Class 11 Physics Kinetic Theory Kinetic theory: Consistent with ideal gas equation and gas l

Kinetic theory: Consistent with ideal gas equation and gas laws

Problem: At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to rms speed of a helium gas atom at -200C?(Atomic mass of Ar=39.9u,of He=4.0u).

Problem:- A flask contains argon andchlorine in the ratio of 2:1 by mass. Thetemperature of the mixture is 27 °C. Obtainthe ratio of (i) average kinetic energy permolecule, and (ii) root mean square speedvrms of the molecules of the two gases.Atomic mass of argon = 39.9 u; Molecularmass of chlorine = 70.9 u.

Answer:-  The important point to remember is thatthe average kinetic energy (per molecule) of any(ideal) gas (be it monatomic like argon, diatomiclike chlorine or polyatomic) is always equal to(3/2) kBT. It depends only on temperature, andis independent of the nature of the gas.

(i) Since argon and chlorine both have the sametemperature in the flask, the ratio of averagekinetic energy (per molecule) of the two gasesis 1:1.

(ii) Now ½ m vrms2 = average kinetic energy permolecule = (3/2) kBT where m is the massof a molecule of the gas. Therefore,

v2rmsAr/ = v2rmscl =Mcl/MAR =70.9/39.9 =1.77

where M = the molecular mass of the gas.(For argon, a molecule is just an atom of argon.)

Taking square root of both sides, vrmsAr = vrmscl = 1.33

Problem:- Uranium has two isotopesof masses 235 and 238 units. If both arepresent in Uranium hexafluoride gas whichwould have the larger average speed? Ifatomic mass of fluorine is 19 units,estimate the percentage difference inspeeds at any temperature.

Answer:-  At a fixed temperature the averageenergy = ½ m <v2> is constant. So smaller the mass of the molecule, faster will be the speed.The ratio of speeds is inversely proportional tothe square root of the ratio of the masses. Themasses are 349 and 352 units. Sov349 / v352 = (352/ 349)1/2 = 1.0044.

Hence difference= 0.44 %.[235U is the isotope needed for nuclear fission.

To separate it from the more abundant isotope238U, the mixture is surrounded by a porouscylinder.

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