Thermodynamics: Kinetic Theory
Thermodynamics: Kinetic Theory
Kinetic Theory
Key Concepts:
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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.
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The assumption that gas particles act independently of each other except during collisions is a critical aspect of the kinetic theory.
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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:
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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.
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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:
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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.
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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:
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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.
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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:
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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.
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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.