Question

Consider a gas with density $\rho$ and $\bar{c}$ 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. $\frac{1}{3} \rho \bar {c}^2 $
• B. $\frac{1}{3} \rho (\bar{c}+v)^2$
• C. $\frac{1}{3} \rho (\bar{c}-v)^2$
• D. $\frac{1}{3} \rho( \bar {c}^2 -v)$

Answer 1

Answer: (A)

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 _{ rms }=\sqrt{\frac{3 RT }{ M }} $
$\Rightarrow C =\sqrt{\frac{3 RT }{ M }}$
$\Rightarrow C =\sqrt{\frac{3 PV }{ M }} $
$\Rightarrow C =\sqrt{\frac{3 P }{\rho}} $
$\Rightarrow P =\frac{\rho}{3} C ^{2}=\frac{1}{3} \rho C ^{2} $