of the constituent particles. Regardless of the identity, density, or molar mass of the gas, equal temperatures correspond to equal average kinetic energies.

Step-by-Step Solution

1
Recall the fundamental postulate of the kinetic molecular theory relating heat and motion.
The average kinetic energy of gas particles is directly proportional to the absolute temperature (TT) measured in Kelvin.
Temperature measures the thermal motion of particles.
2
Examine the mathematical relationship for average kinetic energy.
Eˉk=32kBT\bar{E}_k = \frac{3}{2} k_B T, where kBk_B is Boltzmann's constant and TT is absolute temperature.
This shows that average kinetic energy depends solely on temperature.
3
Evaluate the impact of gas identity and molecular mass.
Different gases at the same temperature have different average speeds (vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}}), but their average kinetic energy remains identical.
Higher mass compensates for lower speed in the formula Ek=12mv2E_k = \frac{1}{2}m v^2.

Key Concept

Direct proportionality between absolute temperature and average kinetic energy of gas particles
Rate this question

Topics

Postulates of Kinetic Theory and States of Matter