Thermodynamics: Kinetic Theory

Thermodynamics: Kinetic Theory

Kinetic Theory

Key Concepts:

  • The Kinetic Theory of Gases assumes that gas molecules are constantly in quick, random motion and these molecules are very small compared to the distances between them.

  • The assumption that gas particles act independently of each other except during collisions is a critical aspect of the kinetic theory.

  • Collisions between gas molecules are assumed to be perfectly elastic, meaning there is no net loss of kinetic energy in the collisions.

Kinetic Energy and Temperature:

  • The average kinetic energy of the gas molecules in a system is proportional to the absolute temperature of the system. This relationship is demonstrated by the equation KE_avg = 3/2kT, where KE_avg is the average kinetic energy per gas molecule, k is the Boltzmann constant, and T is the temperature in Kelvin.

  • As the temperature of a gas increases, the speed – and as a result, the kinetic energy – of the gas molecules will also increase.

Distribution of Molecular Speeds:

  • The distribution of molecular speeds in a gas is described by the Maxwell-Boltzmann Distribution. This curve shows the probability of a molecule moving at a certain speed.

  • The peak of the curve represents the most probable speed, which is not identical to the average or rms speed.

Root Mean Square (RMS) Speed:

  • The Root Mean Square Speed (u_rms) is a measure of the average speed of particles in a gas. This is calculated through the formula u_rms = √(3kT/m), where k is Boltzmann’s constant, T is the temperature of the gas in Kelvin and m is the molar mass of the gas.

  • RMS speed is a more accurate measure of ‘average’ speed for gas molecules, as it accounts for the large spread in the actual speeds of molecules.

Assumptions and Limitations:

  • While the kinetic theory of gases provides a good approximation for many gases under normal conditions, some gases under extreme conditions (very high pressure or very low temperature) can behave non-ideally, deviating from predictions made by the kinetic theory.

  • Deviations from ideal behaviour are often due to intermolecular forces and the finite size of gas particles—factors not accounted for in the kinetic theory of gases.