Kinetic Theory Of Gases Question 108
Question: The molecules of a given mass of a gas have a r.m.s. velocity of 200 m/sec at $ 27{}^\circ C $ and $ 1.0\times 10^{5},N/m^{2} $ pressure. When the temperature is $ 127{}^\circ C $ and pressure is $ 0.5\times 10^{5},N/m^{2} $ , the r.m.s. velocity in m/sec will be
Options:
A) $ \frac{100\sqrt{2}}{3} $
B) $ 100\sqrt{2} $
C) $ \frac{400}{\sqrt{3}} $
D) None of the above
Show Answer
Answer:
Correct Answer: C
Solution:
[c] r.m.s. velocity doesn’t upon pressure, it depends upon temperature only i.e. $ v _{rms}\propto \sqrt{T} $
Therefore $ \frac{v _{1}}{v _{2}}=\sqrt{\frac{T _{1}}{T _{2}}} $
Therefore $ \frac{200}{v _{2}}=\sqrt{\frac{(273+27)}{(273+127)}}=\sqrt{\frac{300}{400}} $
Therefore $ v _{2}=\frac{400}{\sqrt{3}},m/\sec $
BETA
