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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ig164

Which of the following correctly relate the kinetic theory expression $P V = \frac{1}{3} m N u_{rms}^{2}$ to macroscopic quantities?

A $u_{rms} = 3 P / d$ where $d$ is the gas density
BFor 1 mol, $u_{rms} = 3 RT / M$
CAt constant $T$ , $u_{rms}$ is proportional to $P$
DThe translational kinetic energy of the gas is $\frac{3}{2} P V$

Answer: A, B, D

m N / V = d

, so

P = \frac{1}{3} d u_{rms}^{2}

and

u_{rms} = 3 P / d

(A). With

P V = RT

and

m N = M

for 1 mol,

u_{rms} = 3 RT / M

(B).

K E = \frac{1}{2} m N u^{2} = \frac{3}{2} P V

(D). At constant

T

,

P / d

is constant, so

u_{rms}

does not change with

P

(C wrong).

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