Kinetic Theory of Gases
ISC Syllabus
Kinetic Theory: Equation of state of a perfect gas, work done in compressing a gas. Kinetic theory of gases – assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to
specific heat capacities of gases; concept of mean free path, Avogadro’s number.
Elaboration of Syllabus
(a) Kinetic Theory of gases; derive p=1/3(ρ 2 c )from the assumptions and applying Newton’s laws of motion. The average thermal velocity (rms value) crms=√3p/ρ; calculations for air, hydrogen and their comparison with common speeds. Effect of temperature and pressure on rms speed of gas molecules. [Note that pV=nRT the ideal gas equation cannot be derived from kinetic theory of ideal gas. Hence, neither can other gas laws; pV=nRT is an
experimental result. Comparing this with p = ⅓ (ρ 2 c) , from kinetic theory of
gases, a kinetic interpretation of temperature can be obtained as explained in the next subunit]
(b) From kinetic theory for an deal gas (obeying all the assumptions
especially no intermolecular attraction and negligibly small size of molecules,
we get p = (1/3)ρ 2 c or pV = (1/3)M 2 c .
(No further, as temperature is not a concept of kinetic theory). From experimentally obtained gas laws, we have the ideal gas equation (obeyed by
some gases at low pressure and high temperature) pV = RT for one mole.
Combining these two results (assuming they can be combined), RT=(1/3)M2 c =(2/3).½M2 c =(2/3)K; Hence, kinetic energy of 1 mole of an ideal gas K=(3/2)RT. Average K for 1 molecule = K/N = (3/2) RT/N = (3/2) kT where k is Boltzmann’s constant. So, temperature T can be interpreted as a measure of the average kinetic energy of the molecules of a gas.
(c) Degrees of freedom and calculation of specific heat capacities for all types of gases. Concept of the law of equipartition of energy (derivation not
required). Concept of mean free path and Avogadro’s number NA.
