Question

$6\times {10}^{22}$ gas molecules each of mass ${10}^{-24}$ kg are taken in a vessel of 10 litre. What is the pressure exerted by gas molecules if the root mean speed of gas molecules is 100m/s?

• A. $20Pa$
• B. $2\times {10}^4$ Pa
• C. $2\times {10}^5$ Pa
• D. $2\times {10}^7$ Pa

Answer 1

The correct option is B $2\times {10}^4$ Pa

$PH=2RT$

$\Rightarrow \frac{p}{d}=\frac{RT}{M}$ ____ (1)

Now,

Root mean speed $=\sqrt{\frac{3RT}{M}}$

$\Rightarrow 100=\sqrt{\frac{3p}{d}}$ (from (1))

$\Rightarrow {10}^4=\frac{3\times p\times v}{m}$

$\Rightarrow {10}^4=\frac{3\times p\times 10\times {10}^{-3}}{6\times {10}^{22}\times {10}^{-24}}$

$\Rightarrow p=\frac{{10}^4\times {10}^{-2}\times 6}{3\times 10}\times {10}^3$

$\Rightarrow p=2\times {10}^{4}Pa$