Consider a gas with density ρ and barc root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

Question

Consider a gas with density ρ and barc root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is (A) (1/3) ρ bar c2  (B) (1/3) ρ ( barc+v)2 (C) (1/3) ρ ( barc-v)2 (D) (1/3) ρ( bar c2 -v)

Tardigrade Admin · Accepted Answer

Root-mean-square speed is the measure of the speed of particles in a gas which is most convenient for problem solving within the kinetic theory of gases

v_{r m s} = \frac{3 RT}{M}

\Rightarrow C = \frac{3 RT}{M}

\Rightarrow C = \frac{3 P V}{M}

\Rightarrow C = \frac{3 P}{ρ}

\Rightarrow P = \frac{ρ}{3} C^{2} = \frac{1}{3} ρ C^{2}

Q. Consider a gas with density $ρ$ and $\overset{c}{ˉ}$ root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

$\frac{1}{3} ρ \overset{c}{ˉ}^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ} + v)^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ} - v)^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ}^{2} - v)$

Q. Consider a gas with density ρ and cˉ root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

31​ρcˉ2

31​ρ(cˉ+v)2

31​ρ(cˉ−v)2

31​ρ(cˉ2−v)

Root-mean-square speed is the measure of the speed of particles in a gas which is most convenient for problem solving within the kinetic theory of gases vrms​=M3RT​​ ⇒C=M3RT​​ ⇒C=M3PV​​ ⇒C=ρ3P​​ ⇒P=3ρ​C2=31​ρC2

Q. Consider a gas with density $ρ$ and $\overset{c}{ˉ}$ root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

$\frac{1}{3} ρ \overset{c}{ˉ}^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ} + v)^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ} - v)^{2}$

$\frac{1}{3} ρ (\overset{c}{ˉ}^{2} - v)$