The root mean square velocity of one mole of a monatomic gas having molar mass M is U rms . The relation between the average kinetic energy (E) of the gas and Urm s is

Question

The root mean square velocity of one mole of a monatomic gas having molar mass M is U rms . The relation between the average kinetic energy (E) of the gas and Urm s is (A) U rms =√(3 E/2 M) (B) U rms =√(2 E/3 M) (C) U rms =√(2 E/M) (D) U rms =√(E/3 M)

Tardigrade Admin · Accepted Answer

Average kinetic energy, E=(3/2) R T ...(i) Root mean square velocity, U rms =√(3 R T/M) From eq. (i), R T=(2 E/3) On putting the value of R T in the expression of U rms , we get U rms =√(3 × 2 E/3 M)=√(2 E/M)

Q. The root mean square velocity of one mole of a monatomic gas having molar mass $M$ is $U_{r m s}$ . The relation between the average kinetic energy $(E)$ of the gas and $U_{r m s}$ is

$U_{r m s} = \frac{3 E}{2 M}$

$U_{r m s} = \frac{2 E}{3 M}$

$U_{r m s} = \frac{2 E}{M}$

$U_{r m s} = \frac{E}{3 M}$

Average kinetic energy,
$E = \frac{3}{2} RT$ ...(i)
Root mean square velocity,
$U_{r m s} = \frac{3 RT}{M}$
From eq. (i),
$RT = \frac{2 E}{3}$
On putting the value of $RT$ in the expression of $U_{r m s}$ , we get
$U_{r m s} = \frac{3 \times 2 E}{3 M} = \frac{2 E}{M}$

Q. The root mean square velocity of one mole of a monatomic gas having molar mass M is Urms​. The relation between the average kinetic energy (E) of the gas and Urms​ is

Urms​=2M3E​​

Urms​=3M2E​​

Urms​=M2E​​

Urms​=3ME​​