Q. 20

# <span lang="EN-US

In kinetic theory of ideal gas, the average energy is given by Where R=gas constant=8.31Jmol-1K-1

T=temperature of gas

M=molar mass of gas

We know that,

Gas constant R=kBNA

Where kB= Boltzmann constant = 1.38 × 10–23 J K–1.

NA=Avogadro number=6.023 10-23 mol-1 Molar mass of gas molecule M= Avogadro number mass of gas molecule

M=NA m So average velocity becomes Rms speed of gas molecule is given by Where R=gas constant 8.31J/molK

T=temperature of gas

M=molar mass of gas

Putting the value gas constant R=kBNA

So rms speed becomes M=NA m Therefore, Let the mass of molecule in left part=m1

Mass of molecule in right part=m2

According to question, the rms speed of the molecules in the left part equals the mean speed of the molecules in the right part.

So, from equation (I) and(II) we get Since the walls of separator is diathermic therefore temperature of both the parts will be same.

Squaring the above equation, we get   The ratio of the mass of a molecule in the left part to the mass of a molecule in the right part is 1.17.

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