if

Question:

If $10^{22}$ gas molecules each of mass $10^{-26}$ $\mathrm{kg}$ collide with a surface (perpendicular to it) elastically per second over an area $1 \mathrm{~m}^{2}$ with a speed $10^{4}$ $\mathrm{m} / \mathrm{s}$, the pressure exerted by the gas molecules will be of the order of :

  1. (1) $2 \mathrm{~N} / \mathrm{m}^{2}$

  2. (2) $4 \mathrm{~N} / \mathrm{m}^{2}$

  3. (3) $8 \mathrm{~N} / \mathrm{m}^{2}$

  4. (4) $16 \mathrm{~N} / \mathrm{m}^{2}$


Correct Option: 1

Solution:

(1)

Rate of change of momentum during collision

$=\frac{m v-(-m v)}{\Delta t}=\frac{2 m v}{\Delta t} N$

so pressure

$P=\frac{N \times(2 m v)}{\Delta t \times A}$

$\frac{=10^{22} \times 2 \times 10^{-26} \times 10^{4}}{1 \times 1}=2 \mathrm{~N} / \mathrm{m}^{2}$

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