Kinetic Theory Of Gases Question 135
Question: Consider a gas with density $ \rho $ and $ \bar{c} $ as the 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
Options:
A) $ \frac{1}{3}\rho ,{{\bar{c}}^{2}} $
B) $ \frac{1}{3}\rho {{(c+v)}^{2}} $
C) $ \frac{1}{3}\rho {{(\bar{c}-v)}^{2}} $
D) $ \frac{1}{3}\rho {{({{c}^{-2}}-v)}^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Pressure of the gas will not affected by motion of the system, hence by $ v _{rms}=\sqrt{\frac{3P}{\rho }} $
Therefore $ {{\bar{c}}^{2}}=\frac{3P}{\rho } $
Therefore $ P=\frac{1}{3}\rho {{\bar{c}}^{2}} $
BETA
