Question

$6\times {10}^{22}$ gas molecules each of mass ${10}^{-24}$ kg are taken in a vessel of 10 litres. What is the pressure exerted by gas molecules if the average velocity of the gas molecules is $92.62$ m/sec?

• A. $2\times {10}^{5}Pa$
• B. $20Pa$
• C. $2\times {10}^{6}Pa$
• D. $2\times {10}^{4}Pa$

Answer 1

The correct option is B $20Pa$

Density $d=\frac{mass}{volume}$

$=\frac{6\times {10}^{22}\times {10}^{-24}}{10}$

$=6\times {10}^{-3}lg/L$

$=6\times {10}^{-3}g/ml$

$u=1.085\times v=1.085\times 92.62$

$=100.56m/sec$

$u=\sqrt{\frac{3P}{d}}$

$100.56=\sqrt{\frac{3P}{6\times {10}^{-3}}}$

$P=20Pa$