In a mixture of gases, the average number of degrees of freedom per molecule is 6 . The root mean square speed of the molecules of the gas is c . The velocity of sound in the gas is

Question

In a mixture of gases, the average number of degrees of freedom per molecule is 6 . The root mean square speed of the molecules of the gas is c . The velocity of sound in the gas is (A) (c/√2) (B) (3 c/4) (C) (2 c/3) (D) (c/√3)

Tardigrade Admin · Accepted Answer

&gamma; =1+(2/f)=1+(2/6)=(4/3) Root mean square speed, c=√(3 P/ρ ) and speed of sound, v=√(&gamma; P/ρ ) ∴ (v/c)=√(&gamma; /3) (v/c)=√((4/3)/3) v=(2 c/3)

Q. In a mixture of gases, the average number of degrees of freedom per molecule is $6$ . The root mean square speed of the molecules of the gas is $c$ . The velocity of sound in the gas is

$\frac{c}{2}$

$\frac{3 c}{4}$

$\frac{2 c}{3}$

$\frac{c}{3}$

$γ = 1 + \frac{2}{f} = 1 + \frac{2}{6} = \frac{4}{3}$
Root mean square speed, $c = \frac{3 P}{ρ}$
and speed of sound, $v = \frac{γ P}{ρ}$
$∴ \frac{v}{c} = \frac{γ}{3}$
$\frac{v}{c} = \frac{\frac{4}{3}}{3}$
$v = \frac{2 c}{3}$

Q. In a mixture of gases, the average number of degrees of freedom per molecule is 6 . The root mean square speed of the molecules of the gas is c . The velocity of sound in the gas is

2​c​

43c​

32c​

3​c​